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cluster.cpp
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/******************************************************************************
** Filename: cluster.c
** Purpose: Routines for clustering points in N-D space
** Author: Dan Johnson
** History: 5/29/89, DSJ, Created.
**
** (c) Copyright Hewlett-Packard Company, 1988.
** Licensed under the Apache License, Version 2.0 (the "License");
** you may not use this file except in compliance with the License.
** You may obtain a copy of the License at
** http://www.apache.org/licenses/LICENSE-2.0
** Unless required by applicable law or agreed to in writing, software
** distributed under the License is distributed on an "AS IS" BASIS,
** WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
** See the License for the specific language governing permissions and
** limitations under the License.
******************************************************************************/
#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 "freelist.h"
#include <math.h>
#define HOTELLING 1 // If true use Hotelling's test to decide where to split.
#define FTABLE_X 10 // Size of FTable.
#define FTABLE_Y 100 // Size of FTable.
// Table of values approximating the cumulative F-distribution for a confidence of 1%.
const double FTable[FTABLE_Y][FTABLE_X] = {
{4052.19, 4999.52, 5403.34, 5624.62, 5763.65, 5858.97, 5928.33, 5981.10, 6022.50, 6055.85,},
{98.502, 99.000, 99.166, 99.249, 99.300, 99.333, 99.356, 99.374, 99.388, 99.399,},
{34.116, 30.816, 29.457, 28.710, 28.237, 27.911, 27.672, 27.489, 27.345, 27.229,},
{21.198, 18.000, 16.694, 15.977, 15.522, 15.207, 14.976, 14.799, 14.659, 14.546,},
{16.258, 13.274, 12.060, 11.392, 10.967, 10.672, 10.456, 10.289, 10.158, 10.051,},
{13.745, 10.925, 9.780, 9.148, 8.746, 8.466, 8.260, 8.102, 7.976, 7.874,},
{12.246, 9.547, 8.451, 7.847, 7.460, 7.191, 6.993, 6.840, 6.719, 6.620,},
{11.259, 8.649, 7.591, 7.006, 6.632, 6.371, 6.178, 6.029, 5.911, 5.814,},
{10.561, 8.022, 6.992, 6.422, 6.057, 5.802, 5.613, 5.467, 5.351, 5.257,},
{10.044, 7.559, 6.552, 5.994, 5.636, 5.386, 5.200, 5.057, 4.942, 4.849,},
{ 9.646, 7.206, 6.217, 5.668, 5.316, 5.069, 4.886, 4.744, 4.632, 4.539,},
{ 9.330, 6.927, 5.953, 5.412, 5.064, 4.821, 4.640, 4.499, 4.388, 4.296,},
{ 9.074, 6.701, 5.739, 5.205, 4.862, 4.620, 4.441, 4.302, 4.191, 4.100,},
{ 8.862, 6.515, 5.564, 5.035, 4.695, 4.456, 4.278, 4.140, 4.030, 3.939,},
{ 8.683, 6.359, 5.417, 4.893, 4.556, 4.318, 4.142, 4.004, 3.895, 3.805,},
{ 8.531, 6.226, 5.292, 4.773, 4.437, 4.202, 4.026, 3.890, 3.780, 3.691,},
{ 8.400, 6.112, 5.185, 4.669, 4.336, 4.102, 3.927, 3.791, 3.682, 3.593,},
{ 8.285, 6.013, 5.092, 4.579, 4.248, 4.015, 3.841, 3.705, 3.597, 3.508,},
{ 8.185, 5.926, 5.010, 4.500, 4.171, 3.939, 3.765, 3.631, 3.523, 3.434,},
{ 8.096, 5.849, 4.938, 4.431, 4.103, 3.871, 3.699, 3.564, 3.457, 3.368,},
{ 8.017, 5.780, 4.874, 4.369, 4.042, 3.812, 3.640, 3.506, 3.398, 3.310,},
{ 7.945, 5.719, 4.817, 4.313, 3.988, 3.758, 3.587, 3.453, 3.346, 3.258,},
