#include "const.h"
#include "cluster.h"
#include "emalloc.h"
#include "genericheap.h"
#include "helpers.h"
#include "kdpair.h"
#include "matrix.h"
#include "tprintf.h"
#include "danerror.h"
#include <math.h>

Classes
struct	TEMPCLUSTER

struct	STATISTICS

struct	BUCKETS

struct	CHISTRUCT

struct	ClusteringContext

Macros
#define	HOTELLING 1

#define	FTABLE_X 10

#define	FTABLE_Y 100

#define	MINVARIANCE 0.0004

#define	MINSAMPLESPERBUCKET 5

#define	MINSAMPLES (MINBUCKETS * MINSAMPLESPERBUCKET)

#define	MINSAMPLESNEEDED 1

#define	BUCKETTABLESIZE 1024

#define	NORMALEXTENT 3.0

#define	Odd(N) ((N)%2)

#define	Mirror(N, R) ((R) - (N) - 1)

#define	Abs(N) ( ( (N) < 0 ) ? ( -(N) ) : (N) )

#define	SqrtOf2Pi 2.506628275

#define	LOOKUPTABLESIZE 8

#define	MAXDEGREESOFFREEDOM MAXBUCKETS

#define	MAXNEIGHBORS 2

#define	MAXDISTANCE MAX_FLOAT32

#define	CHIACCURACY 0.01

#define	MINALPHA (1e-200)

#define	INITIALDELTA 0.1

#define	DELTARATIO 0.1

#define	ILLEGAL_CHAR 2

Typedefs
typedef tesseract::KDPairInc< float, TEMPCLUSTER * >	ClusterPair

typedef tesseract::GenericHeap< ClusterPair >	ClusterHeap

typedef FLOAT64(*	DENSITYFUNC) (inT32)

typedef FLOAT64(*	SOLVEFUNC) (CHISTRUCT *, double)

Functions
void	CreateClusterTree (CLUSTERER *Clusterer)

void	MakePotentialClusters (ClusteringContext context, CLUSTER Cluster, inT32 Level)

CLUSTER *	FindNearestNeighbor (KDTREE Tree, CLUSTER Cluster, FLOAT32 *Distance)

CLUSTER *	MakeNewCluster (CLUSTERER Clusterer, TEMPCLUSTER TempCluster)

inT32	MergeClusters (inT16 N, register PARAM_DESC ParamDesc[], register inT32 n1, register inT32 n2, register FLOAT32 m[], register FLOAT32 m1[], register FLOAT32 m2[])

void	ComputePrototypes (CLUSTERER Clusterer, CLUSTERCONFIG Config)

PROTOTYPE *	MakePrototype (CLUSTERER Clusterer, CLUSTERCONFIG Config, CLUSTER *Cluster)

PROTOTYPE *	MakeDegenerateProto (uinT16 N, CLUSTER Cluster, STATISTICS Statistics, PROTOSTYLE Style, inT32 MinSamples)

PROTOTYPE *	TestEllipticalProto (CLUSTERER Clusterer, CLUSTERCONFIG Config, CLUSTER Cluster, STATISTICS Statistics)

PROTOTYPE *	MakeSphericalProto (CLUSTERER Clusterer, CLUSTER Cluster, STATISTICS Statistics, BUCKETS Buckets)

PROTOTYPE *	MakeEllipticalProto (CLUSTERER Clusterer, CLUSTER Cluster, STATISTICS Statistics, BUCKETS Buckets)

PROTOTYPE *	MakeMixedProto (CLUSTERER Clusterer, CLUSTER Cluster, STATISTICS Statistics, BUCKETS NormalBuckets, FLOAT64 Confidence)

void	MakeDimRandom (uinT16 i, PROTOTYPE Proto, PARAM_DESC ParamDesc)

void	MakeDimUniform (uinT16 i, PROTOTYPE Proto, STATISTICS Statistics)

STATISTICS *	ComputeStatistics (inT16 N, PARAM_DESC ParamDesc[], CLUSTER *Cluster)

PROTOTYPE *	NewSphericalProto (uinT16 N, CLUSTER Cluster, STATISTICS Statistics)

PROTOTYPE *	NewEllipticalProto (inT16 N, CLUSTER Cluster, STATISTICS Statistics)

PROTOTYPE *	NewMixedProto (inT16 N, CLUSTER Cluster, STATISTICS Statistics)

PROTOTYPE *	NewSimpleProto (inT16 N, CLUSTER *Cluster)

BOOL8	Independent (PARAM_DESC ParamDesc[], inT16 N, FLOAT32 *CoVariance, FLOAT32 Independence)

BUCKETS *	GetBuckets (CLUSTERER *clusterer, DISTRIBUTION Distribution, uinT32 SampleCount, FLOAT64 Confidence)

BUCKETS *	MakeBuckets (DISTRIBUTION Distribution, uinT32 SampleCount, FLOAT64 Confidence)

uinT16	OptimumNumberOfBuckets (uinT32 SampleCount)

FLOAT64	ComputeChiSquared (uinT16 DegreesOfFreedom, FLOAT64 Alpha)

FLOAT64	NormalDensity (inT32 x)

FLOAT64	UniformDensity (inT32 x)

FLOAT64	Integral (FLOAT64 f1, FLOAT64 f2, FLOAT64 Dx)

void	FillBuckets (BUCKETS Buckets, CLUSTER Cluster, uinT16 Dim, PARAM_DESC *ParamDesc, FLOAT32 Mean, FLOAT32 StdDev)

uinT16	NormalBucket (PARAM_DESC *ParamDesc, FLOAT32 x, FLOAT32 Mean, FLOAT32 StdDev)

uinT16	UniformBucket (PARAM_DESC *ParamDesc, FLOAT32 x, FLOAT32 Mean, FLOAT32 StdDev)

BOOL8	DistributionOK (BUCKETS *Buckets)

void	FreeStatistics (STATISTICS *Statistics)

void	FreeBuckets (BUCKETS *Buckets)

void	FreeCluster (CLUSTER *Cluster)

uinT16	DegreesOfFreedom (DISTRIBUTION Distribution, uinT16 HistogramBuckets)

int	NumBucketsMatch (void arg1, void arg2)

int	ListEntryMatch (void arg1, void arg2)

void	AdjustBuckets (BUCKETS *Buckets, uinT32 NewSampleCount)

void	InitBuckets (BUCKETS *Buckets)

int	AlphaMatch (void arg1, void arg2)

CHISTRUCT *	NewChiStruct (uinT16 DegreesOfFreedom, FLOAT64 Alpha)

FLOAT64	Solve (SOLVEFUNC Function, void *FunctionParams, FLOAT64 InitialGuess, FLOAT64 Accuracy)

FLOAT64	ChiArea (CHISTRUCT *ChiParams, FLOAT64 x)

BOOL8	MultipleCharSamples (CLUSTERER Clusterer, CLUSTER Cluster, FLOAT32 MaxIllegal)

double	InvertMatrix (const float input, int size, float inv)

CLUSTERER *	MakeClusterer (inT16 SampleSize, const PARAM_DESC ParamDesc[])

SAMPLE *	MakeSample (CLUSTERER Clusterer, const FLOAT32 Feature, inT32 CharID)

LIST	ClusterSamples (CLUSTERER Clusterer, CLUSTERCONFIG Config)

void	FreeClusterer (CLUSTERER *Clusterer)

void	FreeProtoList (LIST *ProtoList)

void	FreePrototype (void *arg)

CLUSTER *	NextSample (LIST *SearchState)

FLOAT32	Mean (PROTOTYPE *Proto, uinT16 Dimension)

FLOAT32	StandardDeviation (PROTOTYPE *Proto, uinT16 Dimension)

inT32	MergeClusters (inT16 N, PARAM_DESC ParamDesc[], inT32 n1, inT32 n2, FLOAT32 m[], FLOAT32 m1[], FLOAT32 m2[])

Variables
const double	FTable [FTABLE_Y][FTABLE_X]

Macro Definition Documentation

◆ Abs

#define Abs ( N ) ( ( (N) < 0 ) ? ( -(N) ) : (N) )

Definition at line 207 of file cluster.cpp.

◆ BUCKETTABLESIZE

#define BUCKETTABLESIZE 1024

define the size of the table which maps normalized samples to histogram buckets. Also define the number of standard deviations in a normal distribution which are considered to be significant. The mapping table will be defined in such a way that it covers the specified number of standard deviations on either side of the mean. BUCKETTABLESIZE should always be even.

Definition at line 159 of file cluster.cpp.

◆ CHIACCURACY

#define CHIACCURACY 0.01

◆ DELTARATIO

#define DELTARATIO 0.1

◆ FTABLE_X

#define FTABLE_X 10

Definition at line 30 of file cluster.cpp.

◆ FTABLE_Y

#define FTABLE_Y 100

Definition at line 31 of file cluster.cpp.

◆ HOTELLING

#define HOTELLING 1

Definition at line 29 of file cluster.cpp.

◆ ILLEGAL_CHAR

#define ILLEGAL_CHAR 2

◆ INITIALDELTA

#define INITIALDELTA 0.1

◆ LOOKUPTABLESIZE

#define LOOKUPTABLESIZE 8

define lookup tables used to compute the number of histogram buckets that should be used for a given number of samples.

Definition at line 227 of file cluster.cpp.

◆ MAXDEGREESOFFREEDOM

#define MAXDEGREESOFFREEDOM MAXBUCKETS

Definition at line 228 of file cluster.cpp.

◆ MAXDISTANCE

#define MAXDISTANCE MAX_FLOAT32

◆ MAXNEIGHBORS

#define MAXNEIGHBORS 2

◆ MINALPHA

#define MINALPHA (1e-200)

◆ MINSAMPLES

#define MINSAMPLES (MINBUCKETS * MINSAMPLESPERBUCKET)

Definition at line 150 of file cluster.cpp.

◆ MINSAMPLESNEEDED

#define MINSAMPLESNEEDED 1

Definition at line 151 of file cluster.cpp.

◆ MINSAMPLESPERBUCKET

#define MINSAMPLESPERBUCKET 5

define the absolute minimum number of samples which must be present in order to accurately test hypotheses about underlying probability distributions. Define separately the minimum samples that are needed before a statistical analysis is attempted; this number should be equal to MINSAMPLES but can be set to a lower number for early testing when very few samples are available.

Definition at line 149 of file cluster.cpp.

◆ MINVARIANCE

#define MINVARIANCE 0.0004

define the variance which will be used as a minimum variance for any dimension of any feature. Since most features are calculated from numbers with a precision no better than 1 in 128, the variance should never be less than the square of this number for parameters whose range is 1.

Definition at line 141 of file cluster.cpp.

◆ Mirror

#define Mirror	(	N,
		R
	)	((R) - (N) - 1)

Definition at line 206 of file cluster.cpp.

◆ NORMALEXTENT

#define NORMALEXTENT 3.0

Definition at line 160 of file cluster.cpp.

◆ Odd

#define Odd ( N ) ((N)%2)

Definition at line 205 of file cluster.cpp.

◆ SqrtOf2Pi

#define SqrtOf2Pi 2.506628275

the following variables describe a discrete normal distribution which is used by NormalDensity() and NormalBucket(). The constant NORMALEXTENT determines how many standard deviations of the distribution are mapped onto the fixed discrete range of x. x=0 is mapped to -NORMALEXTENT standard deviations and x=BUCKETTABLESIZE is mapped to +NORMALEXTENT standard deviations.

Definition at line 217 of file cluster.cpp.

Typedef Documentation

◆ ClusterHeap

typedef tesseract::GenericHeap<ClusterPair> ClusterHeap

Definition at line 168 of file cluster.cpp.

◆ ClusterPair

typedef tesseract::KDPairInc<float, TEMPCLUSTER*> ClusterPair

Definition at line 167 of file cluster.cpp.

◆ DENSITYFUNC

typedef FLOAT64(* DENSITYFUNC) (inT32)

Definition at line 202 of file cluster.cpp.

◆ SOLVEFUNC

typedef FLOAT64(* SOLVEFUNC) (CHISTRUCT *, double)

Definition at line 203 of file cluster.cpp.

Function Documentation

◆ AdjustBuckets()

void AdjustBuckets	(	BUCKETS *	Buckets,
		uinT32	NewSampleCount
	)

This routine multiplies each ExpectedCount histogram entry by NewSampleCount/OldSampleCount so that the histogram is now adjusted to the new sample count.

Parameters

Buckets	histogram data structure to adjust
NewSampleCount	new sample count to adjust to

Returns: none

Note: Exceptions: none; History: Thu Aug 3 14:31:14 1989, DSJ, Created.

Definition at line 2260 of file cluster.cpp.

