595 lines
22 KiB
Text
595 lines
22 KiB
Text
|
//----------------------------------------------------------------------
|
||
|
|
// File: rand.cpp
|
||
|
|
// Programmer: Sunil Arya and David Mount
|
||
|
|
// Description: Routines for random point generation
|
||
|
|
// Last modified: 08/04/06 (Version 1.1.1)
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// Copyright (c) 1997-2005 University of Maryland and Sunil Arya and
|
||
|
|
// David Mount. All Rights Reserved.
|
||
|
|
//
|
||
|
|
// This software and related documentation is part of the Approximate
|
||
|
|
// Nearest Neighbor Library (ANN). This software is provided under
|
||
|
|
// the provisions of the Lesser GNU Public License (LGPL). See the
|
||
|
|
// file ../ReadMe.txt for further information.
|
||
|
|
//
|
||
|
|
// The University of Maryland (U.M.) and the authors make no
|
||
|
|
// representations about the suitability or fitness of this software for
|
||
|
|
// any purpose. It is provided "as is" without express or implied
|
||
|
|
// warranty.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// History:
|
||
|
|
// Revision 0.1 03/04/98
|
||
|
|
// Initial release
|
||
|
|
// Revision 0.2 03/26/98
|
||
|
|
// Changed random/srandom declarations for SGI's.
|
||
|
|
// Revision 1.0 04/01/05
|
||
|
|
// annClusGauss centers distributed over [-1,1] rather than [0,1]
|
||
|
|
// Added annClusOrthFlats distribution
|
||
|
|
// Changed procedure names to avoid namespace conflicts
|
||
|
|
// Added annClusFlats distribution
|
||
|
|
// Added rand/srand option and fixed annRan0() initialization.
|
||
|
|
// Revision 1.1.1 08/04/06
|
||
|
|
// Added planted distribution
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
#include "rand.h" // random generator declarations
|
||
|
|
|
||
|
|
using namespace std; // make std:: accessible
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// Globals
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
int annIdum = 0; // used for random number generation
|
||
|
|
|
||
|
|
//------------------------------------------------------------------------
|
||
|
|
// annRan0 - (safer) uniform random number generator
|
||
|
|
//
|
||
|
|
// The code given here is taken from "Numerical Recipes in C" by
|
||
|
|
// William Press, Brian Flannery, Saul Teukolsky, and William
|
||
|
|
// Vetterling. The task of the code is to do an additional randomizing
|
||
|
|
// shuffle on the system-supplied random number generator to make it
|
||
|
|
// safer to use.
|
||
|
|
//
|
||
|
|
// Returns a uniform deviate between 0.0 and 1.0 using the
|
||
|
|
// system-supplied routine random() or rand(). Set the global
|
||
|
|
// annIdum to any negative value to initialise or reinitialise
|
||
|
|
// the sequence.
|
||
|
|
//------------------------------------------------------------------------
|
||
|
|
|
||
|
|
double annRan0()
|
||
|
|
{
|
||
|
|
const int TAB_SIZE = 97; // table size: any large number
|
||
|
|
int j;
|
||
|
|
|
||
|
|
static double y, v[TAB_SIZE];
|
||
|
|
static int iff = 0;
|
||
|
|
const double RAN_DIVISOR = double(ANN_RAND_MAX + 1UL);
|
||
|
|
if (RAN_DIVISOR < 0) {
|
||
|
|
cout << "RAN_DIVISOR " << RAN_DIVISOR << endl;
|
||
|
|
exit(0);
|
||
|
|
}
|
||
|
|
|
||
|
|
//--------------------------------------------------------------------
|
||
|
|
// As a precaution against misuse, we will always initialize on the
|
||
|
|
// first call, even if "annIdum" is not set negative. Determine
|
||
|
|
// "maxran", the next integer after the largest representable value
|
||
|
|
// of type int. We assume this is a factor of 2 smaller than the
|
||
|
|
// corresponding value of type unsigned int.