{ 7.881, 5.664, 4.765, 4.264, 3.939, 3.710, 3.539, 3.406, 3.299, 3.211,},
{ 7.823, 5.614, 4.718, 4.218, 3.895, 3.667, 3.496, 3.363, 3.256, 3.168,},
{ 7.770, 5.568, 4.675, 4.177, 3.855, 3.627, 3.457, 3.324, 3.217, 3.129,},
{ 7.721, 5.526, 4.637, 4.140, 3.818, 3.591, 3.421, 3.288, 3.182, 3.094,},
{ 7.677, 5.488, 4.601, 4.106, 3.785, 3.558, 3.388, 3.256, 3.149, 3.062,},
{ 7.636, 5.453, 4.568, 4.074, 3.754, 3.528, 3.358, 3.226, 3.120, 3.032,},
{ 7.598, 5.420, 4.538, 4.045, 3.725, 3.499, 3.330, 3.198, 3.092, 3.005,},
{ 7.562, 5.390, 4.510, 4.018, 3.699, 3.473, 3.305, 3.173, 3.067, 2.979,},
{ 7.530, 5.362, 4.484, 3.993, 3.675, 3.449, 3.281, 3.149, 3.043, 2.955,},
{ 7.499, 5.336, 4.459, 3.969, 3.652, 3.427, 3.258, 3.127, 3.021, 2.934,},
{ 7.471, 5.312, 4.437, 3.948, 3.630, 3.406, 3.238, 3.106, 3.000, 2.913,},
{ 7.444, 5.289, 4.416, 3.927, 3.611, 3.386, 3.218, 3.087, 2.981, 2.894,},
{ 7.419, 5.268, 4.396, 3.908, 3.592, 3.368, 3.200, 3.069, 2.963, 2.876,},
{ 7.396, 5.248, 4.377, 3.890, 3.574, 3.351, 3.183, 3.052, 2.946, 2.859,},
{ 7.373, 5.229, 4.360, 3.873, 3.558, 3.334, 3.167, 3.036, 2.930, 2.843,},
{ 7.353, 5.211, 4.343, 3.858, 3.542, 3.319, 3.152, 3.021, 2.915, 2.828,},
{ 7.333, 5.194, 4.327, 3.843, 3.528, 3.305, 3.137, 3.006, 2.901, 2.814,},
{ 7.314, 5.179, 4.313, 3.828, 3.514, 3.291, 3.124, 2.993, 2.888, 2.801,},
{ 7.296, 5.163, 4.299, 3.815, 3.501, 3.278, 3.111, 2.980, 2.875, 2.788,},
{ 7.280, 5.149, 4.285, 3.802, 3.488, 3.266, 3.099, 2.968, 2.863, 2.776,},
{ 7.264, 5.136, 4.273, 3.790, 3.476, 3.254, 3.087, 2.957, 2.851, 2.764,},
{ 7.248, 5.123, 4.261, 3.778, 3.465, 3.243, 3.076, 2.946, 2.840, 2.754,},
{ 7.234, 5.110, 4.249, 3.767, 3.454, 3.232, 3.066, 2.935, 2.830, 2.743,},
{ 7.220, 5.099, 4.238, 3.757, 3.444, 3.222, 3.056, 2.925, 2.820, 2.733,},
{ 7.207, 5.087, 4.228, 3.747, 3.434, 3.213, 3.046, 2.916, 2.811, 2.724,},
{ 7.194, 5.077, 4.218, 3.737, 3.425, 3.204, 3.037, 2.907, 2.802, 2.715,},
{ 7.182, 5.066, 4.208, 3.728, 3.416, 3.195, 3.028, 2.898, 2.793, 2.706,},
{ 7.171, 5.057, 4.199, 3.720, 3.408, 3.186, 3.020, 2.890, 2.785, 2.698,},
{ 7.159, 5.047, 4.191, 3.711, 3.400, 3.178, 3.012, 2.882, 2.777, 2.690,},
{ 7.149, 5.038, 4.182, 3.703, 3.392, 3.171, 3.005, 2.874, 2.769, 2.683,},
{ 7.139, 5.030, 4.174, 3.695, 3.384, 3.163, 2.997, 2.867, 2.762, 2.675,},
{ 7.129, 5.021, 4.167, 3.688, 3.377, 3.156, 2.990, 2.860, 2.755, 2.668,},
{ 7.119, 5.013, 4.159, 3.681, 3.370, 3.149, 2.983, 2.853, 2.748, 2.662,},
{ 7.110, 5.006, 4.152, 3.674, 3.363, 3.143, 2.977, 2.847, 2.742, 2.655,},
{ 7.102, 4.998, 4.145, 3.667, 3.357, 3.136, 2.971, 2.841, 2.736, 2.649,},
{ 7.093, 4.991, 4.138, 3.661, 3.351, 3.130, 2.965, 2.835, 2.730, 2.643,},
{ 7.085, 4.984, 4.132, 3.655, 3.345, 3.124, 2.959, 2.829, 2.724, 2.637,},
{ 7.077, 4.977, 4.126, 3.649, 3.339, 3.119, 2.953, 2.823, 2.718, 2.632,},
{ 7.070, 4.971, 4.120, 3.643, 3.333, 3.113, 2.948, 2.818, 2.713, 2.626,},
{ 7.062, 4.965, 4.114, 3.638, 3.328, 3.108, 2.942, 2.813, 2.708, 2.621,},
{ 7.055, 4.959, 4.109, 3.632, 3.323, 3.103, 2.937, 2.808, 2.703, 2.616,},