                                                             {
   int i;
   FLOAT64 AdjustFactor;
 
   AdjustFactor = (((FLOAT64) NewSampleCount) /
     ((FLOAT64) Buckets->SampleCount));
 
   for (i = 0; i < Buckets->NumberOfBuckets; i++) {
     Buckets->ExpectedCount[i] *= AdjustFactor;
   }
 
   Buckets->SampleCount = NewSampleCount;
 
 }                                // AdjustBuckets

◆ AlphaMatch()

int AlphaMatch	(	void *	arg1,
		void *	arg2
	)

This routine is used to search a list of structures which hold pre-computed chi-squared values for a chi-squared value whose corresponding alpha field matches the alpha field of SearchKey.

It is called by the list search routines.

Parameters

arg1	chi-squared struct being tested for a match
arg2	chi-squared struct that is the search key

Returns: TRUE if ChiStruct's Alpha matches SearchKey's Alpha

Note: Exceptions: none; History: Thu Aug 3 14:17:33 1989, DSJ, Created.

Definition at line 2306 of file cluster.cpp.

                            {  //CHISTRUCT                             *SearchKey)
   CHISTRUCT *ChiStruct = (CHISTRUCT *) arg1;
   CHISTRUCT *SearchKey = (CHISTRUCT *) arg2;
 
   return (ChiStruct->Alpha == SearchKey->Alpha);
 
 }                                // AlphaMatch

◆ ChiArea()

FLOAT64 ChiArea	(	CHISTRUCT *	ChiParams,
		FLOAT64	x
	)

This routine computes the area under a chi density curve from 0 to x, minus the desired area under the curve. The number of degrees of freedom of the chi curve is specified in the ChiParams structure. The desired area is also specified in the ChiParams structure as Alpha ( or 1 minus the desired area ). This routine is intended to be passed to the Solve() function to find the value of chi-squared which will yield a desired area under the right tail of the chi density curve. The function will only work for even degrees of freedom. The equations are based on integrating the chi density curve in parts to obtain a series that can be used to compute the area under the curve.

Parameters

ChiParams	contains degrees of freedom and alpha
x	value of chi-squared to evaluate

Returns: Error between actual and desired area under the chi curve.

Note: Exceptions: none; History: Fri Aug 4 12:48:41 1989, DSJ, Created.

Definition at line 2418 of file cluster.cpp.

                                                  {
   int i, N;
   FLOAT64 SeriesTotal;
   FLOAT64 Denominator;
   FLOAT64 PowerOfx;
 
   N = ChiParams->DegreesOfFreedom / 2 - 1;
   SeriesTotal = 1;
   Denominator = 1;
   PowerOfx = 1;
   for (i = 1; i <= N; i++) {
     Denominator *= 2 * i;
     PowerOfx *= x;
     SeriesTotal += PowerOfx / Denominator;
   }
   return ((SeriesTotal * exp (-0.5 * x)) - ChiParams->Alpha);
 
 }                                // ChiArea

◆ ClusterSamples()

LIST ClusterSamples	(	CLUSTERER *	Clusterer,
		CLUSTERCONFIG *	Config
	)

This routine first checks to see if the samples in this clusterer have already been clustered before; if so, it does not bother to recreate the cluster tree. It simply recomputes the prototypes based on the new Config info.

If the samples have not been clustered before, the samples in the KD tree are formed into a cluster tree and then the prototypes are computed from the cluster tree.

In either case this routine returns a pointer to a list of prototypes that best represent the samples given the constraints specified in Config.

Parameters

Clusterer	data struct containing samples to be clustered
Config	parameters which control clustering process

Returns: Pointer to a list of prototypes

Note: Exceptions: None; History: 5/29/89, DSJ, Created.

Definition at line 512 of file cluster.cpp.

                                                                  {
   //only create cluster tree if samples have never been clustered before
   if (Clusterer->Root == NULL)
     CreateClusterTree(Clusterer);
 
   //deallocate the old prototype list if one exists
   FreeProtoList (&Clusterer->ProtoList);
   Clusterer->ProtoList = NIL_LIST;
 
   //compute prototypes starting at the root node in the tree
   ComputePrototypes(Clusterer, Config);
   // We don't need the cluster pointers in the protos any more, so null them
   // out, which makes it safe to delete the clusterer.
   LIST proto_list = Clusterer->ProtoList;
   iterate(proto_list) {
     PROTOTYPE *proto = reinterpret_cast<PROTOTYPE *>(first_node(proto_list));
     proto->Cluster = NULL;
   }
   return Clusterer->ProtoList;
 }                                // ClusterSamples

◆ ComputeChiSquared()

FLOAT64 ComputeChiSquared	(	uinT16	DegreesOfFreedom,
		FLOAT64	Alpha
	)

This routine computes the chi-squared value which will leave a cumulative probability of Alpha in the right tail of a chi-squared distribution with the specified number of degrees of freedom. Alpha must be between 0 and 1. DegreesOfFreedom must be even. The routine maintains an array of lists. Each list corresponds to a different number of degrees of freedom. Each entry in the list corresponds to a different alpha value and its corresponding chi-squared value. Therefore, once a particular chi-squared value is computed, it is stored in the list and never needs to be computed again.

Parameters

DegreesOfFreedom	determines shape of distribution
Alpha	probability of right tail

Returns: Desired chi-squared value

Note: Exceptions: none; History: 6/5/89, DSJ, Created.

Definition at line 1869 of file cluster.cpp.

 {
   static LIST ChiWith[MAXDEGREESOFFREEDOM + 1];
 
   CHISTRUCT *OldChiSquared;
   CHISTRUCT SearchKey;
 
   // limit the minimum alpha that can be used - if alpha is too small
   //      it may not be possible to compute chi-squared.
   Alpha = ClipToRange(Alpha, MINALPHA, 1.0);
   if (Odd (DegreesOfFreedom))
     DegreesOfFreedom++;
 
   /* find the list of chi-squared values which have already been computed
      for the specified number of degrees of freedom.  Search the list for
      the desired chi-squared. */
   SearchKey.Alpha = Alpha;
   OldChiSquared = (CHISTRUCT *) first_node (search (ChiWith[DegreesOfFreedom],
     &SearchKey, AlphaMatch));
 
   if (OldChiSquared == NULL) {
     OldChiSquared = NewChiStruct (DegreesOfFreedom, Alpha);
     OldChiSquared->ChiSquared = Solve (ChiArea, OldChiSquared,
       (FLOAT64) DegreesOfFreedom,
       (FLOAT64) CHIACCURACY);
     ChiWith[DegreesOfFreedom] = push (ChiWith[DegreesOfFreedom],
       OldChiSquared);
   }
   else {
     // further optimization might move OldChiSquared to front of list
   }
 
   return (OldChiSquared->ChiSquared);
 
 }                                // ComputeChiSquared

◆ ComputePrototypes()

void ComputePrototypes	(	CLUSTERER *	Clusterer,
		CLUSTERCONFIG *	Config
	)

This routine decides which clusters in the cluster tree should be represented by prototypes, forms a list of these prototypes, and places the list in the Clusterer data structure.

Parameters

Clusterer	data structure holding cluster tree
Config	parameters used to control prototype generation

Returns: None

Note: Exceptions: None; History: 5/30/89, DSJ, Created.

Definition at line 924 of file cluster.cpp.

                                                                     {
   LIST ClusterStack = NIL_LIST;
   CLUSTER *Cluster;
   PROTOTYPE *Prototype;
 
   // use a stack to keep track of clusters waiting to be processed
   // initially the only cluster on the stack is the root cluster
   if (Clusterer->Root != NULL)
     ClusterStack = push (NIL_LIST, Clusterer->Root);
 
   // loop until we have analyzed all clusters which are potential prototypes
   while (ClusterStack != NIL_LIST) {
     // remove the next cluster to be analyzed from the stack
     // try to make a prototype from the cluster
     // if successful, put it on the proto list, else split the cluster
     Cluster = (CLUSTER *) first_node (ClusterStack);
     ClusterStack = pop (ClusterStack);
     Prototype = MakePrototype(Clusterer, Config, Cluster);
     if (Prototype != NULL) {
       Clusterer->ProtoList = push (Clusterer->ProtoList, Prototype);
     }
     else {
       ClusterStack = push (ClusterStack, Cluster->Right);
       ClusterStack = push (ClusterStack, Cluster->Left);
     }
   }
 }                                // ComputePrototypes

◆ ComputeStatistics()

STATISTICS * ComputeStatistics	(	inT16	N,
		PARAM_DESC	ParamDesc[],
		CLUSTER *	Cluster
	)

This routine searches the cluster tree for all leaf nodes which are samples in the specified cluster. It computes a full covariance matrix for these samples as well as keeping track of the ranges (min and max) for each dimension. A special data structure is allocated to return this information to the caller. An incremental algorithm for computing statistics is not used because it will not work with circular dimensions.

Parameters

N	number of dimensions
ParamDesc	array of dimension descriptions
Cluster	cluster whose stats are to be computed

Returns: Pointer to new data structure containing statistics

Note: Exceptions: None; History: 6/2/89, DSJ, Created.

Definition at line 1412 of file cluster.cpp.

                                                                        {
   STATISTICS *Statistics;
   int i, j;
   FLOAT32 *CoVariance;
   FLOAT32 *Distance;
   LIST SearchState;
   SAMPLE *Sample;
   uinT32 SampleCountAdjustedForBias;
 
   // allocate memory to hold the statistics results
   Statistics = (STATISTICS *) Emalloc (sizeof (STATISTICS));
   Statistics->CoVariance = (FLOAT32 *) Emalloc (N * N * sizeof (FLOAT32));
   Statistics->Min = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32));
   Statistics->Max = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32));
 
   // allocate temporary memory to hold the sample to mean distances
   Distance = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32));
 
   // initialize the statistics
   Statistics->AvgVariance = 1.0;
   CoVariance = Statistics->CoVariance;
   for (i = 0; i < N; i++) {
     Statistics->Min[i] = 0.0;
     Statistics->Max[i] = 0.0;
     for (j = 0; j < N; j++, CoVariance++)
       *CoVariance = 0;
   }
   // find each sample in the cluster and merge it into the statistics
   InitSampleSearch(SearchState, Cluster);
   while ((Sample = NextSample (&SearchState)) != NULL) {
     for (i = 0; i < N; i++) {
       Distance[i] = Sample->Mean[i] - Cluster->Mean[i];
       if (ParamDesc[i].Circular) {
         if (Distance[i] > ParamDesc[i].HalfRange)
           Distance[i] -= ParamDesc[i].Range;
         if (Distance[i] < -ParamDesc[i].HalfRange)
           Distance[i] += ParamDesc[i].Range;
       }
       if (Distance[i] < Statistics->Min[i])
         Statistics->Min[i] = Distance[i];
       if (Distance[i] > Statistics->Max[i])
         Statistics->Max[i] = Distance[i];
     }
     CoVariance = Statistics->CoVariance;
     for (i = 0; i < N; i++)
       for (j = 0; j < N; j++, CoVariance++)
         *CoVariance += Distance[i] * Distance[j];
   }
   // normalize the variances by the total number of samples
   // use SampleCount-1 instead of SampleCount to get an unbiased estimate
   // also compute the geometic mean of the diagonal variances
   // ensure that clusters with only 1 sample are handled correctly
   if (Cluster->SampleCount > 1)
     SampleCountAdjustedForBias = Cluster->SampleCount - 1;
   else
     SampleCountAdjustedForBias = 1;
   CoVariance = Statistics->CoVariance;
   for (i = 0; i < N; i++)
   for (j = 0; j < N; j++, CoVariance++) {
     *CoVariance /= SampleCountAdjustedForBias;
     if (j == i) {
       if (*CoVariance < MINVARIANCE)
         *CoVariance = MINVARIANCE;
       Statistics->AvgVariance *= *CoVariance;
     }
   }
   Statistics->AvgVariance = (float)pow((double)Statistics->AvgVariance,
                                        1.0 / N);
 
   // release temporary memory and return
   free(Distance);
   return (Statistics);
 }                                // ComputeStatistics

◆ CreateClusterTree()

void CreateClusterTree ( CLUSTERER * Clusterer )

This routine performs a bottoms-up clustering on the samples held in the kd-tree of the Clusterer data structure. The result is a cluster tree. Each node in the tree represents a cluster which conceptually contains a subset of the samples. More precisely, the cluster contains all of the samples which are contained in its two sub-clusters. The leaves of the tree are the individual samples themselves; they have no sub-clusters. The root node of the tree conceptually contains all of the samples.

Parameters

Clusterer data structure holdings samples to be clustered

Returns: None (the Clusterer data structure is changed)

Note: Exceptions: None; History: 5/29/89, DSJ, Created.

Definition at line 698 of file cluster.cpp.

