t-viSNE: Interactive Assessment and Interpretation of t-SNE Projections https://doi.org/10.1109/TVCG.2020.2986996
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t-viSNE/tsne.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 <cfloat>
#include <cmath>
#include <cstdlib>
#include <cstdio>
#include <cstring>
#include <ctime>
#include "vptree.h"
#include "sptree.h"
#include "tsne.h"
using namespace std;
static double sign(double x) { return (x == .0 ? .0 : (x < .0 ? -1.0 : 1.0)); }
static void zeroMean(double* X, int N, int D);
static void computeGaussianPerplexity(double* X, int N, int D, double* P, double perplexity);
static void computeGaussianPerplexity(double* X, int N, int D, unsigned int** _row_P, unsigned int** _col_P, double** _val_P, double perplexity, int K);
static double randn();
static void computeExactGradient(double* P, double* Y, int N, int D, double* dC);
static void computeGradient(unsigned int* inp_row_P, unsigned int* inp_col_P, double* inp_val_P, double* Y, int N, int D, double* dC, double theta);
static double evaluateError(double* P, double* Y, int N, int D);
static double evaluateError(unsigned int* row_P, unsigned int* col_P, double* val_P, double* Y, int N, int D, double theta, bool save_cost_per_point = false);
static void computeSquaredEuclideanDistance(double* X, int N, int D, double* DD);
static void symmetrizeMatrix(unsigned int** row_P, unsigned int** col_P, double** val_P, int N);
static void save_1D_array(double* array, int n, const char* filename);
// Perform t-SNE
void TSNE::run(double* X, int N, int D, double* Y, int no_dims, double perplexity, double theta, int rand_seed,
bool skip_random_init, int max_iter, int stop_lying_iter, int mom_switch_iter, int cost_iter_step) {
// Set random seed
if (skip_random_init != true) {
if(rand_seed >= 0) {
printf("Using random seed: %d\n", rand_seed);
srand((unsigned int) rand_seed);
} else {
printf("Using current time as random seed...\n");
srand(time(NULL));
}
}
// Determine whether we are using an exact algorithm
if(N - 1 < 3 * perplexity) { printf("Perplexity too large for the number of data points!\n"); exit(1); }
printf("Using no_dims = %d, perplexity = %f, and theta = %f\n", no_dims, perplexity, theta);
bool exact = (theta == .0) ? true : false;
// Set learning parameters
float total_time = .0;
clock_t start, end;
double momentum = .5, final_momentum = .8;
double eta = 200.0;
// Allocate some memory
double* dY = (double*) malloc(N * no_dims * sizeof(double));
double* uY = (double*) malloc(N * no_dims * sizeof(double));
double* gains = (double*) malloc(N * no_dims * sizeof(double));
if(dY == NULL || uY == NULL || gains == NULL) { printf("Memory allocation failed!\n"); exit(1); }
for(int i = 0; i < N * no_dims; i++) uY[i] = .0;
for(int i = 0; i < N * no_dims; i++) gains[i] = 1.0;
// Normalize input data (to prevent numerical problems)
printf("Computing input similarities...\n");
start = clock();
zeroMean(X, N, D);
double max_X = .0;
for(int i = 0; i < N * D; i++) {
if(fabs(X[i]) > max_X) max_X = fabs(X[i]);