|
||
|
|
//--------------------------------------------------------------------
|
||
|
|
|
||
|
|
if (annIdum < 0 || iff == 0) { // initialize
|
||
|
|
iff = 1;
|
||
|
|
ANN_SRAND(annIdum); // (re)seed the generator
|
||
|
|
annIdum = 1;
|
||
|
|
|
||
|
|
for (j = 0; j < TAB_SIZE; j++) // exercise the system routine
|
||
|
|
ANN_RAND(); // (values intentionally ignored)
|
||
|
|
|
||
|
|
for (j = 0; j < TAB_SIZE; j++) // then save TAB_SIZE-1 values
|
||
|
|
v[j] = ANN_RAND();
|
||
|
|
y = ANN_RAND(); // generate starting value
|
||
|
|
}
|
||
|
|
|
||
|
|
//--------------------------------------------------------------------
|
||
|
|
// This is where we start if not initializing. Use the previously
|
||
|
|
// saved random number y to get an index j between 1 and TAB_SIZE-1.
|
||
|
|
// Then use the corresponding v[j] for both the next j and as the
|
||
|
|
// output number.
|
||
|
|
//--------------------------------------------------------------------
|
||
|
|
|
||
|
|
j = int(TAB_SIZE * (y / RAN_DIVISOR));
|
||
|
|
y = v[j];
|
||
|
|
v[j] = ANN_RAND(); // refill the table entry
|
||
|
|
return y / RAN_DIVISOR;
|
||
|
|
}
|
||
|
|
|
||
|
|
//------------------------------------------------------------------------
|
||
|
|
// annRanInt - generate a random integer from {0,1,...,n-1}
|
||
|
|
//
|
||
|
|
// If n == 0, then -1 is returned.
|
||
|
|
//------------------------------------------------------------------------
|
||
|
|
|
||
|
|
static int annRanInt(
|
||
|
|
int n)
|
||
|
|
{
|
||
|
|
int r = (int) (annRan0()*n);
|
||
|
|
if (r == n) r--; // (in case annRan0() == 1 or n == 0)
|
||
|
|
return r;
|
||
|
|
}
|
||
|
|
|
||
|
|
//------------------------------------------------------------------------
|
||
|
|
// annRanUnif - generate a random uniform in [lo,hi]
|
||
|
|
//------------------------------------------------------------------------
|
||
|
|
|
||
|
|
static double annRanUnif(
|
||
|
|
double lo,
|
||
|
|
double hi)
|
||
|
|
{
|
||
|
|
return annRan0()*(hi-lo) + lo;
|
||
|
|
}
|
||
|
|
|
||
|
|
//------------------------------------------------------------------------
|
||
|
|
// annRanGauss - Gaussian random number generator
|
||
|
|
// Returns a normally distributed deviate with zero mean and unit
|
||
|
|
// variance, using annRan0() as the source of uniform deviates.
|
||
|
|
//------------------------------------------------------------------------
|
||
|
|
|
||
|
|
static double annRanGauss()
|
||
|
|
{
|
||
|
|
static int iset=0;
|
||
|
|
static double gset;
|
||
|
|
|
||
|
|
if (iset == 0) { // we don't have a deviate handy
|
||
|
|
double v1, v2;
|
||
|
|
double r = 2.0;
|
||
|
|
while (r >= 1.0) {
|
||
|
|
//------------------------------------------------------------
|
||
|
|
// Pick two uniform numbers in the square extending from -1 to
|
||
|
|
// +1 in each direction, see if they are in the circle of radius
|
||
|
|
// 1. If not, try again
|
||
|
|
//------------------------------------------------------------
|
||
|
|
v1 = annRanUnif(-1, 1);
|
||
|
|
v2 = annRanUnif(-1, 1);
|
||
|
|
r = v1 * v1 + v2 * v2;
|
||
|
|
}
|
||
|
|
double fac = sqrt(-2.0 * log(r) / r);
|
||
|
|
//-----------------------------------------------------------------
|
||
|
|
// Now make the Box-Muller transformation to get two normal
|
||
|
|
// deviates. Return one and save the other for next time.