                                              {
   ClusteringContext context;
   ClusterPair HeapEntry;
   TEMPCLUSTER *PotentialCluster;
 
   // each sample and its nearest neighbor form a "potential" cluster
   // save these in a heap with the "best" potential clusters on top
   context.tree = Clusterer->KDTree;
   context.candidates = (TEMPCLUSTER *)
     Emalloc(Clusterer->NumberOfSamples * sizeof(TEMPCLUSTER));
   context.next = 0;
   context.heap = new ClusterHeap(Clusterer->NumberOfSamples);
   KDWalk(context.tree, (void_proc)MakePotentialClusters, &context);
 
   // form potential clusters into actual clusters - always do "best" first
   while (context.heap->Pop(&HeapEntry)) {
     PotentialCluster = HeapEntry.data;
 
     // if main cluster of potential cluster is already in another cluster
     // then we don't need to worry about it
     if (PotentialCluster->Cluster->Clustered) {
       continue;
     }
 
     // if main cluster is not yet clustered, but its nearest neighbor is
     // then we must find a new nearest neighbor
     else if (PotentialCluster->Neighbor->Clustered) {
       PotentialCluster->Neighbor =
         FindNearestNeighbor(context.tree, PotentialCluster->Cluster,
                             &HeapEntry.key);
       if (PotentialCluster->Neighbor != NULL) {
         context.heap->Push(&HeapEntry);
       }
     }
 
     // if neither cluster is already clustered, form permanent cluster
     else {
       PotentialCluster->Cluster =
           MakeNewCluster(Clusterer, PotentialCluster);
       PotentialCluster->Neighbor =
           FindNearestNeighbor(context.tree, PotentialCluster->Cluster,
                               &HeapEntry.key);
       if (PotentialCluster->Neighbor != NULL) {
         context.heap->Push(&HeapEntry);
       }
     }
   }
 
   // the root node in the cluster tree is now the only node in the kd-tree
   Clusterer->Root = (CLUSTER *) RootOf(Clusterer->KDTree);
 
   // free up the memory used by the K-D tree, heap, and temp clusters
   FreeKDTree(context.tree);
   Clusterer->KDTree = NULL;
   delete context.heap;
   free(context.candidates);
 }                                // CreateClusterTree

◆ DegreesOfFreedom()

uinT16 DegreesOfFreedom	(	DISTRIBUTION	Distribution,
		uinT16	HistogramBuckets
	)

This routine computes the degrees of freedom that should be used in a chi-squared test with the specified number of histogram buckets. The result is always rounded up to the next even number so that the value of chi-squared can be computed more easily. This will cause the value of chi-squared to be higher than the optimum value, resulting in the chi-square test being more lenient than optimum.

Parameters

Distribution	distribution being tested for
HistogramBuckets	number of buckets in chi-square test

Returns: The number of degrees of freedom for a chi-square test

Note: Exceptions: none; History: Thu Aug 3 14:04:18 1989, DSJ, Created.

Definition at line 2205 of file cluster.cpp.

                                                                             {
   static uinT8 DegreeOffsets[] = { 3, 3, 1 };
 
   uinT16 AdjustedNumBuckets;
 
   AdjustedNumBuckets = HistogramBuckets - DegreeOffsets[(int) Distribution];
   if (Odd (AdjustedNumBuckets))
     AdjustedNumBuckets++;
   return (AdjustedNumBuckets);
 
 }                                // DegreesOfFreedom

◆ DistributionOK()

BOOL8 DistributionOK ( BUCKETS * Buckets )

This routine performs a chi-square goodness of fit test on the histogram data in the Buckets data structure. TRUE is returned if the histogram matches the probability distribution which was specified when the Buckets structure was originally created. Otherwise FALSE is returned.

Parameters

Buckets histogram data to perform chi-square test on

Returns: TRUE if samples match distribution, FALSE otherwise

Note: Exceptions: None; History: 6/5/89, DSJ, Created.

Definition at line 2125 of file cluster.cpp.

                                        {
   FLOAT32 FrequencyDifference;
   FLOAT32 TotalDifference;
   int i;
 
   // compute how well the histogram matches the expected histogram
   TotalDifference = 0.0;
   for (i = 0; i < Buckets->NumberOfBuckets; i++) {
     FrequencyDifference = Buckets->Count[i] - Buckets->ExpectedCount[i];
     TotalDifference += (FrequencyDifference * FrequencyDifference) /
       Buckets->ExpectedCount[i];
   }
 
   // test to see if the difference is more than expected
   if (TotalDifference > Buckets->ChiSquared)
     return FALSE;
   else
     return TRUE;
 }                                // DistributionOK

◆ FillBuckets()

void FillBuckets	(	BUCKETS *	Buckets,
		CLUSTER *	Cluster,
		uinT16	Dim,
		PARAM_DESC *	ParamDesc,
		FLOAT32	Mean,
		FLOAT32	StdDev
	)

This routine counts the number of cluster samples which fall within the various histogram buckets in Buckets. Only one dimension of each sample is examined. The exact meaning of the Mean and StdDev parameters depends on the distribution which is being analyzed (this info is in the Buckets data structure). For normal distributions, Mean and StdDev have the expected meanings. For uniform and random distributions the Mean is the center point of the range and the StdDev is 1/2 the range. A dimension with zero standard deviation cannot be statistically analyzed. In this case, a pseudo-analysis is used.

Parameters

Buckets	histogram buckets to count samples
Cluster	cluster whose samples are being analyzed
Dim	dimension of samples which is being analyzed
ParamDesc	description of the dimension
Mean	"mean" of the distribution
StdDev	"standard deviation" of the distribution

Returns: None (the Buckets data structure is filled in)

Note: Exceptions: None; History: 6/5/89, DSJ, Created.

Definition at line 1984 of file cluster.cpp.

                                  {
   uinT16 BucketID;
   int i;
   LIST SearchState;
   SAMPLE *Sample;
 
   // initialize the histogram bucket counts to 0
   for (i = 0; i < Buckets->NumberOfBuckets; i++)
     Buckets->Count[i] = 0;
 
   if (StdDev == 0.0) {
     /* if the standard deviation is zero, then we can't statistically
        analyze the cluster.  Use a pseudo-analysis: samples exactly on
        the mean are distributed evenly across all buckets.  Samples greater
        than the mean are placed in the last bucket; samples less than the
        mean are placed in the first bucket. */
 
     InitSampleSearch(SearchState, Cluster);
     i = 0;
     while ((Sample = NextSample (&SearchState)) != NULL) {
       if (Sample->Mean[Dim] > Mean)
         BucketID = Buckets->NumberOfBuckets - 1;
       else if (Sample->Mean[Dim] < Mean)
         BucketID = 0;
       else
         BucketID = i;
       Buckets->Count[BucketID] += 1;
       i++;
       if (i >= Buckets->NumberOfBuckets)
         i = 0;
     }
   }
   else {
     // search for all samples in the cluster and add to histogram buckets
     InitSampleSearch(SearchState, Cluster);
     while ((Sample = NextSample (&SearchState)) != NULL) {
       switch (Buckets->Distribution) {
         case normal:
           BucketID = NormalBucket (ParamDesc, Sample->Mean[Dim],
             Mean, StdDev);
           break;
         case D_random:
         case uniform:
           BucketID = UniformBucket (ParamDesc, Sample->Mean[Dim],
             Mean, StdDev);
           break;
         default:
           BucketID = 0;
       }
       Buckets->Count[Buckets->Bucket[BucketID]] += 1;
     }
   }
 }                                // FillBuckets

◆ FindNearestNeighbor()

CLUSTER * FindNearestNeighbor	(	KDTREE *	Tree,
		CLUSTER *	Cluster,
		FLOAT32 *	Distance
	)

This routine searches the specified kd-tree for the nearest neighbor of the specified cluster. It actually uses the kd routines to find the 2 nearest neighbors since one of them will be the original cluster. A pointer to the nearest neighbor is returned, if it can be found, otherwise NULL is returned. The distance between the 2 nodes is placed in the specified variable.

Parameters

Tree	kd-tree to search in for nearest neighbor
Cluster	cluster whose nearest neighbor is to be found
Distance	ptr to variable to report distance found

Returns: Pointer to the nearest neighbor of Cluster, or NULL

Note: Exceptions: none; History: 5/29/89, DSJ, Created. 7/13/89, DSJ, Removed visibility of kd-tree node data struct

Definition at line 798 of file cluster.cpp.

 {
   CLUSTER *Neighbor[MAXNEIGHBORS];
   FLOAT32 Dist[MAXNEIGHBORS];
   int NumberOfNeighbors;
   inT32 i;
   CLUSTER *BestNeighbor;
 
   // find the 2 nearest neighbors of the cluster
   KDNearestNeighborSearch(Tree, Cluster->Mean, MAXNEIGHBORS, MAXDISTANCE,
                           &NumberOfNeighbors, (void **)Neighbor, Dist);
 
   // search for the nearest neighbor that is not the cluster itself
   *Distance = MAXDISTANCE;
   BestNeighbor = NULL;
   for (i = 0; i < NumberOfNeighbors; i++) {
     if ((Dist[i] < *Distance) && (Neighbor[i] != Cluster)) {
       *Distance = Dist[i];
       BestNeighbor = Neighbor[i];
     }
   }
   return BestNeighbor;
 }                                // FindNearestNeighbor

◆ FreeBuckets()

void FreeBuckets ( BUCKETS * buckets )

This routine properly frees the memory used by a BUCKETS.

Parameters

buckets pointer to data structure to be freed

Definition at line 2165 of file cluster.cpp.

                                    {
   Efree(buckets->Count);
   Efree(buckets->ExpectedCount);
   Efree(buckets);
 }                                // FreeBuckets

◆ FreeCluster()

void FreeCluster ( CLUSTER * Cluster )

This routine frees the memory consumed by the specified cluster and all of its subclusters. This is done by recursive calls to FreeCluster().

Parameters

Cluster pointer to cluster to be freed

Returns: None

Note: Exceptions: None; History: 6/6/89, DSJ, Created.

Definition at line 2183 of file cluster.cpp.

                                    {
   if (Cluster != NULL) {
     FreeCluster (Cluster->Left);
     FreeCluster (Cluster->Right);
     free(Cluster);
   }
 }                                // FreeCluster

◆ FreeClusterer()

void FreeClusterer ( CLUSTERER * Clusterer )

This routine frees all of the memory allocated to the specified data structure. It will not, however, free the memory used by the prototype list. The pointers to the clusters for each prototype in the list will be set to NULL to indicate that the cluster data structures no longer exist. Any sample lists that have been obtained via calls to GetSamples are no longer valid.

Parameters

Clusterer pointer to data structure to be freed

Returns: None

Note: Exceptions: None; History: 6/6/89, DSJ, Created.

Definition at line 546 of file cluster.cpp.

                                          {
   if (Clusterer != NULL) {
     free(Clusterer->ParamDesc);
     if (Clusterer->KDTree != NULL)
       FreeKDTree (Clusterer->KDTree);
     if (Clusterer->Root != NULL)
       FreeCluster (Clusterer->Root);
     // Free up all used buckets structures.
     for (int d = 0; d < DISTRIBUTION_COUNT; ++d) {
       for (int c = 0; c < MAXBUCKETS + 1 - MINBUCKETS; ++c)
         if (Clusterer->bucket_cache[d][c] != NULL)
           FreeBuckets(Clusterer->bucket_cache[d][c]);
     }
 
     free(Clusterer);
   }
 }                                // FreeClusterer

◆ FreeProtoList()

void FreeProtoList ( LIST * ProtoList )

This routine frees all of the memory allocated to the specified list of prototypes. The clusters which are pointed to by the prototypes are not freed.

Parameters

ProtoList pointer to list of prototypes to be freed

Returns: None

Note: Exceptions: None; History: 6/6/89, DSJ, Created.

Definition at line 573 of file cluster.cpp.

                                     {
   destroy_nodes(*ProtoList, FreePrototype);
 }                                // FreeProtoList

◆ FreePrototype()

void FreePrototype ( void * arg )

This routine deallocates the memory consumed by the specified prototype and modifies the corresponding cluster so that it is no longer marked as a prototype. The cluster is NOT deallocated by this routine.

Parameters

arg	prototype data structure to be deallocated

Returns: None

Note: Exceptions: None; History: 5/30/89, DSJ, Created.

Definition at line 587 of file cluster.cpp.

                               {  //PROTOTYPE     *Prototype)
   PROTOTYPE *Prototype = (PROTOTYPE *) arg;
 
   // unmark the corresponding cluster (if there is one
   if (Prototype->Cluster != NULL)
     Prototype->Cluster->Prototype = FALSE;
 
   // deallocate the prototype statistics and then the prototype itself
   free (Prototype->Distrib);
   free (Prototype->Mean);
   if (Prototype->Style != spherical) {
     free (Prototype->Variance.Elliptical);
     free (Prototype->Magnitude.Elliptical);
     free (Prototype->Weight.Elliptical);
   }
   free(Prototype);
 }                                // FreePrototype

◆ FreeStatistics()

void FreeStatistics ( STATISTICS * Statistics )

This routine frees the memory used by the statistics data structure.

Parameters

Statistics pointer to data structure to be freed

Returns: None

Note: Exceptions: None; History: 6/5/89, DSJ, Created.

