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sptree.cpp
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sptree.cpp
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/*
*
* Copyright (c) 2014, Laurens van der Maaten (Delft University of Technology)
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* This product includes software developed by the Delft University of Technology.
* 4. Neither the name of the Delft University of Technology nor the names of
* its contributors may be used to endorse or promote products derived from
* this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY LAURENS VAN DER MAATEN ''AS IS'' AND ANY EXPRESS
* OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
* EVENT SHALL LAURENS VAN DER MAATEN BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
* SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
* PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR
* BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
* CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
* IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
* OF SUCH DAMAGE.
*
*/
#include <math.h>
#include <float.h>
#include <stdlib.h>
#include <stdio.h>
#include <cmath>
#include "sptree.h"
// Constructs cell
Cell::Cell(unsigned int inp_dimension) {
dimension = inp_dimension;
corner = (double*) malloc(dimension * sizeof(double));
width = (double*) malloc(dimension * sizeof(double));
}
Cell::Cell(unsigned int inp_dimension, double* inp_corner, double* inp_width) {
dimension = inp_dimension;
corner = (double*) malloc(dimension * sizeof(double));
width = (double*) malloc(dimension * sizeof(double));
for(int d = 0; d < dimension; d++) setCorner(d, inp_corner[d]);
for(int d = 0; d < dimension; d++) setWidth( d, inp_width[d]);
}
// Destructs cell
Cell::~Cell() {
free(corner);
free(width);
}
double Cell::getCorner(unsigned int d) {
return corner[d];
}
double Cell::getWidth(unsigned int d) {
return width[d];
}
void Cell::setCorner(unsigned int d, double val) {
corner[d] = val;
}
void Cell::setWidth(unsigned int d, double val) {
width[d] = val;
}
// Checks whether a point lies in a cell
bool Cell::containsPoint(double point[])
{
for(int d = 0; d < dimension; d++) {
if(corner[d] - width[d] > point[d]) return false;
if(corner[d] + width[d] < point[d]) return false;
}
return true;
}
// Default constructor for SPTree -- build tree, too!
SPTree::SPTree(unsigned int D, double* inp_data, unsigned int N)
{
// Compute mean, width, and height of current map (boundaries of SPTree)
int nD = 0;
double* mean_Y = (double*) calloc(D, sizeof(double));
double* min_Y = (double*) malloc(D * sizeof(double)); for(unsigned int d = 0; d < D; d++) min_Y[d] = DBL_MAX;
double* max_Y = (double*) malloc(D * sizeof(double)); for(unsigned int d = 0; d < D; d++) max_Y[d] = -DBL_MAX;
for(unsigned int n = 0; n < N; n++) {
for(unsigned int d = 0; d < D; d++) {
mean_Y[d] += inp_data[n * D + d];
if(inp_data[nD + d] < min_Y[d]) min_Y[d] = inp_data[nD + d];
if(inp_data[nD + d] > max_Y[d]) max_Y[d] = inp_data[nD + d];
}
nD += D;
}
for(int d = 0; d < D; d++) mean_Y[d] /= (double) N;
// Construct SPTree
double* width = (double*) malloc(D * sizeof(double));
for(int d = 0; d < D; d++) width[d] = fmax(max_Y[d] - mean_Y[d], mean_Y[d] - min_Y[d]) + 1e-5;
init(NULL, D, inp_data, mean_Y, width);
fill(N);
// Clean up memory
free(mean_Y);
free(max_Y);
free(min_Y);
free(width);
}
// Constructor for SPTree with particular size and parent -- build the tree, too!
SPTree::SPTree(unsigned int D, double* inp_data, unsigned int N, double* inp_corner, double* inp_width)
{
init(NULL, D, inp_data, inp_corner, inp_width);
fill(N);
}
// Constructor for SPTree with particular size (do not fill the tree)
SPTree::SPTree(unsigned int D, double* inp_data, double* inp_corner, double* inp_width)
{
init(NULL, D, inp_data, inp_corner, inp_width);
}
// Constructor for SPTree with particular size and parent (do not fill tree)
SPTree::SPTree(SPTree* inp_parent, unsigned int D, double* inp_data, double* inp_corner, double* inp_width) {
init(inp_parent, D, inp_data, inp_corner, inp_width);
}
// Constructor for SPTree with particular size and parent -- build the tree, too!