|
||
|
|
//-----------------------------------------------------------------
|
||
|
|
gset = v1 * fac;
|
||
|
|
iset = 1; // set flag
|
||
|
|
return v2 * fac;
|
||
|
|
}
|
||
|
|
else { // we have an extra deviate handy
|
||
|
|
iset = 0; // so unset the flag
|
||
|
|
return gset; // and return it
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//------------------------------------------------------------------------
|
||
|
|
// annRanLaplace - Laplacian random number generator
|
||
|
|
// Returns a Laplacian distributed deviate with zero mean and
|
||
|
|
// unit variance, using annRan0() as the source of uniform deviates.
|
||
|
|
//
|
||
|
|
// prob(x) = b/2 * exp(-b * |x|).
|
||
|
|
//
|
||
|
|
// b is chosen to be sqrt(2.0) so that the variance of the Laplacian
|
||
|
|
// distribution [2/(b^2)] becomes 1.
|
||
|
|
//------------------------------------------------------------------------
|
||
|
|
|
||
|
|
static double annRanLaplace()
|
||
|
|
{
|
||
|
|
const double b = 1.4142136;
|
||
|
|
|
||
|
|
double laprand = -log(annRan0()) / b;
|
||
|
|
double sign = annRan0();
|
||
|
|
if (sign < 0.5) laprand = -laprand;
|
||
|
|
return(laprand);
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// annUniformPts - Generate uniformly distributed points
|
||
|
|
// A uniform distribution over [-1,1].
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
void annUniformPts( // uniform distribution
|
||
|
|
ANNpointArray pa, // point array (modified)
|
||
|
|
int n, // number of points
|
||
|
|
int dim) // dimension
|
||
|
|
{
|
||
|
|
for (int i = 0; i < n; i++) {
|
||
|
|
for (int d = 0; d < dim; d++) {
|
||
|
|
pa[i][d] = (ANNcoord) (annRanUnif(-1,1));
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// annGaussPts - Generate Gaussian distributed points
|
||
|
|
// A Gaussian distribution with zero mean and the given standard
|
||
|
|
// deviation.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
void annGaussPts( // Gaussian distribution
|
||
|
|
ANNpointArray pa, // point array (modified)
|
||
|
|
int n, // number of points
|
||
|
|
int dim, // dimension
|
||
|
|
double std_dev) // standard deviation
|
||
|
|
{
|
||
|
|
for (int i = 0; i < n; i++) {
|
||
|
|
for (int d = 0; d < dim; d++) {
|
||
|
|
pa[i][d] = (ANNcoord) (annRanGauss() * std_dev);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// annLaplacePts - Generate Laplacian distributed points
|
||
|
|
// Generates a Laplacian distribution (zero mean and unit variance).
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
void annLaplacePts( // Laplacian distribution
|
||
|
|
ANNpointArray pa, // point array (modified)
|
||
|
|
int n, // number of points
|
||
|
|
int dim) // dimension
|
||
|
|
{
|
||
|
|
for (int i = 0; i < n; i++) {
|
||
|
|
for (int d = 0; d < dim; d++) {
|
||
|
|
pa[i][d] = (ANNcoord) annRanLaplace();
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// annCoGaussPts - Generate correlated Gaussian distributed points
|
||
|
|
// Generates a Gauss-Markov distribution of zero mean and unit
|
||
|
|
// variance.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
void annCoGaussPts( // correlated-Gaussian distribution
|
||
|
|
ANNpointArray pa, // point array (modified)
|
||
|
|
int n, // number of points
|
||
|
|
int dim, // dimension
|
||
|
|
double correlation) // correlation
|
||
|
|
{
|
||
|
|
double std_dev_w = sqrt(1.0 - correlation * correlation);
|
||
|
|
for (int i = 0; i < n; i++) {
|
||
|
|
double previous = annRanGauss();
|
||
|
|
pa[i][0] = (ANNcoord) previous;
|
||
|
|
for (int d = 1; d < dim; d++) {
|
||
|
|
previous = correlation*previous + std_dev_w*annRanGauss();
|
||