Definition at line 2153 of file cluster.cpp.

                                             {
   free(Statistics->CoVariance);
   free(Statistics->Min);
   free(Statistics->Max);
   free(Statistics);
 }                                // FreeStatistics

◆ GetBuckets()

BUCKETS * GetBuckets	(	CLUSTERER *	clusterer,
		DISTRIBUTION	Distribution,
		uinT32	SampleCount,
		FLOAT64	Confidence
	)

This routine returns a histogram data structure which can be used by other routines to place samples into histogram buckets, and then apply a goodness of fit test to the histogram data to determine if the samples belong to the specified probability distribution. The routine keeps a list of bucket data structures which have already been created so that it minimizes the computation time needed to create a new bucket.

Parameters

clusterer	which keeps a bucket_cache for us.
Distribution	type of probability distribution to test for
SampleCount	number of samples that are available
Confidence	probability of a Type I error

Returns: Bucket data structure

Note: Exceptions: none; History: Thu Aug 3 12:58:10 1989, DSJ, Created.

Definition at line 1688 of file cluster.cpp.

                                         {
   // Get an old bucket structure with the same number of buckets.
   uinT16 NumberOfBuckets = OptimumNumberOfBuckets(SampleCount);
   BUCKETS *Buckets =
       clusterer->bucket_cache[Distribution][NumberOfBuckets - MINBUCKETS];
 
   // If a matching bucket structure is not found, make one and save it.
   if (Buckets == NULL) {
     Buckets = MakeBuckets(Distribution, SampleCount, Confidence);
     clusterer->bucket_cache[Distribution][NumberOfBuckets - MINBUCKETS] =
         Buckets;
   } else {
     // Just adjust the existing buckets.
     if (SampleCount != Buckets->SampleCount)
       AdjustBuckets(Buckets, SampleCount);
     if (Confidence != Buckets->Confidence) {
       Buckets->Confidence = Confidence;
       Buckets->ChiSquared = ComputeChiSquared(
           DegreesOfFreedom(Distribution, Buckets->NumberOfBuckets),
           Confidence);
     }
     InitBuckets(Buckets);
   }
   return Buckets;
 }                                // GetBuckets

◆ Independent()

BOOL8 Independent	(	PARAM_DESC	ParamDesc[],
		inT16	N,
		FLOAT32 *	CoVariance,
		FLOAT32	Independence
	)

This routine returns TRUE if the specified covariance matrix indicates that all N dimensions are independent of one another. One dimension is judged to be independent of another when the magnitude of the corresponding correlation coefficient is less than the specified Independence factor. The correlation coefficient is calculated as: (see Duda and Hart, pg. 247) coeff[ij] = stddev[ij] / sqrt (stddev[ii] * stddev[jj]) The covariance matrix is assumed to be symmetric (which should always be true).

Parameters

ParamDesc	descriptions of each feature space dimension
N	number of dimensions
CoVariance	ptr to a covariance matrix
Independence	max off-diagonal correlation coefficient

Returns: TRUE if dimensions are independent, FALSE otherwise

Note: Exceptions: None; History: 6/4/89, DSJ, Created.

Definition at line 1641 of file cluster.cpp.

                                                      {
   int i, j;
   FLOAT32 *VARii;                // points to ith on-diagonal element
   FLOAT32 *VARjj;                // points to jth on-diagonal element
   FLOAT32 CorrelationCoeff;
 
   VARii = CoVariance;
   for (i = 0; i < N; i++, VARii += N + 1) {
     if (ParamDesc[i].NonEssential)
       continue;
 
     VARjj = VARii + N + 1;
     CoVariance = VARii + 1;
     for (j = i + 1; j < N; j++, CoVariance++, VARjj += N + 1) {
       if (ParamDesc[j].NonEssential)
         continue;
 
       if ((*VARii == 0.0) || (*VARjj == 0.0))
         CorrelationCoeff = 0.0;
       else
         CorrelationCoeff =
           sqrt (sqrt (*CoVariance * *CoVariance / (*VARii * *VARjj)));
       if (CorrelationCoeff > Independence)
         return (FALSE);
     }
   }
   return (TRUE);
 }                                // Independent

◆ InitBuckets()

void InitBuckets ( BUCKETS * Buckets )

This routine sets the bucket counts in the specified histogram to zero.

Parameters

Buckets histogram data structure to init

Returns: none

Note: Exceptions: none; History: Thu Aug 3 14:31:14 1989, DSJ, Created.

Definition at line 2283 of file cluster.cpp.

                                    {
   int i;
 
   for (i = 0; i < Buckets->NumberOfBuckets; i++) {
     Buckets->Count[i] = 0;
   }
 
 }                                // InitBuckets

◆ Integral()

FLOAT64 Integral	(	FLOAT64	f1,
		FLOAT64	f2,
		FLOAT64	Dx
	)

This routine computes a trapezoidal approximation to the integral of a function over a small delta in x.

Parameters

f1	value of function at x1
f2	value of function at x2
Dx	x2 - x1 (should always be positive)

Returns: Approximation of the integral of the function from x1 to x2.

Note: Exceptions: None; History: 6/5/89, DSJ, Created.

Definition at line 1958 of file cluster.cpp.

                                                      {
   return (f1 + f2) * Dx / 2.0;
 }                                // Integral

◆ InvertMatrix()

double InvertMatrix	(	const float *	input,
		int	size,
		float *	inv
	)

Compute the inverse of a matrix using LU decomposition with partial pivoting. The return value is the sum of norms of the off-diagonal terms of the product of a and inv. (A measure of the error.)

Definition at line 2521 of file cluster.cpp.

                                                               {
   // Allocate memory for the 2D arrays.
   GENERIC_2D_ARRAY<double> U(size, size, 0.0);
   GENERIC_2D_ARRAY<double> U_inv(size, size, 0.0);
   GENERIC_2D_ARRAY<double> L(size, size, 0.0);
 
   // Initialize the working matrices. U starts as input, L as I and U_inv as O.
   int row;
   int col;
   for (row = 0; row < size; row++) {
     for (col = 0; col < size; col++) {
       U[row][col] = input[row*size + col];
       L[row][col] = row == col ? 1.0 : 0.0;
       U_inv[row][col] = 0.0;
     }
   }
 
   // Compute forward matrix by inversion by LU decomposition of input.
   for (col = 0; col < size; ++col) {
     // Find best pivot
     int best_row = 0;
     double best_pivot = -1.0;
     for (row = col; row < size; ++row) {
       if (Abs(U[row][col]) > best_pivot) {
         best_pivot = Abs(U[row][col]);
         best_row = row;
       }
     }
     // Exchange pivot rows.
     if (best_row != col) {
       for (int k = 0; k < size; ++k) {
         double tmp = U[best_row][k];
         U[best_row][k] = U[col][k];
         U[col][k] = tmp;
         tmp = L[best_row][k];
         L[best_row][k] = L[col][k];
         L[col][k] = tmp;
       }
     }
     // Now do the pivot itself.
     for (row = col + 1; row < size; ++row) {
       double ratio = -U[row][col] / U[col][col];
       for (int j = col; j < size; ++j) {
         U[row][j] += U[col][j] * ratio;
       }
       for (int k = 0; k < size; ++k) {
         L[row][k] += L[col][k] * ratio;
       }
     }
   }
   // Next invert U.
   for (col = 0; col < size; ++col) {
     U_inv[col][col] = 1.0 / U[col][col];
     for (row = col - 1; row >= 0; --row) {
       double total = 0.0;
       for (int k = col; k > row; --k) {
         total += U[row][k] * U_inv[k][col];
       }
       U_inv[row][col] = -total / U[row][row];
     }
   }
   // Now the answer is U_inv.L.
   for (row = 0; row < size; row++) {
     for (col = 0; col < size; col++) {
       double sum = 0.0;
       for (int k = row; k < size; ++k) {
         sum += U_inv[row][k] * L[k][col];
       }
       inv[row*size + col] = sum;
     }
   }
   // Check matrix product.
   double error_sum = 0.0;
   for (row = 0; row < size; row++) {
     for (col = 0; col < size; col++) {
       double sum = 0.0;
       for (int k = 0; k < size; ++k) {
         sum += input[row*size + k] * inv[k *size + col];
       }
       if (row != col) {
         error_sum += Abs(sum);
       }
     }
   }
   return error_sum;
 }

◆ ListEntryMatch()

int ListEntryMatch	(	void *	arg1,
		void *	arg2
	)

This routine is used to search a list for a list node whose contents match Key. It is called by the list delete_d routine.

Returns: TRUE if ListNode matches Key

Note: Exceptions: none; History: Thu Aug 3 14:23:58 1989, DSJ, Created.

Definition at line 2244 of file cluster.cpp.

                                {  //Key
   return (arg1 == arg2);
 
 }                                // ListEntryMatch

◆ MakeBuckets()

BUCKETS * MakeBuckets	(	DISTRIBUTION	Distribution,
		uinT32	SampleCount,
		FLOAT64	Confidence
	)

This routine creates a histogram data structure which can be used by other routines to place samples into histogram buckets, and then apply a goodness of fit test to the histogram data to determine if the samples belong to the specified probability distribution. The buckets are allocated in such a way that the expected frequency of samples in each bucket is approximately the same. In order to make this possible, a mapping table is computed which maps "normalized" samples into the appropriate bucket.

Parameters

Distribution	type of probability distribution to test for
SampleCount	number of samples that are available
Confidence	probability of a Type I error

Returns: Pointer to new histogram data structure

Note: Exceptions: None; History: 6/4/89, DSJ, Created.

Definition at line 1735 of file cluster.cpp.

                                          {
   const DENSITYFUNC DensityFunction[] =
     { NormalDensity, UniformDensity, UniformDensity };
   int i, j;
   BUCKETS *Buckets;
   FLOAT64 BucketProbability;
   FLOAT64 NextBucketBoundary;
   FLOAT64 Probability;
   FLOAT64 ProbabilityDelta;
   FLOAT64 LastProbDensity;
   FLOAT64 ProbDensity;
   uinT16 CurrentBucket;
   BOOL8 Symmetrical;
 
   // allocate memory needed for data structure
   Buckets = static_cast<BUCKETS*>(Emalloc(sizeof(BUCKETS)));
   Buckets->NumberOfBuckets = OptimumNumberOfBuckets(SampleCount);
   Buckets->SampleCount = SampleCount;
   Buckets->Confidence = Confidence;
   Buckets->Count = static_cast<uinT32*>(
       Emalloc(Buckets->NumberOfBuckets * sizeof(uinT32)));
   Buckets->ExpectedCount = static_cast<FLOAT32*>(
       Emalloc(Buckets->NumberOfBuckets * sizeof(FLOAT32)));
 
   // initialize simple fields
   Buckets->Distribution = Distribution;
   for (i = 0; i < Buckets->NumberOfBuckets; i++) {
     Buckets->Count[i] = 0;
     Buckets->ExpectedCount[i] = 0.0;
   }
 
   // all currently defined distributions are symmetrical
   Symmetrical = TRUE;
   Buckets->ChiSquared = ComputeChiSquared(
       DegreesOfFreedom(Distribution, Buckets->NumberOfBuckets), Confidence);
 
   if (Symmetrical) {
     // allocate buckets so that all have approx. equal probability
     BucketProbability = 1.0 / (FLOAT64) (Buckets->NumberOfBuckets);
 
     // distribution is symmetric so fill in upper half then copy
     CurrentBucket = Buckets->NumberOfBuckets / 2;
     if (Odd (Buckets->NumberOfBuckets))
       NextBucketBoundary = BucketProbability / 2;
     else
       NextBucketBoundary = BucketProbability;
 
     Probability = 0.0;
     LastProbDensity =
       (*DensityFunction[(int) Distribution]) (BUCKETTABLESIZE / 2);
     for (i = BUCKETTABLESIZE / 2; i < BUCKETTABLESIZE; i++) {
       ProbDensity = (*DensityFunction[(int) Distribution]) (i + 1);
       ProbabilityDelta = Integral (LastProbDensity, ProbDensity, 1.0);
       Probability += ProbabilityDelta;
       if (Probability > NextBucketBoundary) {
         if (CurrentBucket < Buckets->NumberOfBuckets - 1)
           CurrentBucket++;
         NextBucketBoundary += BucketProbability;
       }
       Buckets->Bucket[i] = CurrentBucket;
       Buckets->ExpectedCount[CurrentBucket] +=
         (FLOAT32) (ProbabilityDelta * SampleCount);
       LastProbDensity = ProbDensity;
     }
     // place any leftover probability into the last bucket
     Buckets->ExpectedCount[CurrentBucket] +=
       (FLOAT32) ((0.5 - Probability) * SampleCount);
 
     // copy upper half of distribution to lower half
     for (i = 0, j = BUCKETTABLESIZE - 1; i < j; i++, j--)
       Buckets->Bucket[i] =
         Mirror(Buckets->Bucket[j], Buckets->NumberOfBuckets);
 
     // copy upper half of expected counts to lower half
     for (i = 0, j = Buckets->NumberOfBuckets - 1; i <= j; i++, j--)
       Buckets->ExpectedCount[i] += Buckets->ExpectedCount[j];
   }
   return Buckets;
 }                                // MakeBuckets

◆ MakeClusterer()

CLUSTERER* MakeClusterer	(	inT16	SampleSize,
		const PARAM_DESC	ParamDesc[]
	)

This routine creates a new clusterer data structure, initializes it, and returns a pointer to it.