SPTree::SPTree(SPTree* inp_parent, unsigned int D, double* inp_data, unsigned int N, double* inp_corner, double* inp_width)
{
init(inp_parent, D, inp_data, inp_corner, inp_width);
fill(N);
}
// Main initialization function
void SPTree::init(SPTree* inp_parent, unsigned int D, double* inp_data, double* inp_corner, double* inp_width)
{
parent = inp_parent;
dimension = D;
no_children = 2;
for(unsigned int d = 1; d < D; d++) no_children *= 2;
data = inp_data;
is_leaf = true;
size = 0;
cum_size = 0;
boundary = new Cell(dimension);
for(unsigned int d = 0; d < D; d++) boundary->setCorner(d, inp_corner[d]);
for(unsigned int d = 0; d < D; d++) boundary->setWidth( d, inp_width[d]);
children = (SPTree**) malloc(no_children * sizeof(SPTree*));
for(unsigned int i = 0; i < no_children; i++) children[i] = NULL;
center_of_mass = (double*) malloc(D * sizeof(double));
for(unsigned int d = 0; d < D; d++) center_of_mass[d] = .0;
buff = (double*) malloc(D * sizeof(double));
}
// Destructor for SPTree
SPTree::~SPTree()
{
for(unsigned int i = 0; i < no_children; i++) {
if(children[i] != NULL) delete children[i];
}
free(children);
free(center_of_mass);
free(buff);
delete boundary;
}
// Update the data underlying this tree
void SPTree::setData(double* inp_data)
{
data = inp_data;
}
// Get the parent of the current tree
SPTree* SPTree::getParent()
{
return parent;
}
// Insert a point into the SPTree
bool SPTree::insert(unsigned int new_index)
{
// Ignore objects which do not belong in this quad tree
double* point = data + new_index * dimension;
if(!boundary->containsPoint(point))
return false;
// Online update of cumulative size and center-of-mass
cum_size++;
double mult1 = (double) (cum_size - 1) / (double) cum_size;
double mult2 = 1.0 / (double) cum_size;
for(unsigned int d = 0; d < dimension; d++) center_of_mass[d] *= mult1;
for(unsigned int d = 0; d < dimension; d++) center_of_mass[d] += mult2 * point[d];
// If there is space in this quad tree and it is a leaf, add the object here
if(is_leaf && size < QT_NODE_CAPACITY) {
index[size] = new_index;
size++;
return true;
}
// Don't add duplicates for now (this is not very nice)
bool any_duplicate = false;
for(unsigned int n = 0; n < size; n++) {
bool duplicate = true;
for(unsigned int d = 0; d < dimension; d++) {
if(point[d] != data[index[n] * dimension + d]) { duplicate = false; break; }
}
any_duplicate = any_duplicate | duplicate;
}
if(any_duplicate) return true;
// Otherwise, we need to subdivide the current cell
if(is_leaf) subdivide();
// Find out where the point can be inserted
for(unsigned int i = 0; i < no_children; i++) {
if(children[i]->insert(new_index)) return true;
}
// Otherwise, the point cannot be inserted (this should never happen)
return false;
}
// Create four children which fully divide this cell into four quads of equal area
void SPTree::subdivide() {
// Create new children
double* new_corner = (double*) malloc(dimension * sizeof(double));
double* new_width = (double*) malloc(dimension * sizeof(double));
for(unsigned int i = 0; i < no_children; i++) {
unsigned int div = 1;
for(unsigned int d = 0; d < dimension; d++) {
new_width[d] = .5 * boundary->getWidth(d);
if((i / div) % 2 == 1) new_corner[d] = boundary->getCorner(d) - .5 * boundary->getWidth(d);
else new_corner[d] = boundary->getCorner(d) + .5 * boundary->getWidth(d);
div *= 2;
}
children[i] = new SPTree(this, dimension, data, new_corner, new_width);
}
free(new_corner);
free(new_width);
// Move existing points to correct children
for(unsigned int i = 0; i < size; i++) {
bool success = false;
for(unsigned int j = 0; j < no_children; j++) {
if(!success) success = children[j]->insert(index[i]);
}
index[i] = -1;
}
// Empty parent node
size = 0;