|
|
pa[i][d] = (ANNcoord) previous;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// annCoLaplacePts - Generate correlated Laplacian distributed points
|
||
|
|
// Generates a Laplacian-Markov distribution of zero mean and unit
|
||
|
|
// variance.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
void annCoLaplacePts( // correlated-Laplacian distribution
|
||
|
|
ANNpointArray pa, // point array (modified)
|
||
|
|
int n, // number of points
|
||
|
|
int dim, // dimension
|
||
|
|
double correlation) // correlation
|
||
|
|
{
|
||
|
|
double wn;
|
||
|
|
double corr_sq = correlation * correlation;
|
||
|
|
|
||
|
|
for (int i = 0; i < n; i++) {
|
||
|
|
double previous = annRanLaplace();
|
||
|
|
pa[i][0] = (ANNcoord) previous;
|
||
|
|
for (int d = 1; d < dim; d++) {
|
||
|
|
double temp = annRan0();
|
||
|
|
if (temp < corr_sq)
|
||
|
|
wn = 0.0;
|
||
|
|
else
|
||
|
|
wn = annRanLaplace();
|
||
|
|
previous = correlation * previous + wn;
|
||
|
|
pa[i][d] = (ANNcoord) previous;
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// annClusGaussPts - Generate clusters of Gaussian distributed points
|
||
|
|
// Cluster centers are uniformly distributed over [-1,1], and the
|
||
|
|
// standard deviation within each cluster is fixed.
|
||
|
|
//
|
||
|
|
// Note: Once cluster centers have been set, they are not changed,
|
||
|
|
// unless new_clust = true. This is so that subsequent calls generate
|
||
|
|
// points from the same distribution. It follows, of course, that any
|
||
|
|
// attempt to change the dimension or number of clusters without
|
||
|
|
// generating new clusters is asking for trouble.
|
||
|
|
//
|
||
|
|
// Note: Cluster centers are not generated by a call to uniformPts().
|
||
|
|
// Although this could be done, it has been omitted for
|
||
|
|
// compatibility with annClusGaussPts() in the colored version,
|
||
|
|
// rand_c.cc.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
void annClusGaussPts( // clustered-Gaussian distribution
|
||
|
|
ANNpointArray pa, // point array (modified)
|
||
|
|
int n, // number of points
|
||
|
|
int dim, // dimension
|
||
|
|
int n_clus, // number of colors
|
||
|
|
ANNbool new_clust, // generate new clusters.
|
||
|
|
double std_dev) // standard deviation within clusters
|
||
|
|
{
|
||
|
|
static ANNpointArray clusters = NULL;// cluster storage
|
||
|
|
|
||
|
|
if (clusters == NULL || new_clust) {// need new cluster centers
|
||
|
|
if (clusters != NULL) // clusters already exist
|
||
|
|
annDeallocPts(clusters); // get rid of them
|
||
|
|
clusters = annAllocPts(n_clus, dim);
|
||
|
|
// generate cluster center coords
|
||
|
|
for (int i = 0; i < n_clus; i++) {
|
||
|
|
for (int d = 0; d < dim; d++) {
|
||
|
|
clusters[i][d] = (ANNcoord) annRanUnif(-1,1);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
for (int i = 0; i < n; i++) {
|
||
|
|
int c = annRanInt(n_clus); // generate cluster index
|
||
|
|
for (int d = 0; d < dim; d++) {
|
||
|
|
pa[i][d] = (ANNcoord) (std_dev*annRanGauss() + clusters[c][d]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// annClusOrthFlats - points clustered along orthogonal flats
|
||
|
|
//
|
||
|
|
// This distribution consists of a collection points clustered
|
||
|
|
// among a collection of axis-aligned low dimensional flats in
|
||
|
|
// the hypercube [-1,1]^d. A set of n_clus orthogonal flats are
|
||
|
|
// generated, each whose dimension is a random number between 1
|
||
|
|
// and max_dim. The points are evenly distributed among the clusters.
|
||
|
|
// For each cluster, we generate points uniformly distributed along
|
||
|
|
// the flat within the hypercube.