Parameters

SampleSize	number of dimensions in feature space
ParamDesc	description of each dimension

Returns: pointer to the new clusterer data structure

Note: Exceptions: None; History: 5/29/89, DSJ, Created.

Definition at line 399 of file cluster.cpp.

                                                                {
   CLUSTERER *Clusterer;
   int i;
 
   // allocate main clusterer data structure and init simple fields
   Clusterer = (CLUSTERER *) Emalloc (sizeof (CLUSTERER));
   Clusterer->SampleSize = SampleSize;
   Clusterer->NumberOfSamples = 0;
   Clusterer->NumChar = 0;
 
   // init fields which will not be used initially
   Clusterer->Root = NULL;
   Clusterer->ProtoList = NIL_LIST;
 
   // maintain a copy of param descriptors in the clusterer data structure
   Clusterer->ParamDesc =
     (PARAM_DESC *) Emalloc (SampleSize * sizeof (PARAM_DESC));
   for (i = 0; i < SampleSize; i++) {
     Clusterer->ParamDesc[i].Circular = ParamDesc[i].Circular;
     Clusterer->ParamDesc[i].NonEssential = ParamDesc[i].NonEssential;
     Clusterer->ParamDesc[i].Min = ParamDesc[i].Min;
     Clusterer->ParamDesc[i].Max = ParamDesc[i].Max;
     Clusterer->ParamDesc[i].Range = ParamDesc[i].Max - ParamDesc[i].Min;
     Clusterer->ParamDesc[i].HalfRange = Clusterer->ParamDesc[i].Range / 2;
     Clusterer->ParamDesc[i].MidRange =
       (ParamDesc[i].Max + ParamDesc[i].Min) / 2;
   }
 
   // allocate a kd tree to hold the samples
   Clusterer->KDTree = MakeKDTree (SampleSize, ParamDesc);
 
   // Initialize cache of histogram buckets to minimize recomputing them.
   for (int d = 0; d < DISTRIBUTION_COUNT; ++d) {
     for (int c = 0; c < MAXBUCKETS + 1 - MINBUCKETS; ++c)
       Clusterer->bucket_cache[d][c] = NULL;
   }
 
   return Clusterer;
 }                                // MakeClusterer

◆ MakeDegenerateProto()

PROTOTYPE * MakeDegenerateProto	(	uinT16	N,
		CLUSTER *	Cluster,
		STATISTICS *	Statistics,
		PROTOSTYLE	Style,
		inT32	MinSamples
	)

This routine checks for clusters which are degenerate and therefore cannot be analyzed in a statistically valid way. A cluster is defined as degenerate if it does not have at least MINSAMPLESNEEDED samples in it. If the cluster is found to be degenerate, a prototype of the specified style is generated and marked as insignificant. A cluster is also degenerate if it does not have at least MinSamples samples in it.

If the cluster is not degenerate, NULL is returned.

Parameters

N	number of dimensions
Cluster	cluster being analyzed
Statistics	statistical info about cluster
Style	type of prototype to be generated
MinSamples	minimum number of samples in a cluster

Returns: Pointer to degenerate prototype or NULL.

Note: Exceptions: None; History: 6/20/89, DSJ, Created. 7/12/89, DSJ, Changed name and added check for 0 stddev. 8/8/89, DSJ, Removed check for 0 stddev (handled elsewhere).

Definition at line 1063 of file cluster.cpp.

                                                  {
   PROTOTYPE *Proto = NULL;
 
   if (MinSamples < MINSAMPLESNEEDED)
     MinSamples = MINSAMPLESNEEDED;
 
   if (Cluster->SampleCount < MinSamples) {
     switch (Style) {
       case spherical:
         Proto = NewSphericalProto (N, Cluster, Statistics);
         break;
       case elliptical:
       case automatic:
         Proto = NewEllipticalProto (N, Cluster, Statistics);
         break;
       case mixed:
         Proto = NewMixedProto (N, Cluster, Statistics);
         break;
     }
     Proto->Significant = FALSE;
   }
   return (Proto);
 }                                // MakeDegenerateProto

◆ MakeDimRandom()

void MakeDimRandom	(	uinT16	i,
		PROTOTYPE *	Proto,
		PARAM_DESC *	ParamDesc
	)

This routine alters the ith dimension of the specified mixed prototype to be D_random.

Parameters

i	index of dimension to be changed
Proto	prototype whose dimension is to be altered
ParamDesc	description of specified dimension

Returns: None

Note: Exceptions: None; History: 6/20/89, DSJ, Created.

Definition at line 1352 of file cluster.cpp.

                                                                       {
   Proto->Distrib[i] = D_random;
   Proto->Mean[i] = ParamDesc->MidRange;
   Proto->Variance.Elliptical[i] = ParamDesc->HalfRange;
 
   // subtract out the previous magnitude of this dimension from the total
   Proto->TotalMagnitude /= Proto->Magnitude.Elliptical[i];
   Proto->Magnitude.Elliptical[i] = 1.0 / ParamDesc->Range;
   Proto->TotalMagnitude *= Proto->Magnitude.Elliptical[i];
   Proto->LogMagnitude = log ((double) Proto->TotalMagnitude);
 
   // note that the proto Weight is irrelevant for D_random protos
 }                                // MakeDimRandom

◆ MakeDimUniform()

void MakeDimUniform	(	uinT16	i,
		PROTOTYPE *	Proto,
		STATISTICS *	Statistics
	)

This routine alters the ith dimension of the specified mixed prototype to be uniform.

Parameters

i	index of dimension to be changed
Proto	prototype whose dimension is to be altered
Statistics	statistical info about prototype

Returns: None

Note: Exceptions: None; History: 6/20/89, DSJ, Created.

Definition at line 1376 of file cluster.cpp.

                                                                         {
   Proto->Distrib[i] = uniform;
   Proto->Mean[i] = Proto->Cluster->Mean[i] +
     (Statistics->Min[i] + Statistics->Max[i]) / 2;
   Proto->Variance.Elliptical[i] =
     (Statistics->Max[i] - Statistics->Min[i]) / 2;
   if (Proto->Variance.Elliptical[i] < MINVARIANCE)
     Proto->Variance.Elliptical[i] = MINVARIANCE;
 
   // subtract out the previous magnitude of this dimension from the total
   Proto->TotalMagnitude /= Proto->Magnitude.Elliptical[i];
   Proto->Magnitude.Elliptical[i] =
     1.0 / (2.0 * Proto->Variance.Elliptical[i]);
   Proto->TotalMagnitude *= Proto->Magnitude.Elliptical[i];
   Proto->LogMagnitude = log ((double) Proto->TotalMagnitude);
 
   // note that the proto Weight is irrelevant for uniform protos
 }                                // MakeDimUniform

◆ MakeEllipticalProto()

PROTOTYPE * MakeEllipticalProto	(	CLUSTERER *	Clusterer,
		CLUSTER *	Cluster,
		STATISTICS *	Statistics,
		BUCKETS *	Buckets
	)

This routine tests the specified cluster to see if it can be approximated by an elliptical normal distribution. If it can be, then a new prototype is formed and returned to the caller. If it can't be, then NULL is returned to the caller.

Parameters

Clusterer	data struct containing samples being clustered
Cluster	cluster to be made into an elliptical prototype
Statistics	statistical info about cluster
Buckets	histogram struct used to analyze distribution

Returns: Pointer to new elliptical prototype or NULL.

Note: Exceptions: None; History: 6/12/89, DSJ, Created.

Definition at line 1249 of file cluster.cpp.

                                                  {
   PROTOTYPE *Proto = NULL;
   int i;
 
   // check that each dimension is a normal distribution
   for (i = 0; i < Clusterer->SampleSize; i++) {
     if (Clusterer->ParamDesc[i].NonEssential)
       continue;
 
     FillBuckets (Buckets, Cluster, i, &(Clusterer->ParamDesc[i]),
       Cluster->Mean[i],
       sqrt ((FLOAT64) Statistics->
       CoVariance[i * (Clusterer->SampleSize + 1)]));
     if (!DistributionOK (Buckets))
       break;
   }
   // if all dimensions matched a normal distribution, make a proto
   if (i >= Clusterer->SampleSize)
     Proto = NewEllipticalProto (Clusterer->SampleSize, Cluster, Statistics);
   return (Proto);
 }                                // MakeEllipticalProto

◆ MakeMixedProto()

PROTOTYPE * MakeMixedProto	(	CLUSTERER *	Clusterer,
		CLUSTER *	Cluster,
		STATISTICS *	Statistics,
		BUCKETS *	NormalBuckets,
		FLOAT64	Confidence
	)

This routine tests each dimension of the specified cluster to see what distribution would best approximate that dimension. Each dimension is compared to the following distributions in order: normal, random, uniform. If each dimension can be represented by one of these distributions, then a new prototype is formed and returned to the caller. If it can't be, then NULL is returned to the caller.

Parameters

Clusterer	data struct containing samples being clustered
Cluster	cluster to be made into a prototype
Statistics	statistical info about cluster
NormalBuckets	histogram struct used to analyze distribution
Confidence	confidence level for alternate distributions

Returns: Pointer to new mixed prototype or NULL.

Note: Exceptions: None; History: 6/12/89, DSJ, Created.

Definition at line 1291 of file cluster.cpp.

                                               {
   PROTOTYPE *Proto;
   int i;
   BUCKETS *UniformBuckets = NULL;
   BUCKETS *RandomBuckets = NULL;
 
   // create a mixed proto to work on - initially assume all dimensions normal*/
   Proto = NewMixedProto (Clusterer->SampleSize, Cluster, Statistics);
 
   // find the proper distribution for each dimension
   for (i = 0; i < Clusterer->SampleSize; i++) {
     if (Clusterer->ParamDesc[i].NonEssential)
       continue;
 
     FillBuckets (NormalBuckets, Cluster, i, &(Clusterer->ParamDesc[i]),
       Proto->Mean[i],
       sqrt ((FLOAT64) Proto->Variance.Elliptical[i]));
     if (DistributionOK (NormalBuckets))
       continue;
 
     if (RandomBuckets == NULL)
       RandomBuckets =
         GetBuckets(Clusterer, D_random, Cluster->SampleCount, Confidence);
     MakeDimRandom (i, Proto, &(Clusterer->ParamDesc[i]));
     FillBuckets (RandomBuckets, Cluster, i, &(Clusterer->ParamDesc[i]),
       Proto->Mean[i], Proto->Variance.Elliptical[i]);
     if (DistributionOK (RandomBuckets))
       continue;
 
     if (UniformBuckets == NULL)
       UniformBuckets =
         GetBuckets(Clusterer, uniform, Cluster->SampleCount, Confidence);
     MakeDimUniform(i, Proto, Statistics);
     FillBuckets (UniformBuckets, Cluster, i, &(Clusterer->ParamDesc[i]),
       Proto->Mean[i], Proto->Variance.Elliptical[i]);
     if (DistributionOK (UniformBuckets))
       continue;
     break;
   }
   // if any dimension failed to match a distribution, discard the proto
   if (i < Clusterer->SampleSize) {
     FreePrototype(Proto);
     Proto = NULL;
   }
   return (Proto);
 }                                // MakeMixedProto

◆ MakeNewCluster()

CLUSTER * MakeNewCluster	(	CLUSTERER *	Clusterer,
		TEMPCLUSTER *	TempCluster
	)

This routine creates a new permanent cluster from the clusters specified in TempCluster. The 2 clusters in TempCluster are marked as "clustered" and deleted from the kd-tree. The new cluster is then added to the kd-tree.

Parameters

Clusterer	current clustering environment
TempCluster	potential cluster to make permanent

Returns: Pointer to the new permanent cluster

Note: Exceptions: none; History: 5/29/89, DSJ, Created. 7/13/89, DSJ, Removed visibility of kd-tree node data struct

Definition at line 836 of file cluster.cpp.