}
for(int i = 0; i < N * D; i++) X[i] /= max_X;
// Compute input similarities for exact t-SNE
double* P; unsigned int* row_P; unsigned int* col_P; double* val_P;
if(exact) {
// Compute similarities
printf("Exact?");
P = (double*) malloc(N * N * sizeof(double));
if(P == NULL) { printf("Memory allocation failed!\n"); exit(1); }
computeGaussianPerplexity(X, N, D, P, perplexity);
// Symmetrize input similarities
printf("Symmetrizing...\n");
int nN = 0;
for(int n = 0; n < N; n++) {
int mN = (n + 1) * N;
for(int m = n + 1; m < N; m++) {
P[nN + m] += P[mN + n];
P[mN + n] = P[nN + m];
mN += N;
}
nN += N;
}
double sum_P = .0;
for(int i = 0; i < N * N; i++) sum_P += P[i];
for(int i = 0; i < N * N; i++) P[i] /= sum_P;
}
// Compute input similarities for approximate t-SNE
else {
// Compute asymmetric pairwise input similarities
computeGaussianPerplexity(X, N, D, &row_P, &col_P, &val_P, perplexity, (int) (3 * perplexity));
// Symmetrize input similarities
symmetrizeMatrix(&row_P, &col_P, &val_P, N);
double sum_P = .0;
for(int i = 0; i < row_P[N]; i++) sum_P += val_P[i];
for(int i = 0; i < row_P[N]; i++) val_P[i] /= sum_P;
}
end = clock();
// Lie about the P-values
if(exact) { for(int i = 0; i < N * N; i++) P[i] *= 12.0; }
else { for(int i = 0; i < row_P[N]; i++) val_P[i] *= 12.0; }
// Initialize solution (randomly)
if (skip_random_init != true) {
for(int i = 0; i < N * no_dims; i++) Y[i] = randn() * .0001;
}
// Perform main training loop
if(exact) printf("Input similarities computed in %4.2f seconds!\nLearning embedding...\n", (float) (end - start) / CLOCKS_PER_SEC);
else printf("Input similarities computed in %4.2f seconds (sparsity = %f)!\nLearning embedding...\n", (float) (end - start) / CLOCKS_PER_SEC, (double) row_P[N] / ((double) N * (double) N));
start = clock();
double* cost_per_iter = new double[max_iter];
for(int iter = 0; iter < max_iter; iter++) {
// Compute (approximate) gradient
if(exact) computeExactGradient(P, Y, N, no_dims, dY);
else computeGradient(row_P, col_P, val_P, Y, N, no_dims, dY, theta);
// Update gains
for(int i = 0; i < N * no_dims; i++) gains[i] = (sign(dY[i]) != sign(uY[i])) ? (gains[i] + .2) : (gains[i] * .8);
for(int i = 0; i < N * no_dims; i++) if(gains[i] < .01) gains[i] = .01;
// Perform gradient update (with momentum and gains)
for(int i = 0; i < N * no_dims; i++) uY[i] = momentum * uY[i] - eta * gains[i] * dY[i];
for(int i = 0; i < N * no_dims; i++) Y[i] = Y[i] + uY[i];
// Make solution zero-mean
zeroMean(Y, N, no_dims);
// Stop lying about the P-values after a while, and switch momentum
if(iter == stop_lying_iter) {
if(exact) { for(int i = 0; i < N * N; i++) P[i] /= 12.0; }
else { for(int i = 0; i < row_P[N]; i++) val_P[i] /= 12.0; }
}
if(iter == mom_switch_iter) momentum = final_momentum;
// Print out progress
if (iter % cost_iter_step == 0 || iter == max_iter - 1) {
end = clock();
double C = .0;
if(exact) C = evaluateError(P, Y, N, no_dims);
else C = evaluateError(row_P, col_P, val_P, Y, N, no_dims, theta); // doing approximate computation here!