is_leaf = false;
}
// Build SPTree on dataset
void SPTree::fill(unsigned int N)
{
for(unsigned int i = 0; i < N; i++) insert(i);
}
// Checks whether the specified tree is correct
bool SPTree::isCorrect()
{
for(unsigned int n = 0; n < size; n++) {
double* point = data + index[n] * dimension;
if(!boundary->containsPoint(point)) return false;
}
if(!is_leaf) {
bool correct = true;
for(int i = 0; i < no_children; i++) correct = correct && children[i]->isCorrect();
return correct;
}
else return true;
}
// Build a list of all indices in SPTree
void SPTree::getAllIndices(unsigned int* indices)
{
getAllIndices(indices, 0);
}
// Build a list of all indices in SPTree
unsigned int SPTree::getAllIndices(unsigned int* indices, unsigned int loc)
{
// Gather indices in current quadrant
for(unsigned int i = 0; i < size; i++) indices[loc + i] = index[i];
loc += size;
// Gather indices in children
if(!is_leaf) {
for(int i = 0; i < no_children; i++) loc = children[i]->getAllIndices(indices, loc);
}
return loc;
}
unsigned int SPTree::getDepth() {
if(is_leaf) return 1;
int depth = 0;
for(unsigned int i = 0; i < no_children; i++) depth = fmax(depth, children[i]->getDepth());
return 1 + depth;
}
// Compute non-edge forces using Barnes-Hut algorithm
void SPTree::computeNonEdgeForces(unsigned int point_index, double theta, double neg_f[], double* sum_Q)
{
// Make sure that we spend no time on empty nodes or self-interactions
if(cum_size == 0 || (is_leaf && size == 1 && index[0] == point_index)) return;
// Compute distance between point and center-of-mass
double D = .0;
unsigned int ind = point_index * dimension;
for(unsigned int d = 0; d < dimension; d++) buff[d] = data[ind + d] - center_of_mass[d];
for(unsigned int d = 0; d < dimension; d++) D += buff[d] * buff[d];
// Check whether we can use this node as a "summary"
double max_width = 0.0;
double cur_width;
for(unsigned int d = 0; d < dimension; d++) {
cur_width = boundary->getWidth(d);
max_width = (max_width > cur_width) ? max_width : cur_width;
}
if(is_leaf || max_width / sqrt(D) < theta) {
// Compute and add t-SNE force between point and current node
D = 1.0 / (1.0 + D);
double mult = cum_size * D;
*sum_Q += mult;
mult *= D;
for(unsigned int d = 0; d < dimension; d++) neg_f[d] += mult * buff[d];
}
else {
// Recursively apply Barnes-Hut to children
for(unsigned int i = 0; i < no_children; i++) children[i]->computeNonEdgeForces(point_index, theta, neg_f, sum_Q);
}
}
// Computes edge forces
void SPTree::computeEdgeForces(unsigned int* row_P, unsigned int* col_P, double* val_P, int N, double* pos_f)
{
// Loop over all edges in the graph
unsigned int ind1 = 0;
unsigned int ind2 = 0;
double D;
for(unsigned int n = 0; n < N; n++) {
for(unsigned int i = row_P[n]; i < row_P[n + 1]; i++) {
// Compute pairwise distance and Q-value
D = 1.0;
ind2 = col_P[i] * dimension;
for(unsigned int d = 0; d < dimension; d++) buff[d] = data[ind1 + d] - data[ind2 + d];
for(unsigned int d = 0; d < dimension; d++) D += buff[d] * buff[d];
D = val_P[i] / D;
// Sum positive force
for(unsigned int d = 0; d < dimension; d++) pos_f[ind1 + d] += D * buff[d];
}
ind1 += dimension;
}
}
// Print out tree
void SPTree::print()
{
if(cum_size == 0) {
printf("Empty node\n");
return;
}
if(is_leaf) {
printf("Leaf node; data = [");
for(int i = 0; i < size; i++) {
double* point = data + index[i] * dimension;
for(int d = 0; d < dimension; d++) printf("%f, ", point[d]);
printf(" (index = %d)", index[i]);
if(i < size - 1) printf("\n");
else printf("]\n");
}
}
else {
printf("Intersection node with center-of-mass = [");
for(int d = 0; d < dimension; d++) printf("%f, ", center_of_mass[d]);
printf("]; children are:\n");
for(int i = 0; i < no_children; i++) children[i]->print();
}
}