                                                                         {
   CLUSTER *Cluster;
 
   // allocate the new cluster and initialize it
   Cluster = (CLUSTER *) Emalloc(
       sizeof(CLUSTER) + (Clusterer->SampleSize - 1) * sizeof(FLOAT32));
   Cluster->Clustered = FALSE;
   Cluster->Prototype = FALSE;
   Cluster->Left = TempCluster->Cluster;
   Cluster->Right = TempCluster->Neighbor;
   Cluster->CharID = -1;
 
   // mark the old clusters as "clustered" and delete them from the kd-tree
   Cluster->Left->Clustered = TRUE;
   Cluster->Right->Clustered = TRUE;
   KDDelete(Clusterer->KDTree, Cluster->Left->Mean, Cluster->Left);
   KDDelete(Clusterer->KDTree, Cluster->Right->Mean, Cluster->Right);
 
   // compute the mean and sample count for the new cluster
   Cluster->SampleCount =
       MergeClusters(Clusterer->SampleSize, Clusterer->ParamDesc,
                     Cluster->Left->SampleCount, Cluster->Right->SampleCount,
                     Cluster->Mean, Cluster->Left->Mean, Cluster->Right->Mean);
 
   // add the new cluster to the KD tree
   KDStore(Clusterer->KDTree, Cluster->Mean, Cluster);
   return Cluster;
 }                                // MakeNewCluster

◆ MakePotentialClusters()

void MakePotentialClusters	(	ClusteringContext *	context,
		CLUSTER *	Cluster,
		inT32	Level
	)

This routine is designed to be used in concert with the KDWalk routine. It will create a potential cluster for each sample in the kd-tree that is being walked. This potential cluster will then be pushed on the heap.

Parameters

context	ClusteringContext (see definition above)
Cluster	current cluster being visited in kd-tree walk
Level	level of this cluster in the kd-tree

Definition at line 765 of file cluster.cpp.

                                                           {
   ClusterPair HeapEntry;
   int next = context->next;
   context->candidates[next].Cluster = Cluster;
   HeapEntry.data = &(context->candidates[next]);
   context->candidates[next].Neighbor =
       FindNearestNeighbor(context->tree,
                           context->candidates[next].Cluster,
                           &HeapEntry.key);
   if (context->candidates[next].Neighbor != NULL) {
     context->heap->Push(&HeapEntry);
     context->next++;
   }
 }                                // MakePotentialClusters

◆ MakePrototype()

PROTOTYPE * MakePrototype	(	CLUSTERER *	Clusterer,
		CLUSTERCONFIG *	Config,
		CLUSTER *	Cluster
	)

This routine attempts to create a prototype from the specified cluster that conforms to the distribution specified in Config. If there are too few samples in the cluster to perform a statistical analysis, then a prototype is generated but labelled as insignificant. If the dimensions of the cluster are not independent, no prototype is generated and NULL is returned. If a prototype can be found that matches the desired distribution then a pointer to it is returned, otherwise NULL is returned.

Parameters

Clusterer	data structure holding cluster tree
Config	parameters used to control prototype generation
Cluster	cluster to be made into a prototype

Returns: Pointer to new prototype or NULL

Note: Exceptions: None; History: 6/19/89, DSJ, Created.

Definition at line 969 of file cluster.cpp.

                                            {
   STATISTICS *Statistics;
   PROTOTYPE *Proto;
   BUCKETS *Buckets;
 
   // filter out clusters which contain samples from the same character
   if (MultipleCharSamples (Clusterer, Cluster, Config->MaxIllegal))
     return NULL;
 
   // compute the covariance matrix and ranges for the cluster
   Statistics =
       ComputeStatistics(Clusterer->SampleSize, Clusterer->ParamDesc, Cluster);
 
   // check for degenerate clusters which need not be analyzed further
   // note that the MinSamples test assumes that all clusters with multiple
   // character samples have been removed (as above)
   Proto = MakeDegenerateProto(
       Clusterer->SampleSize, Cluster, Statistics, Config->ProtoStyle,
       (inT32) (Config->MinSamples * Clusterer->NumChar));
   if (Proto != NULL) {
     FreeStatistics(Statistics);
     return Proto;
   }
   // check to ensure that all dimensions are independent
   if (!Independent(Clusterer->ParamDesc, Clusterer->SampleSize,
                    Statistics->CoVariance, Config->Independence)) {
     FreeStatistics(Statistics);
     return NULL;
   }
 
   if (HOTELLING && Config->ProtoStyle == elliptical) {
     Proto = TestEllipticalProto(Clusterer, Config, Cluster, Statistics);
     if (Proto != NULL) {
       FreeStatistics(Statistics);
       return Proto;
     }
   }
 
   // create a histogram data structure used to evaluate distributions
   Buckets = GetBuckets(Clusterer, normal, Cluster->SampleCount,
                        Config->Confidence);
 
   // create a prototype based on the statistics and test it
   switch (Config->ProtoStyle) {
     case spherical:
       Proto = MakeSphericalProto(Clusterer, Cluster, Statistics, Buckets);
       break;
     case elliptical:
       Proto = MakeEllipticalProto(Clusterer, Cluster, Statistics, Buckets);
       break;
     case mixed:
       Proto = MakeMixedProto(Clusterer, Cluster, Statistics, Buckets,
                              Config->Confidence);
       break;
     case automatic:
       Proto = MakeSphericalProto(Clusterer, Cluster, Statistics, Buckets);
       if (Proto != NULL)
         break;
       Proto = MakeEllipticalProto(Clusterer, Cluster, Statistics, Buckets);
       if (Proto != NULL)
         break;
       Proto = MakeMixedProto(Clusterer, Cluster, Statistics, Buckets,
                              Config->Confidence);
       break;
   }
   FreeStatistics(Statistics);
   return Proto;
 }                                // MakePrototype

◆ MakeSample()

SAMPLE* MakeSample	(	CLUSTERER *	Clusterer,
		const FLOAT32 *	Feature,
		inT32	CharID
	)

This routine creates a new sample data structure to hold the specified feature. This sample is added to the clusterer data structure (so that it knows which samples are to be clustered later), and a pointer to the sample is returned to the caller.

Parameters

Clusterer	clusterer data structure to add sample to
Feature	feature to be added to clusterer
CharID	unique ident. of char that sample came from

Returns: Pointer to the new sample data structure

Note: Exceptions: ALREADYCLUSTERED MakeSample can't be called after ClusterSamples has been called; History: 5/29/89, DSJ, Created.

Definition at line 455 of file cluster.cpp.

                                  {
   SAMPLE *Sample;
   int i;
 
   // see if the samples have already been clustered - if so trap an error
   if (Clusterer->Root != NULL)
     DoError (ALREADYCLUSTERED,
       "Can't add samples after they have been clustered");
 
   // allocate the new sample and initialize it
   Sample = (SAMPLE *) Emalloc (sizeof (SAMPLE) +
     (Clusterer->SampleSize -
     1) * sizeof (FLOAT32));
   Sample->Clustered = FALSE;
   Sample->Prototype = FALSE;
   Sample->SampleCount = 1;
   Sample->Left = NULL;
   Sample->Right = NULL;
   Sample->CharID = CharID;
 
   for (i = 0; i < Clusterer->SampleSize; i++)
     Sample->Mean[i] = Feature[i];
 
   // add the sample to the KD tree - keep track of the total # of samples
   Clusterer->NumberOfSamples++;
   KDStore (Clusterer->KDTree, Sample->Mean, (char *) Sample);
   if (CharID >= Clusterer->NumChar)
     Clusterer->NumChar = CharID + 1;
 
   // execute hook for monitoring clustering operation
   // (*SampleCreationHook)( Sample );
 
   return (Sample);
 }                                // MakeSample

◆ MakeSphericalProto()

PROTOTYPE * MakeSphericalProto	(	CLUSTERER *	Clusterer,
		CLUSTER *	Cluster,
		STATISTICS *	Statistics,
		BUCKETS *	Buckets
	)

This routine tests the specified cluster to see if it can be approximated by a spherical normal distribution. If it can be, then a new prototype is formed and returned to the caller. If it can't be, then NULL is returned to the caller.

Parameters

Clusterer	data struct containing samples being clustered
Cluster	cluster to be made into a spherical prototype
Statistics	statistical info about cluster
Buckets	histogram struct used to analyze distribution

Returns: Pointer to new spherical prototype or NULL.

Note: Exceptions: None; History: 6/1/89, DSJ, Created.

Definition at line 1212 of file cluster.cpp.

                                                 {
   PROTOTYPE *Proto = NULL;
   int i;
 
   // check that each dimension is a normal distribution
   for (i = 0; i < Clusterer->SampleSize; i++) {
     if (Clusterer->ParamDesc[i].NonEssential)
       continue;
 
     FillBuckets (Buckets, Cluster, i, &(Clusterer->ParamDesc[i]),
       Cluster->Mean[i],
       sqrt ((FLOAT64) (Statistics->AvgVariance)));
     if (!DistributionOK (Buckets))
       break;
   }
   // if all dimensions matched a normal distribution, make a proto
   if (i >= Clusterer->SampleSize)
     Proto = NewSphericalProto (Clusterer->SampleSize, Cluster, Statistics);
   return (Proto);
 }                                // MakeSphericalProto

◆ Mean()

FLOAT32 Mean	(	PROTOTYPE *	Proto,
		uinT16	Dimension
	)

This routine returns the mean of the specified prototype in the indicated dimension.

Parameters

Proto	prototype to return mean of
Dimension	dimension whose mean is to be returned

Returns: Mean of Prototype in Dimension

Note: Exceptions: none; History: 7/6/89, DSJ, Created.

Definition at line 644 of file cluster.cpp.

                                                  {
   return (Proto->Mean[Dimension]);
 }                                // Mean

◆ MergeClusters() [1/2]

inT32 MergeClusters	(	inT16	N,
		register PARAM_DESC	ParamDesc[],
		register inT32	n1,
		register inT32	n2,
		register FLOAT32	m[],
		register FLOAT32	m1[],
		register FLOAT32	m2[]
	)

◆ MergeClusters() [2/2]

inT32 MergeClusters	(	inT16	N,
		PARAM_DESC	ParamDesc[],
		inT32	n1,
		inT32	n2,
		FLOAT32	m[],
		FLOAT32	m1[],
		FLOAT32	m2[]
	)

This routine merges two clusters into one larger cluster. To do this it computes the number of samples in the new cluster and the mean of the new cluster. The ParamDesc information is used to ensure that circular dimensions are handled correctly.

Parameters

N	# of dimensions (size of arrays)
ParamDesc	array of dimension descriptions
n1,n2	number of samples in each old cluster
m	array to hold mean of new cluster
m1,m2	arrays containing means of old clusters

Returns: The number of samples in the new cluster.

Note: Exceptions: None; History: 5/31/89, DSJ, Created.

Definition at line 880 of file cluster.cpp.

                                                 {
   inT32 i, n;
 
   n = n1 + n2;
   for (i = N; i > 0; i--, ParamDesc++, m++, m1++, m2++) {
     if (ParamDesc->Circular) {
       // if distance between means is greater than allowed
       // reduce upper point by one "rotation" to compute mean
       // then normalize the mean back into the accepted range
       if ((*m2 - *m1) > ParamDesc->HalfRange) {
         *m = (n1 * *m1 + n2 * (*m2 - ParamDesc->Range)) / n;
         if (*m < ParamDesc->Min)
           *m += ParamDesc->Range;
       }
       else if ((*m1 - *m2) > ParamDesc->HalfRange) {
         *m = (n1 * (*m1 - ParamDesc->Range) + n2 * *m2) / n;
         if (*m < ParamDesc->Min)
           *m += ParamDesc->Range;
       }
       else
         *m = (n1 * *m1 + n2 * *m2) / n;
     }
     else
       *m = (n1 * *m1 + n2 * *m2) / n;
   }
   return n;
 }                                // MergeClusters

◆ MultipleCharSamples()

BOOL8 MultipleCharSamples	(	CLUSTERER *	Clusterer,
		CLUSTER *	Cluster,
		FLOAT32	MaxIllegal
	)

This routine looks at all samples in the specified cluster. It computes a running estimate of the percentage of the charaters which have more than 1 sample in the cluster. When this percentage exceeds MaxIllegal, TRUE is returned. Otherwise FALSE is returned. The CharID fields must contain integers which identify the training characters which were used to generate the sample. One integer is used for each sample. The NumChar field in the Clusterer must contain the number of characters in the training set. All CharID fields must be between 0 and NumChar-1. The main function of this routine is to help identify clusters which need to be split further, i.e. if numerous training characters have 2 or more features which are contained in the same cluster, then the cluster should be split.

Parameters

Clusterer	data structure holding cluster tree
Cluster	cluster containing samples to be tested
MaxIllegal	max percentage of samples allowed to have more than 1 feature in the cluster

Returns: TRUE if the cluster should be split, FALSE otherwise.

Note: Exceptions: none; History: Wed Aug 30 11:13:05 1989, DSJ, Created. 2/22/90, DSJ, Added MaxIllegal control rather than always splitting illegal clusters.

Definition at line 2465 of file cluster.cpp.