{ 7.048, 4.953, 4.103, 3.627, 3.318, 3.098, 2.932, 2.803, 2.698, 2.611,},
{ 7.042, 4.947, 4.098, 3.622, 3.313, 3.093, 2.928, 2.798, 2.693, 2.607,},
{ 7.035, 4.942, 4.093, 3.618, 3.308, 3.088, 2.923, 2.793, 2.689, 2.602,},
{ 7.029, 4.937, 4.088, 3.613, 3.304, 3.084, 2.919, 2.789, 2.684, 2.598,},
{ 7.023, 4.932, 4.083, 3.608, 3.299, 3.080, 2.914, 2.785, 2.680, 2.593,},
{ 7.017, 4.927, 4.079, 3.604, 3.295, 3.075, 2.910, 2.781, 2.676, 2.589,},
{ 7.011, 4.922, 4.074, 3.600, 3.291, 3.071, 2.906, 2.777, 2.672, 2.585,},
{ 7.006, 4.917, 4.070, 3.596, 3.287, 3.067, 2.902, 2.773, 2.668, 2.581,},
{ 7.001, 4.913, 4.066, 3.591, 3.283, 3.063, 2.898, 2.769, 2.664, 2.578,},
{ 6.995, 4.908, 4.062, 3.588, 3.279, 3.060, 2.895, 2.765, 2.660, 2.574,},
{ 6.990, 4.904, 4.058, 3.584, 3.275, 3.056, 2.891, 2.762, 2.657, 2.570,},
{ 6.985, 4.900, 4.054, 3.580, 3.272, 3.052, 2.887, 2.758, 2.653, 2.567,},
{ 6.981, 4.896, 4.050, 3.577, 3.268, 3.049, 2.884, 2.755, 2.650, 2.563,},
{ 6.976, 4.892, 4.047, 3.573, 3.265, 3.046, 2.881, 2.751, 2.647, 2.560,},
{ 6.971, 4.888, 4.043, 3.570, 3.261, 3.042, 2.877, 2.748, 2.644, 2.557,},
{ 6.967, 4.884, 4.040, 3.566, 3.258, 3.039, 2.874, 2.745, 2.640, 2.554,},
{ 6.963, 4.881, 4.036, 3.563, 3.255, 3.036, 2.871, 2.742, 2.637, 2.551,},
{ 6.958, 4.877, 4.033, 3.560, 3.252, 3.033, 2.868, 2.739, 2.634, 2.548,},
{ 6.954, 4.874, 4.030, 3.557, 3.249, 3.030, 2.865, 2.736, 2.632, 2.545,},
{ 6.950, 4.870, 4.027, 3.554, 3.246, 3.027, 2.863, 2.733, 2.629, 2.542,},
{ 6.947, 4.867, 4.024, 3.551, 3.243, 3.025, 2.860, 2.731, 2.626, 2.539,},
{ 6.943, 4.864, 4.021, 3.548, 3.240, 3.022, 2.857, 2.728, 2.623, 2.537,},
{ 6.939, 4.861, 4.018, 3.545, 3.238, 3.019, 2.854, 2.725, 2.621, 2.534,},
{ 6.935, 4.858, 4.015, 3.543, 3.235, 3.017, 2.852, 2.723, 2.618, 2.532,},
{ 6.932, 4.855, 4.012, 3.540, 3.233, 3.014, 2.849, 2.720, 2.616, 2.529,},
{ 6.928, 4.852, 4.010, 3.538, 3.230, 3.012, 2.847, 2.718, 2.613, 2.527,},
{ 6.925, 4.849, 4.007, 3.535, 3.228, 3.009, 2.845, 2.715, 2.611, 2.524,},
{ 6.922, 4.846, 4.004, 3.533, 3.225, 3.007, 2.842, 2.713, 2.609, 2.522,},
{ 6.919, 4.844, 4.002, 3.530, 3.223, 3.004, 2.840, 2.711, 2.606, 2.520,},
{ 6.915, 4.841, 3.999, 3.528, 3.221, 3.002, 2.838, 2.709, 2.604, 2.518,},
{ 6.912, 4.838, 3.997, 3.525, 3.218, 3.000, 2.835, 2.706, 2.602, 2.515,},
{ 6.909, 4.836, 3.995, 3.523, 3.216, 2.998, 2.833, 2.704, 2.600, 2.513,},
{ 6.906, 4.833, 3.992, 3.521, 3.214, 2.996, 2.831, 2.702, 2.598, 2.511,},
{ 6.904, 4.831, 3.990, 3.519, 3.212, 2.994, 2.829, 2.700, 2.596, 2.509,},
{ 6.901, 4.829, 3.988, 3.517, 3.210, 2.992, 2.827, 2.698, 2.594, 2.507,},
{ 6.898, 4.826, 3.986, 3.515, 3.208, 2.990, 2.825, 2.696, 2.592, 2.505,},
{ 6.895, 4.824, 3.984, 3.513, 3.206, 2.988, 2.823, 2.694, 2.590, 2.503}
};
/** 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. */
#define MINVARIANCE 0.0004
/** 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. */
#define MINSAMPLESPERBUCKET 5
#define MINSAMPLES (MINBUCKETS * MINSAMPLESPERBUCKET)
#define MINSAMPLESNEEDED 1
/** 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. */