|
||
|
|
//
|
||
|
|
// This is done as follows. Each cluster is defined by a d-element
|
||
|
|
// control vector whose components are either:
|
||
|
|
//
|
||
|
|
// CO_FLAG indicating that this component is to be generated
|
||
|
|
// uniformly in [-1,1],
|
||
|
|
// x a value other than CO_FLAG in the range [-1,1],
|
||
|
|
// which indicates that this coordinate is to be
|
||
|
|
// generated as x plus a Gaussian random deviation
|
||
|
|
// with the given standard deviation.
|
||
|
|
//
|
||
|
|
// The number of zero components is the dimension of the flat, which
|
||
|
|
// is a random integer in the range from 1 to max_dim. The points
|
||
|
|
// are disributed between clusters in nearly equal sized groups.
|
||
|
|
//
|
||
|
|
// Note: Once cluster centers have been set, they are not changed,
|
||
|
|
// unless new_clust = true. This is so that subsequent calls generate
|
||
|
|
// points from the same distribution. It follows, of course, that any
|
||
|
|
// attempt to change the dimension or number of clusters without
|
||
|
|
// generating new clusters is asking for trouble.
|
||
|
|
//
|
||
|
|
// To make this a bad scenario at query time, query points should be
|
||
|
|
// selected from a different distribution, e.g. uniform or Gaussian.
|
||
|
|
//
|
||
|
|
// We use a little programming trick to generate groups of roughly
|
||
|
|
// equal size. If n is the total number of points, and n_clus is
|
||
|
|
// the number of clusters, then the c-th cluster (0 <= c < n_clus)
|
||
|
|
// is given floor((n+c)/n_clus) points. It can be shown that this
|
||
|
|
// will exactly consume all n points.
|
||
|
|
//
|
||
|
|
// This procedure makes use of the utility procedure, genOrthFlat
|
||
|
|
// which generates points in one orthogonal flat, according to
|
||
|
|
// the given control vector.
|
||
|
|
//
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
const double CO_FLAG = 999; // special flag value
|
||
|
|
|
||
|
|
static void genOrthFlat( // generate points on an orthog flat
|
||
|
|
ANNpointArray pa, // point array
|
||
|
|
int n, // number of points
|
||
|
|
int dim, // dimension
|
||
|
|
double *control, // control vector
|
||
|
|
double std_dev) // standard deviation
|
||
|
|
{
|
||
|
|
for (int i = 0; i < n; i++) { // generate each point
|
||
|
|
for (int d = 0; d < dim; d++) { // generate each coord
|
||
|
|
if (control[d] == CO_FLAG) // dimension on flat
|
||
|
|
pa[i][d] = (ANNcoord) annRanUnif(-1,1);
|
||
|
|
else // dimension off flat
|
||
|
|
pa[i][d] = (ANNcoord) (std_dev*annRanGauss() + control[d]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
void annClusOrthFlats( // clustered along orthogonal flats
|
||
|
|
ANNpointArray pa, // point array (modified)
|
||
|
|
int n, // number of points
|
||
|
|
int dim, // dimension
|
||
|
|
int n_clus, // number of colors
|
||
|
|
ANNbool new_clust, // generate new clusters.
|
||
|
|
double std_dev, // standard deviation within clusters
|
||
|
|
int max_dim) // maximum dimension of the flats
|
||
|
|
{
|
||
|
|
static ANNpointArray control = NULL; // control vectors
|
||
|
|
|
||
|
|
if (control == NULL || new_clust) { // need new cluster centers
|
||
|
|
if (control != NULL) { // clusters already exist
|
||
|
|
annDeallocPts(control); // get rid of them
|
||
|
|
}
|
||
|
|
control = annAllocPts(n_clus, dim);
|
||
|
|
|
||
|
|
for (int c = 0; c < n_clus; c++) { // generate clusters
|
||
|
|
int n_dim = 1 + annRanInt(max_dim); // number of dimensions in flat
|
||
|
|
for (int d = 0; d < dim; d++) { // generate side locations
|
||
|
|
// prob. of picking next dim
|
||
|
|
double Prob = ((double) n_dim)/((double) (dim-d));
|
||
|
|
if (annRan0() < Prob) { // add this one to flat
|
||
|
|
control[c][d] = CO_FLAG; // flag this entry
|
||
|
|
n_dim--; // one fewer dim to fill
|
||
|
|
}
|
||
|
|
else { // don't take this one
|
||
|
|
control[c][d] = annRanUnif(-1,1);// random value in [-1,1]
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
int offset = 0; // offset in pa array
|
||
|
|
for (int c = 0; c < n_clus; c++) { // generate clusters
|
||
|
|
int pick = (n+c)/n_clus; // number of points to pick
|
||
|
|
// generate the points
|
||
|
|
genOrthFlat(pa+offset, pick, dim, control[c], std_dev);
|
||
|
|
offset += pick; // increment offset
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// annClusEllipsoids - points clustered around axis-aligned ellipsoids
|
||
|
|
//
|
||
|
|
// This distribution consists of a collection points clustered
|
||
|
|
// among a collection of low dimensional ellipsoids whose axes
|
||
|
|
// are alligned with the coordinate axes in the hypercube [-1,1]^d.