 {
   static BOOL8 *CharFlags = NULL;
   static inT32 NumFlags = 0;
   int i;
   LIST SearchState;
   SAMPLE *Sample;
   inT32 CharID;
   inT32 NumCharInCluster;
   inT32 NumIllegalInCluster;
   FLOAT32 PercentIllegal;
 
   // initial estimate assumes that no illegal chars exist in the cluster
   NumCharInCluster = Cluster->SampleCount;
   NumIllegalInCluster = 0;
 
   if (Clusterer->NumChar > NumFlags) {
     free(CharFlags);
     NumFlags = Clusterer->NumChar;
     CharFlags = (BOOL8 *) Emalloc (NumFlags * sizeof (BOOL8));
   }
 
   for (i = 0; i < NumFlags; i++)
     CharFlags[i] = FALSE;
 
   // find each sample in the cluster and check if we have seen it before
   InitSampleSearch(SearchState, Cluster);
   while ((Sample = NextSample (&SearchState)) != NULL) {
     CharID = Sample->CharID;
     if (CharFlags[CharID] == FALSE) {
       CharFlags[CharID] = TRUE;
     }
     else {
       if (CharFlags[CharID] == TRUE) {
         NumIllegalInCluster++;
         CharFlags[CharID] = ILLEGAL_CHAR;
       }
       NumCharInCluster--;
       PercentIllegal = (FLOAT32) NumIllegalInCluster / NumCharInCluster;
       if (PercentIllegal > MaxIllegal) {
         destroy(SearchState);
         return (TRUE);
       }
     }
   }
   return (FALSE);
 
 }                                // MultipleCharSamples

◆ NewChiStruct()

CHISTRUCT * NewChiStruct	(	uinT16	DegreesOfFreedom,
		FLOAT64	Alpha
	)

This routine allocates a new data structure which is used to hold a chi-squared value along with its associated number of degrees of freedom and alpha value.

Parameters

DegreesOfFreedom	degrees of freedom for new chi value
Alpha	confidence level for new chi value

Returns: none

Note: Exceptions: none; History: Fri Aug 4 11:04:59 1989, DSJ, Created.

Definition at line 2326 of file cluster.cpp.

                                                                 {
   CHISTRUCT *NewChiStruct;
 
   NewChiStruct = (CHISTRUCT *) Emalloc (sizeof (CHISTRUCT));
   NewChiStruct->DegreesOfFreedom = DegreesOfFreedom;
   NewChiStruct->Alpha = Alpha;
   return (NewChiStruct);
 
 }                                // NewChiStruct

◆ NewEllipticalProto()

PROTOTYPE * NewEllipticalProto	(	inT16	N,
		CLUSTER *	Cluster,
		STATISTICS *	Statistics
	)

This routine creates an elliptical prototype data structure to approximate the samples in the specified cluster. Elliptical prototypes have a variance for each dimension. All dimensions are normally distributed and independent.

Parameters

N	number of dimensions
Cluster	cluster to be made into an elliptical prototype
Statistics	statistical info about samples in cluster

Returns: Pointer to a new elliptical prototype data structure

Note: Exceptions: None; History: 6/19/89, DSJ, Created.

Definition at line 1532 of file cluster.cpp.

                                                       {
   PROTOTYPE *Proto;
   FLOAT32 *CoVariance;
   int i;
 
   Proto = NewSimpleProto (N, Cluster);
   Proto->Variance.Elliptical = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32));
   Proto->Magnitude.Elliptical = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32));
   Proto->Weight.Elliptical = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32));
 
   CoVariance = Statistics->CoVariance;
   Proto->TotalMagnitude = 1.0;
   for (i = 0; i < N; i++, CoVariance += N + 1) {
     Proto->Variance.Elliptical[i] = *CoVariance;
     if (Proto->Variance.Elliptical[i] < MINVARIANCE)
       Proto->Variance.Elliptical[i] = MINVARIANCE;
 
     Proto->Magnitude.Elliptical[i] =
       1.0 / sqrt ((double) (2.0 * PI * Proto->Variance.Elliptical[i]));
     Proto->Weight.Elliptical[i] = 1.0 / Proto->Variance.Elliptical[i];
     Proto->TotalMagnitude *= Proto->Magnitude.Elliptical[i];
   }
   Proto->LogMagnitude = log ((double) Proto->TotalMagnitude);
   Proto->Style = elliptical;
   return (Proto);
 }                                // NewEllipticalProto

◆ NewMixedProto()

PROTOTYPE * NewMixedProto	(	inT16	N,
		CLUSTER *	Cluster,
		STATISTICS *	Statistics
	)

This routine creates a mixed prototype data structure to approximate the samples in the specified cluster. Mixed prototypes can have different distributions for each dimension. All dimensions are independent. The structure is initially filled in as though it were an elliptical prototype. The actual distributions of the dimensions can be altered by other routines.

Parameters

N	number of dimensions
Cluster	cluster to be made into a mixed prototype
Statistics	statistical info about samples in cluster

Returns: Pointer to a new mixed prototype data structure

Note: Exceptions: None; History: 6/19/89, DSJ, Created.

Definition at line 1576 of file cluster.cpp.

                                                                             {
   PROTOTYPE *Proto;
   int i;
 
   Proto = NewEllipticalProto (N, Cluster, Statistics);
   Proto->Distrib = (DISTRIBUTION *) Emalloc (N * sizeof (DISTRIBUTION));
 
   for (i = 0; i < N; i++) {
     Proto->Distrib[i] = normal;
   }
   Proto->Style = mixed;
   return (Proto);
 }                                // NewMixedProto

◆ NewSimpleProto()

PROTOTYPE * NewSimpleProto	(	inT16	N,
		CLUSTER *	Cluster
	)

This routine allocates memory to hold a simple prototype data structure, i.e. one without independent distributions and variances for each dimension.

Parameters

N	number of dimensions
Cluster	cluster to be made into a prototype

Returns: Pointer to new simple prototype

Note: Exceptions: None; History: 6/19/89, DSJ, Created.

Definition at line 1600 of file cluster.cpp.

                                                      {
   PROTOTYPE *Proto;
   int i;
 
   Proto = (PROTOTYPE *) Emalloc (sizeof (PROTOTYPE));
   Proto->Mean = (FLOAT32 *) Emalloc (N * sizeof (FLOAT32));
 
   for (i = 0; i < N; i++)
     Proto->Mean[i] = Cluster->Mean[i];
   Proto->Distrib = NULL;
 
   Proto->Significant = TRUE;
   Proto->Merged = FALSE;
   Proto->Style = spherical;
   Proto->NumSamples = Cluster->SampleCount;
   Proto->Cluster = Cluster;
   Proto->Cluster->Prototype = TRUE;
   return (Proto);
 }                                // NewSimpleProto

◆ NewSphericalProto()

PROTOTYPE * NewSphericalProto	(	uinT16	N,
		CLUSTER *	Cluster,
		STATISTICS *	Statistics
	)

This routine creates a spherical prototype data structure to approximate the samples in the specified cluster. Spherical prototypes have a single variance which is common across all dimensions. All dimensions are normally distributed and independent.

Parameters

N	number of dimensions
Cluster	cluster to be made into a spherical prototype
Statistics	statistical info about samples in cluster

Returns: Pointer to a new spherical prototype data structure

Note: Exceptions: None; History: 6/19/89, DSJ, Created.

Definition at line 1499 of file cluster.cpp.

                                                      {
   PROTOTYPE *Proto;
 
   Proto = NewSimpleProto (N, Cluster);
 
   Proto->Variance.Spherical = Statistics->AvgVariance;
   if (Proto->Variance.Spherical < MINVARIANCE)
     Proto->Variance.Spherical = MINVARIANCE;
 
   Proto->Magnitude.Spherical =
     1.0 / sqrt ((double) (2.0 * PI * Proto->Variance.Spherical));
   Proto->TotalMagnitude = (float)pow((double)Proto->Magnitude.Spherical,
                                      (double) N);
   Proto->Weight.Spherical = 1.0 / Proto->Variance.Spherical;
   Proto->LogMagnitude = log ((double) Proto->TotalMagnitude);
 
   return (Proto);
 }                                // NewSphericalProto

◆ NextSample()

CLUSTER* NextSample ( LIST * SearchState )

This routine is used to find all of the samples which belong to a cluster. It starts by removing the top cluster on the cluster list (SearchState). If this cluster is a leaf it is returned. Otherwise, the right subcluster is pushed on the list and we continue the search in the left subcluster. This continues until a leaf is found. If all samples have been found, NULL is returned. InitSampleSearch() must be called before NextSample() to initialize the search.

Parameters

SearchState ptr to list containing clusters to be searched

Returns: Pointer to the next leaf cluster (sample) or NULL.

Note: Exceptions: None; History: 6/16/89, DSJ, Created.

Definition at line 620 of file cluster.cpp.

                                        {
   CLUSTER *Cluster;
 
   if (*SearchState == NIL_LIST)
     return (NULL);
   Cluster = (CLUSTER *) first_node (*SearchState);
   *SearchState = pop (*SearchState);
   while (TRUE) {
     if (Cluster->Left == NULL)
       return (Cluster);
     *SearchState = push (*SearchState, Cluster->Right);
     Cluster = Cluster->Left;
   }
 }                                // NextSample

◆ NormalBucket()

uinT16 NormalBucket	(	PARAM_DESC *	ParamDesc,
		FLOAT32	x,
		FLOAT32	Mean,
		FLOAT32	StdDev
	)

This routine determines which bucket x falls into in the discrete normal distribution defined by kNormalMean and kNormalStdDev. x values which exceed the range of the discrete distribution are clipped.

Parameters

ParamDesc	used to identify circular dimensions
x	value to be normalized
Mean	mean of normal distribution
StdDev	standard deviation of normal distribution

Returns: Bucket number into which x falls

Note: Exceptions: None; History: 6/5/89, DSJ, Created.

Definition at line 2056 of file cluster.cpp.

                                     {
   FLOAT32 X;
 
   // wraparound circular parameters if necessary
   if (ParamDesc->Circular) {
     if (x - Mean > ParamDesc->HalfRange)
       x -= ParamDesc->Range;
     else if (x - Mean < -ParamDesc->HalfRange)
       x += ParamDesc->Range;
   }
 
   X = ((x - Mean) / StdDev) * kNormalStdDev + kNormalMean;
   if (X < 0)
     return 0;
   if (X > BUCKETTABLESIZE - 1)
     return ((uinT16) (BUCKETTABLESIZE - 1));
   return (uinT16) floor((FLOAT64) X);
 }                                // NormalBucket

◆ NormalDensity()

FLOAT64 NormalDensity ( inT32 x )

This routine computes the probability density function of a discrete normal distribution defined by the global variables kNormalMean, kNormalVariance, and kNormalMagnitude. Normal magnitude could, of course, be computed in terms of the normal variance but it is precomputed for efficiency.

Parameters

x	number to compute the normal probability density for

Note: Globals: kNormalMean mean of a discrete normal distribution kNormalVariance variance of a discrete normal distribution kNormalMagnitude magnitude of a discrete normal distribution

Returns: The value of the normal distribution at x.

Note: Exceptions: None; History: 6/4/89, DSJ, Created.

Definition at line 1923 of file cluster.cpp.

                                {
   FLOAT64 Distance;
 
   Distance = x - kNormalMean;
   return kNormalMagnitude * exp(-0.5 * Distance * Distance / kNormalVariance);
 }                                // NormalDensity

◆ NumBucketsMatch()

int NumBucketsMatch	(	void *	arg1,
		void *	arg2
	)

This routine is used to search a list of histogram data structures to find one with the specified number of buckets. It is called by the list search routines.

Parameters

arg1	current histogram being tested for a match
arg2	match key

Returns: TRUE if arg1 matches arg2

Note: Exceptions: none; History: Thu Aug 3 14:17:33 1989, DSJ, Created.

Definition at line 2227 of file cluster.cpp.

                                 {  // uinT16 *DesiredNumberOfBuckets)
   BUCKETS *Histogram = (BUCKETS *) arg1;
   uinT16 *DesiredNumberOfBuckets = (uinT16 *) arg2;
 
   return (*DesiredNumberOfBuckets == Histogram->NumberOfBuckets);
 
 }                                // NumBucketsMatch

◆ OptimumNumberOfBuckets()

uinT16 OptimumNumberOfBuckets ( uinT32 SampleCount )

This routine computes the optimum number of histogram buckets that should be used in a chi-squared goodness of fit test for the specified number of samples. The optimum number is computed based on Table 4.1 on pg. 147 of "Measurement and Analysis of Random Data" by Bendat & Piersol. Linear interpolation is used to interpolate between table values. The table is intended for a 0.05 level of significance (alpha). This routine assumes that it is equally valid for other alpha's, which may not be true.

Parameters

SampleCount number of samples to be tested

Returns: Optimum number of histogram buckets

Note: Exceptions: None; History: 6/5/89, DSJ, Created.

Definition at line 1832 of file cluster.cpp.