#define BUCKETTABLESIZE 1024
#define NORMALEXTENT 3.0
struct TEMPCLUSTER {
CLUSTER *Cluster;
CLUSTER *Neighbor;
};
typedef tesseract::KDPairInc<float, TEMPCLUSTER*> ClusterPair;
typedef tesseract::GenericHeap<ClusterPair> ClusterHeap;
struct STATISTICS {
FLOAT32 AvgVariance;
FLOAT32 *CoVariance;
FLOAT32 *Min; // largest negative distance from the mean
FLOAT32 *Max; // largest positive distance from the mean
};
struct BUCKETS {
DISTRIBUTION Distribution; // distribution being tested for
uinT32 SampleCount; // # of samples in histogram
FLOAT64 Confidence; // confidence level of test
FLOAT64 ChiSquared; // test threshold
uinT16 NumberOfBuckets; // number of cells in histogram
uinT16 Bucket[BUCKETTABLESIZE];// mapping to histogram buckets
uinT32 *Count; // frequency of occurrence histogram
FLOAT32 *ExpectedCount; // expected histogram
};
struct CHISTRUCT{
uinT16 DegreesOfFreedom;
FLOAT64 Alpha;
FLOAT64 ChiSquared;
};
// For use with KDWalk / MakePotentialClusters
struct ClusteringContext {
ClusterHeap *heap; // heap used to hold temp clusters, "best" on top
TEMPCLUSTER *candidates; // array of potential clusters
KDTREE *tree; // kd-tree to be searched for neighbors
inT32 next; // next candidate to be used
};
typedef FLOAT64 (*DENSITYFUNC) (inT32);
typedef FLOAT64 (*SOLVEFUNC) (CHISTRUCT *, double);
#define Odd(N) ((N)%2)
#define Mirror(N,R) ((R) - (N) - 1)
#define Abs(N) ( ( (N) < 0 ) ? ( -(N) ) : (N) )
//--------------Global Data Definitions and Declarations----------------------
/** 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. */
#define SqrtOf2Pi 2.506628275
static const FLOAT64 kNormalStdDev = BUCKETTABLESIZE / (2.0 * NORMALEXTENT);
static const FLOAT64 kNormalVariance =
(BUCKETTABLESIZE * BUCKETTABLESIZE) / (4.0 * NORMALEXTENT * NORMALEXTENT);
static const FLOAT64 kNormalMagnitude =
(2.0 * NORMALEXTENT) / (SqrtOf2Pi * BUCKETTABLESIZE);
static const FLOAT64 kNormalMean = BUCKETTABLESIZE / 2;
/** define lookup tables used to compute the number of histogram buckets
that should be used for a given number of samples. */
#define LOOKUPTABLESIZE 8
#define MAXDEGREESOFFREEDOM MAXBUCKETS
static const uinT32 kCountTable[LOOKUPTABLESIZE] = {
MINSAMPLES, 200, 400, 600, 800, 1000, 1500, 2000
}; // number of samples
static const uinT16 kBucketsTable[LOOKUPTABLESIZE] = {
MINBUCKETS, 16, 20, 24, 27, 30, 35, MAXBUCKETS
}; // number of buckets
/*-------------------------------------------------------------------------
Private Function Prototypes
--------------------------------------------------------------------------*/
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, // BUCKETS *Histogram,
void *arg2); // uinT16 *DesiredNumberOfBuckets);
int ListEntryMatch(void *arg1, void *arg2);
void AdjustBuckets(BUCKETS *Buckets, uinT32 NewSampleCount);
void InitBuckets(BUCKETS *Buckets);
int AlphaMatch(void *arg1, // CHISTRUCT *ChiStruct,
void *arg2); // CHISTRUCT *SearchKey);
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);