|
||
|
|
// The objective is to model distributions in which the points are
|
||
|
|
// distributed in lower dimensional subspaces, and within this
|
||
|
|
// lower dimensional space the points are distributed with a
|
||
|
|
// Gaussian distribution (with no correlation between the
|
||
|
|
// dimensions).
|
||
|
|
//
|
||
|
|
// The distribution is given the number of clusters or "colors"
|
||
|
|
// (n_clus), maximum number of dimensions (max_dim) of the lower
|
||
|
|
// dimensional subspace, a "small" standard deviation
|
||
|
|
// (std_dev_small), and a "large" standard deviation range
|
||
|
|
// (std_dev_lo, std_dev_hi).
|
||
|
|
//
|
||
|
|
// The algorithm generates n_clus cluster centers uniformly from
|
||
|
|
// the hypercube [-1,1]^d. For each cluster, it selects the
|
||
|
|
// dimension of the subspace as a random number r between 1 and
|
||
|
|
// max_dim. These are the dimensions of the ellipsoid. Then it
|
||
|
|
// generates a d-element std dev vector whose entries are the
|
||
|
|
// standard deviation for the coordinates of each cluster in the
|
||
|
|
// distribution. Among the d-element control vector, r randomly
|
||
|
|
// chosen values are chosen uniformly from the range [std_dev_lo,
|
||
|
|
// std_dev_hi]. The remaining values are set to std_dev_small.
|
||
|
|
//
|
||
|
|
// Note that annClusGaussPts is a special case of this in which
|
||
|
|
// max_dim = 0, and std_dev = std_dev_small.
|
||
|
|
//
|
||
|
|
// If the flag new_clust is set, then new cluster centers are
|
||
|
|
// generated.
|
||
|
|
//
|
||
|
|
// This procedure makes use of the utility procedure genGauss
|
||
|
|
// which generates points distributed according to a Gaussian
|
||
|
|
// distribution.
|
||
|
|
//
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
static void genGauss( // generate points on a general Gaussian
|
||
|
|
ANNpointArray pa, // point array
|
||
|
|
int n, // number of points
|
||
|
|
int dim, // dimension
|
||
|
|
double *center, // center vector
|
||
|
|
double *std_dev) // standard deviation vector
|
||
|
|
{
|
||
|
|
for (int i = 0; i < n; i++) {
|
||
|
|
for (int d = 0; d < dim; d++) {
|
||
|
|
pa[i][d] = (ANNcoord) (std_dev[d]*annRanGauss() + center[d]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
void annClusEllipsoids( // clustered around ellipsoids
|
||
|
|
ANNpointArray pa, // point array (modified)
|
||
|
|
int n, // number of points
|
||
|
|
int dim, // dimension
|
||
|
|
int n_clus, // number of colors
|
||
|
|
ANNbool new_clust, // generate new clusters.