                                                   {
   uinT8 Last, Next;
   FLOAT32 Slope;
 
   if (SampleCount < kCountTable[0])
     return kBucketsTable[0];
 
   for (Last = 0, Next = 1; Next < LOOKUPTABLESIZE; Last++, Next++) {
     if (SampleCount <= kCountTable[Next]) {
       Slope = (FLOAT32) (kBucketsTable[Next] - kBucketsTable[Last]) /
           (FLOAT32) (kCountTable[Next] - kCountTable[Last]);
       return ((uinT16) (kBucketsTable[Last] +
           Slope * (SampleCount - kCountTable[Last])));
     }
   }
   return kBucketsTable[Last];
 }                                // OptimumNumberOfBuckets

◆ Solve()

FLOAT64 Solve	(	SOLVEFUNC	Function,
		void *	FunctionParams,
		FLOAT64	InitialGuess,
		FLOAT64	Accuracy
	)

This routine attempts to find an x value at which Function goes to zero (i.e. a root of the function ). It will only work correctly if a solution actually exists and there are no extrema between the solution and the InitialGuess. The algorithms used are extremely primitive.

Parameters

Function	function whose zero is to be found
FunctionParams	arbitrary data to pass to function
InitialGuess	point to start solution search at
Accuracy	maximum allowed error

Returns: Solution of function ( x for which f(x) = 0 ).

Note: Exceptions: none; History: Fri Aug 4 11:08:59 1989, DSJ, Created.

Definition at line 2352 of file cluster.cpp.

 {
   FLOAT64 x;
   FLOAT64 f;
   FLOAT64 Slope;
   FLOAT64 Delta;
   FLOAT64 NewDelta;
   FLOAT64 xDelta;
   FLOAT64 LastPosX, LastNegX;
 
   x = InitialGuess;
   Delta = INITIALDELTA;
   LastPosX = MAX_FLOAT32;
   LastNegX = -MAX_FLOAT32;
   f = (*Function) ((CHISTRUCT *) FunctionParams, x);
   while (Abs (LastPosX - LastNegX) > Accuracy) {
     // keep track of outer bounds of current estimate
     if (f < 0)
       LastNegX = x;
     else
       LastPosX = x;
 
     // compute the approx. slope of f(x) at the current point
     Slope =
       ((*Function) ((CHISTRUCT *) FunctionParams, x + Delta) - f) / Delta;
 
     // compute the next solution guess */
     xDelta = f / Slope;
     x -= xDelta;
 
     // reduce the delta used for computing slope to be a fraction of
     //the amount moved to get to the new guess
     NewDelta = Abs (xDelta) * DELTARATIO;
     if (NewDelta < Delta)
       Delta = NewDelta;
 
     // compute the value of the function at the new guess
     f = (*Function) ((CHISTRUCT *) FunctionParams, x);
   }
   return (x);
 
 }                                // Solve

◆ StandardDeviation()

FLOAT32 StandardDeviation	(	PROTOTYPE *	Proto,
		uinT16	Dimension
	)

This routine returns the standard deviation of the prototype in the indicated dimension.

Parameters

Proto	prototype to return standard deviation of
Dimension	dimension whose stddev is to be returned

Returns: Standard deviation of Prototype in Dimension

Note: Exceptions: none; History: 7/6/89, DSJ, Created.

Definition at line 657 of file cluster.cpp.

                                                               {
   switch (Proto->Style) {
     case spherical:
       return ((FLOAT32) sqrt ((double) Proto->Variance.Spherical));
     case elliptical:
       return ((FLOAT32)
         sqrt ((double) Proto->Variance.Elliptical[Dimension]));
     case mixed:
       switch (Proto->Distrib[Dimension]) {
         case normal:
           return ((FLOAT32)
             sqrt ((double) Proto->Variance.Elliptical[Dimension]));
         case uniform:
         case D_random:
           return (Proto->Variance.Elliptical[Dimension]);
         case DISTRIBUTION_COUNT:
           ASSERT_HOST(!"Distribution count not allowed!");
       }
   }
   return 0.0f;
 }                                // StandardDeviation

◆ TestEllipticalProto()

PROTOTYPE * TestEllipticalProto	(	CLUSTERER *	Clusterer,
		CLUSTERCONFIG *	Config,
		CLUSTER *	Cluster,
		STATISTICS *	Statistics
	)

This routine tests the specified cluster to see if ** there is a statistically significant difference between the sub-clusters that would be made if the cluster were to be split. If not, then a new prototype is formed and returned to the caller. If there is, then NULL is returned to the caller.

Parameters

Clusterer	data struct containing samples being clustered
Config	provides the magic number of samples that make a good cluster
Cluster	cluster to be made into an elliptical prototype
Statistics	statistical info about cluster

Returns: Pointer to new elliptical prototype or NULL.

Definition at line 1105 of file cluster.cpp.

                                                        {
   // Fraction of the number of samples used as a range around 1 within
   // which a cluster has the magic size that allows a boost to the
   // FTable by kFTableBoostMargin, thus allowing clusters near the
   // magic size (equal to the number of sample characters) to be more
   // likely to stay together.
   const double kMagicSampleMargin = 0.0625;
   const double kFTableBoostMargin = 2.0;
 
   int N = Clusterer->SampleSize;
   CLUSTER* Left = Cluster->Left;
   CLUSTER* Right = Cluster->Right;
   if (Left == NULL || Right == NULL)
     return NULL;
   int TotalDims = Left->SampleCount + Right->SampleCount;
   if (TotalDims < N + 1 || TotalDims < 2)
     return NULL;
   const int kMatrixSize = N * N * sizeof(FLOAT32);
   FLOAT32* Covariance = static_cast<FLOAT32 *>(Emalloc(kMatrixSize));
   FLOAT32* Inverse = static_cast<FLOAT32 *>(Emalloc(kMatrixSize));
   FLOAT32* Delta = static_cast<FLOAT32*>(Emalloc(N * sizeof(FLOAT32)));
   // Compute a new covariance matrix that only uses essential features.
   for (int i = 0; i < N; ++i) {
     int row_offset = i * N;
     if (!Clusterer->ParamDesc[i].NonEssential) {
       for (int j = 0; j < N; ++j) {
         if (!Clusterer->ParamDesc[j].NonEssential)
           Covariance[j + row_offset] = Statistics->CoVariance[j + row_offset];
         else
           Covariance[j + row_offset] = 0.0f;
       }
     } else {
       for (int j = 0; j < N; ++j) {
         if (i == j)
           Covariance[j + row_offset] = 1.0f;
         else
           Covariance[j + row_offset] = 0.0f;
       }
     }
   }
   double err = InvertMatrix(Covariance, N, Inverse);
   if (err > 1) {
     tprintf("Clustering error: Matrix inverse failed with error %g\n", err);
   }
   int EssentialN = 0;
   for (int dim = 0; dim < N; ++dim) {
     if (!Clusterer->ParamDesc[dim].NonEssential) {
       Delta[dim] = Left->Mean[dim] - Right->Mean[dim];
       ++EssentialN;
     } else {
       Delta[dim] = 0.0f;
     }
   }
   // Compute Hotelling's T-squared.
   double Tsq = 0.0;
   for (int x = 0; x < N; ++x) {
     double temp = 0.0;
     for (int y = 0; y < N; ++y) {
       temp += Inverse[y + N*x] * Delta[y];
     }
     Tsq += Delta[x] * temp;
   }
   free(Covariance);
   free(Inverse);
   free(Delta);
   // Changed this function to match the formula in
   // Statistical Methods in Medical Research p 473
   // By Peter Armitage, Geoffrey Berry, J. N. S. Matthews.
   // Tsq *= Left->SampleCount * Right->SampleCount / TotalDims;
   double F = Tsq * (TotalDims - EssentialN - 1) / ((TotalDims - 2)*EssentialN);
   int Fx = EssentialN;
   if (Fx > FTABLE_X)
     Fx = FTABLE_X;
   --Fx;
   int Fy = TotalDims - EssentialN - 1;
   if (Fy > FTABLE_Y)
     Fy = FTABLE_Y;
   --Fy;
   double FTarget = FTable[Fy][Fx];
   if (Config->MagicSamples > 0 &&
       TotalDims >= Config->MagicSamples * (1.0 - kMagicSampleMargin) &&
       TotalDims <= Config->MagicSamples * (1.0 + kMagicSampleMargin)) {
     // Give magic-sized clusters a magic FTable boost.
     FTarget += kFTableBoostMargin;
   }
   if (F < FTarget) {
     return NewEllipticalProto (Clusterer->SampleSize, Cluster, Statistics);
   }
   return NULL;
 }

◆ UniformBucket()

uinT16 UniformBucket	(	PARAM_DESC *	ParamDesc,
		FLOAT32	x,
		FLOAT32	Mean,
		FLOAT32	StdDev
	)

This routine determines which bucket x falls into in the discrete uniform distribution defined by BUCKETTABLESIZE. x values which exceed the range of the discrete distribution are clipped.

Parameters

ParamDesc	used to identify circular dimensions
x	value to be normalized
Mean	center of range of uniform distribution
StdDev	1/2 the range of the uniform distribution

Returns: Bucket number into which x falls

Note: Exceptions: None; History: 6/5/89, DSJ, Created.

Definition at line 2091 of file cluster.cpp.

                                      {
   FLOAT32 X;
 
   // wraparound circular parameters if necessary
   if (ParamDesc->Circular) {
     if (x - Mean > ParamDesc->HalfRange)
       x -= ParamDesc->Range;
     else if (x - Mean < -ParamDesc->HalfRange)
       x += ParamDesc->Range;
   }
 
   X = ((x - Mean) / (2 * StdDev) * BUCKETTABLESIZE + BUCKETTABLESIZE / 2.0);
   if (X < 0)
     return 0;
   if (X > BUCKETTABLESIZE - 1)
     return (uinT16) (BUCKETTABLESIZE - 1);
   return (uinT16) floor((FLOAT64) X);
 }                                // UniformBucket

◆ UniformDensity()

FLOAT64 UniformDensity ( inT32 x )

This routine computes the probability density function of a uniform distribution at the specified point. The range of the distribution is from 0 to BUCKETTABLESIZE.

Parameters

x	number to compute the uniform probability density for

Returns: The value of the uniform distribution at x.

Note: Exceptions: None; History: 6/5/89, DSJ, Created.

Definition at line 1939 of file cluster.cpp.

                                 {
   static FLOAT64 UniformDistributionDensity = (FLOAT64) 1.0 / BUCKETTABLESIZE;
 
   if ((x >= 0.0) && (x <= BUCKETTABLESIZE))
     return UniformDistributionDensity;
   else
     return (FLOAT64) 0.0;
 }                                // UniformDensity

Variable Documentation

◆ FTable

const double FTable[FTABLE_Y][FTABLE_X]

Definition at line 34 of file cluster.cpp.

Classes

Macros

Typedefs

Functions

Variables

Macro Definition Documentation

◆ Abs

◆ BUCKETTABLESIZE

◆ CHIACCURACY

◆ DELTARATIO

◆ FTABLE_X

◆ FTABLE_Y

◆ HOTELLING

◆ ILLEGAL_CHAR

◆ INITIALDELTA

◆ LOOKUPTABLESIZE

◆ MAXDEGREESOFFREEDOM

◆ MAXDISTANCE

◆ MAXNEIGHBORS

◆ MINALPHA

◆ MINSAMPLES

◆ MINSAMPLESNEEDED

◆ MINSAMPLESPERBUCKET

◆ MINVARIANCE

◆ Mirror

◆ NORMALEXTENT

◆ Odd

◆ SqrtOf2Pi

Typedef Documentation

◆ ClusterHeap

◆ ClusterPair

◆ DENSITYFUNC

◆ SOLVEFUNC

Function Documentation

◆ AdjustBuckets()

◆ AlphaMatch()

◆ ChiArea()

◆ ClusterSamples()

◆ ComputeChiSquared()

◆ ComputePrototypes()

◆ ComputeStatistics()

◆ CreateClusterTree()

◆ DegreesOfFreedom()

◆ DistributionOK()

◆ FillBuckets()

◆ FindNearestNeighbor()

◆ FreeBuckets()

◆ FreeCluster()

◆ FreeClusterer()

◆ FreeProtoList()

◆ FreePrototype()

◆ FreeStatistics()

◆ GetBuckets()

◆ Independent()

◆ InitBuckets()

◆ Integral()

◆ InvertMatrix()

◆ ListEntryMatch()

◆ MakeBuckets()

◆ MakeClusterer()

◆ MakeDegenerateProto()

◆ MakeDimRandom()

◆ MakeDimUniform()

◆ MakeEllipticalProto()

◆ MakeMixedProto()

◆ MakeNewCluster()

◆ MakePotentialClusters()

◆ MakePrototype()

◆ MakeSample()

◆ MakeSphericalProto()

◆ Mean()

◆ MergeClusters() [1/2]

◆ MergeClusters() [2/2]

◆ MultipleCharSamples()

◆ NewChiStruct()

◆ NewEllipticalProto()

◆ NewMixedProto()

◆ NewSimpleProto()

◆ NewSphericalProto()

◆ NextSample()