//--------------------------Public Code--------------------------------------
/**
* This routine creates a new clusterer data structure,
* initializes it, and returns a pointer to it.
*
* @param SampleSize number of dimensions in feature space
* @param ParamDesc description of each dimension
* @return pointer to the new clusterer data structure
* @note Exceptions: None
* @note History: 5/29/89, DSJ, Created.
*/
CLUSTERER *
MakeClusterer (inT16 SampleSize, const PARAM_DESC ParamDesc[]) {
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
/**
* 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.
*
* @param Clusterer clusterer data structure to add sample to
* @param Feature feature to be added to clusterer
* @param CharID unique ident. of char that sample came from
*
* @return Pointer to the new sample data structure
* @note Exceptions: ALREADYCLUSTERED MakeSample can't be called after
* ClusterSamples has been called
* @note History: 5/29/89, DSJ, Created.
*/
SAMPLE* MakeSample(CLUSTERER * Clusterer, const FLOAT32* Feature,
inT32 CharID) {
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
/**
* 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.
*
* @param Clusterer data struct containing samples to be clustered
* @param Config parameters which control clustering process
*
* @return Pointer to a list of prototypes
* @note Exceptions: None
* @note History: 5/29/89, DSJ, Created.
*/
LIST ClusterSamples(CLUSTERER *Clusterer, CLUSTERCONFIG *Config) {
//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);
return (Clusterer->ProtoList);
} // ClusterSamples
/**
* 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.
* @param Clusterer pointer to data structure to be freed
* @return None
* @note Exceptions: None
* @note History: 6/6/89, DSJ, Created.
*/
void FreeClusterer(CLUSTERER *Clusterer) {
if (Clusterer != NULL) {
memfree (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]);
}
memfree(Clusterer);
}
} // FreeClusterer
/**
* 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.
* @param ProtoList pointer to list of prototypes to be freed
* @return None
* @note Exceptions: None
* @note History: 6/6/89, DSJ, Created.
*/
void FreeProtoList(LIST *ProtoList) {
destroy_nodes(*ProtoList, FreePrototype);
} // FreeProtoList
/**
* 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.
* @param arg prototype data structure to be deallocated
* @return None
* @note Exceptions: None
* @note History: 5/30/89, DSJ, Created.
*/
void FreePrototype(void *arg) { //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
if (Prototype->Distrib != NULL)
memfree (Prototype->Distrib);
if (Prototype->Mean != NULL)
memfree (Prototype->Mean);
if (Prototype->Style != spherical) {
if (Prototype->Variance.Elliptical != NULL)
memfree (Prototype->Variance.Elliptical);
if (Prototype->Magnitude.Elliptical != NULL)
memfree (Prototype->Magnitude.Elliptical);
if (Prototype->Weight.Elliptical != NULL)
memfree (Prototype->Weight.Elliptical);
}
memfree(Prototype);
} // FreePrototype
/**
* 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.