|
||
|
|
double std_dev_small, // small standard deviation
|
||
|
|
double std_dev_lo, // low standard deviation for ellipses
|
||
|
|
double std_dev_hi, // high standard deviation for ellipses
|
||
|
|
int max_dim) // maximum dimension of the flats
|
||
|
|
{
|
||
|
|
static ANNpointArray centers = NULL; // cluster centers
|
||
|
|
static ANNpointArray std_dev = NULL; // standard deviations
|
||
|
|
|
||
|
|
if (centers == NULL || new_clust) { // need new cluster centers
|
||
|
|
if (centers != NULL) // clusters already exist
|
||
|
|
annDeallocPts(centers); // get rid of them
|
||
|
|
if (std_dev != NULL) // std deviations already exist
|
||
|
|
annDeallocPts(std_dev); // get rid of them
|
||
|
|
|
||
|
|
centers = annAllocPts(n_clus, dim); // alloc new clusters and devs
|
||
|
|
std_dev = annAllocPts(n_clus, dim);
|
||
|
|
|
||
|
|
for (int i = 0; i < n_clus; i++) { // gen cluster center coords
|
||
|
|
for (int d = 0; d < dim; d++) {
|
||
|
|
centers[i][d] = (ANNcoord) annRanUnif(-1,1);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
for (int c = 0; c < n_clus; c++) { // generate cluster std dev
|
||
|
|
int n_dim = 1 + annRanInt(max_dim); // number of dimensions in flat
|
||
|
|
for (int d = 0; d < dim; d++) { // generate std dev's
|
||
|
|
// prob. of picking next dim
|
||
|
|
double Prob = ((double) n_dim)/((double) (dim-d));
|
||
|
|
if (annRan0() < Prob) { // add this one to ellipse
|
||
|
|
// generate random std dev
|
||
|
|
std_dev[c][d] = annRanUnif(std_dev_lo, std_dev_hi);
|
||
|
|
n_dim--; // one fewer dim to fill
|
||
|
|
}
|
||
|
|
else { // don't take this one
|
||
|
|
std_dev[c][d] = std_dev_small;// use small std dev
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
int offset = 0; // next slot to fill
|
||
|
|
for (int c = 0; c < n_clus; c++) { // generate clusters
|
||
|
|
int pick = (n+c)/n_clus; // number of points to pick
|
||
|
|
// generate the points
|
||
|
|
genGauss(pa+offset, pick, dim, centers[c], std_dev[c]);
|
||
|
|
offset += pick; // increment offset in array
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
// annPlanted - Generates points from a "planted" distribution
|
||
|
|
// In high dimensional spaces, interpoint distances tend to be
|
||
|
|
// highly clustered around the mean value. Approximate nearest
|
||
|
|
// neighbor searching makes little sense in this context, unless it
|
||
|
|
// is the case that each query point is significantly closer to its
|
||
|
|
// nearest neighbor than to other points. Thus, the query points
|
||
|
|
// should be planted close to the data points. Given a source data
|
||
|
|
// set, this procedure generates a set of query points having this
|
||
|
|
// property.
|
||
|
|
//
|
||
|
|
// We are given a source data array and a standard deviation. We
|
||
|
|
// generate points as follows. We select a random point from the
|
||
|
|
// source data set, and we generate a Gaussian point centered about
|
||
|
|
// this random point and perturbed by a normal distributed random
|
||
|
|
// variable with mean zero and the given standard deviation along
|
||
|
|
// each coordinate.
|
||
|
|
//
|
||
|
|
// Note that this essentially the same a clustered Gaussian
|
||
|
|
// distribution, but where the cluster centers are given by the
|
||
|
|
// source data set.
|
||
|
|
//----------------------------------------------------------------------
|
||
|
|
|
||
|
|
void annPlanted( // planted nearest neighbors
|
||
|
|
ANNpointArray pa, // point array (modified)
|
||
|
|
int n, // number of points
|
||
|
|
int dim, // dimension
|
||
|
|
ANNpointArray src, // source point array
|
||
|
|
int n_src, // source size
|
||
|
|
double std_dev) // standard deviation about source
|
||
|
|
{
|
||
|
|
for (int i = 0; i < n; i++) {
|
||
|
|
int c = annRanInt(n_src); // generate source index
|
||
|
|
for (int d = 0; d < dim; d++) {
|
||
|
|
pa[i][d] = (ANNcoord) (std_dev*annRanGauss() + src[c][d]);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
}
|