* @param SearchState ptr to list containing clusters to be searched
* @return Pointer to the next leaf cluster (sample) or NULL.
* @note Exceptions: None
* @note History: 6/16/89, DSJ, Created.
*/
CLUSTER *NextSample(LIST *SearchState) {
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
/**
* This routine returns the mean of the specified
* prototype in the indicated dimension.
* @param Proto prototype to return mean of
* @param Dimension dimension whose mean is to be returned
* @return Mean of Prototype in Dimension
* @note Exceptions: none
* @note History: 7/6/89, DSJ, Created.
*/
FLOAT32 Mean(PROTOTYPE *Proto, uinT16 Dimension) {
return (Proto->Mean[Dimension]);
} // Mean
/**
* This routine returns the standard deviation of the
* prototype in the indicated dimension.
* @param Proto prototype to return standard deviation of
* @param Dimension dimension whose stddev is to be returned
* @return Standard deviation of Prototype in Dimension
* @note Exceptions: none
* @note History: 7/6/89, DSJ, Created.
*/
FLOAT32 StandardDeviation(PROTOTYPE *Proto, uinT16 Dimension) {
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
/*---------------------------------------------------------------------------
Private Code
----------------------------------------------------------------------------*/
/**
* 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.
* @param Clusterer data structure holdings samples to be clustered
* @return None (the Clusterer data structure is changed)
* @note Exceptions: None
* @note History: 5/29/89, DSJ, Created.
*/
void CreateClusterTree(CLUSTERER *Clusterer) {
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;
memfree(context.candidates);
} // CreateClusterTree
/**
* 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.
* @param context ClusteringContext (see definition above)
* @param Cluster current cluster being visited in kd-tree walk
* @param Level level of this cluster in the kd-tree
*/
void MakePotentialClusters(ClusteringContext *context,
CLUSTER *Cluster, inT32 Level) {
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
/**
* 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.
* @param Tree kd-tree to search in for nearest neighbor
* @param Cluster cluster whose nearest neighbor is to be found
* @param Distance ptr to variable to report distance found
* @return Pointer to the nearest neighbor of Cluster, or NULL
* @note Exceptions: none
* @note History: 5/29/89, DSJ, Created.
* 7/13/89, DSJ, Removed visibility of kd-tree node data struct
*/
CLUSTER *
FindNearestNeighbor(KDTREE * Tree, CLUSTER * Cluster, FLOAT32 * Distance)
#define MAXNEIGHBORS 2
#define MAXDISTANCE MAX_FLOAT32
{
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
/**
* 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.
* @param Clusterer current clustering environment
* @param TempCluster potential cluster to make permanent
* @return Pointer to the new permanent cluster
* @note Exceptions: none
* @note History: 5/29/89, DSJ, Created.
* 7/13/89, DSJ, Removed visibility of kd-tree node data struct
*/
CLUSTER *MakeNewCluster(CLUSTERER *Clusterer, TEMPCLUSTER *TempCluster) {
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
/**
* 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.
* @param N # of dimensions (size of arrays)
* @param ParamDesc array of dimension descriptions
* @param n1, n2 number of samples in each old cluster
* @param m array to hold mean of new cluster
* @param m1, m2 arrays containing means of old clusters
* @return The number of samples in the new cluster.
* @note Exceptions: None
* @note History: 5/31/89, DSJ, Created.
*/
inT32 MergeClusters(inT16 N,
PARAM_DESC ParamDesc[],
inT32 n1,
inT32 n2,
FLOAT32 m[],
FLOAT32 m1[], FLOAT32 m2[]) {
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
/**
* 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.
* @param Clusterer data structure holding cluster tree
* @param Config parameters used to control prototype generation
* @return None
* @note Exceptions: None
* @note History: 5/30/89, DSJ, Created.
*/
void ComputePrototypes(CLUSTERER *Clusterer, CLUSTERCONFIG *Config) {
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
/**
* 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.
* @param Clusterer data structure holding cluster tree
* @param Config parameters used to control prototype generation
* @param Cluster cluster to be made into a prototype
* @return Pointer to new prototype or NULL
* @note Exceptions: None
* @note History: 6/19/89, DSJ, Created.
*/
PROTOTYPE *MakePrototype(CLUSTERER *Clusterer,
CLUSTERCONFIG *Config,
CLUSTER *Cluster) {
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(