if(iter == 0)
printf("Iteration %d: error is %f\n", iter, C);
else {
total_time += (float) (end - start) / CLOCKS_PER_SEC;
printf("Iteration %d: error is %f (%d iterations in %4.2f seconds)\n", iter, C, cost_iter_step, (float) (end - start) / CLOCKS_PER_SEC);
}
cost_per_iter[iter] = C;
start = clock();
}
}
end = clock(); total_time += (float) (end - start) / CLOCKS_PER_SEC;
// Save the cost per iteration to file
save_1D_array(cost_per_iter, max_iter, "cost_per_iter.txt");
// This time it's for saving the final cost per point
evaluateError(row_P, col_P, val_P, Y, N, no_dims, theta, true);
// Clean up memory
free(dY);
free(uY);
free(gains);
if(exact) free(P);
else {
free(row_P); row_P = NULL;
free(col_P); col_P = NULL;
free(val_P); val_P = NULL;
}
delete[] cost_per_iter;
printf("Fitting performed in %4.2f seconds.\n", total_time);
}
// Compute gradient of the t-SNE cost function (using Barnes-Hut algorithm)
static void computeGradient(unsigned int* inp_row_P, unsigned int* inp_col_P, double* inp_val_P, double* Y, int N, int D, double* dC, double theta)
{
// Construct space-partitioning tree on current map
SPTree* tree = new SPTree(D, Y, N);
// Compute all terms required for t-SNE gradient
double sum_Q = .0;
double* pos_f = (double*) calloc(N * D, sizeof(double));
double* neg_f = (double*) calloc(N * D, sizeof(double));
if(pos_f == NULL || neg_f == NULL) { printf("Memory allocation failed!\n"); exit(1); }
tree->computeEdgeForces(inp_row_P, inp_col_P, inp_val_P, N, pos_f);
for(int n = 0; n < N; n++) tree->computeNonEdgeForces(n, theta, neg_f + n * D, &sum_Q);
// Compute final t-SNE gradient
for(int i = 0; i < N * D; i++) {
dC[i] = pos_f[i] - (neg_f[i] / sum_Q);
}
free(pos_f);
free(neg_f);
delete tree;
}
// Compute gradient of the t-SNE cost function (exact)
static void computeExactGradient(double* P, double* Y, int N, int D, double* dC) {
// Make sure the current gradient contains zeros
for(int i = 0; i < N * D; i++) dC[i] = 0.0;
// Compute the squared Euclidean distance matrix
double* DD = (double*) malloc(N * N * sizeof(double));
if(DD == NULL) { printf("Memory allocation failed!\n"); exit(1); }
computeSquaredEuclideanDistance(Y, N, D, DD);
// Compute Q-matrix and normalization sum
double* Q = (double*) malloc(N * N * sizeof(double));
if(Q == NULL) { printf("Memory allocation failed!\n"); exit(1); }
double sum_Q = .0;
int nN = 0;
for(int n = 0; n < N; n++) {
for(int m = 0; m < N; m++) {
if(n != m) {
Q[nN + m] = 1 / (1 + DD[nN + m]);
sum_Q += Q[nN + m];
}
}
nN += N;
}
// Perform the computation of the gradient
nN = 0;
int nD = 0;
for(int n = 0; n < N; n++) {
int mD = 0;
for(int m = 0; m < N; m++) {
if(n != m) {
double mult = (P[nN + m] - (Q[nN + m] / sum_Q)) * Q[nN + m];
for(int d = 0; d < D; d++) {
dC[nD + d] += (Y[nD + d] - Y[mD + d]) * mult;
}
}
mD += D;
}
nN += N;
nD += D;
}
// Free memory
free(DD); DD = NULL;
free(Q); Q = NULL;
}
// Evaluate t-SNE cost function (exactly)
static double evaluateError(double* P, double* Y, int N, int D) {
// Compute the squared Euclidean distance matrix
double* DD = (double*) malloc(N * N * sizeof(double));
double* Q = (double*) malloc(N * N * sizeof(double));
if(DD == NULL || Q == NULL) { printf("Memory allocation failed!\n"); exit(1); }
computeSquaredEuclideanDistance(Y, N, D, DD);
// Compute Q-matrix and normalization sum
int nN = 0;
double sum_Q = DBL_MIN;
for(int n = 0; n < N; n++) {
for(int m = 0; m < N; m++) {
if(n != m) {
Q[nN + m] = 1 / (1 + DD[nN + m]);
sum_Q += Q[nN + m];
}
else Q[nN + m] = DBL_MIN;
}
nN += N;
}
for(int i = 0; i < N * N; i++) Q[i] /= sum_Q;
// Sum t-SNE error
double C = .0;
for(int n = 0; n < N * N; n++) {
C += P[n] * log((P[n] + FLT_MIN) / (Q[n] + FLT_MIN));
}
// Clean up memory
free(DD);
free(Q);
return C;
}
// Evaluate t-SNE cost function (approximately)
static double evaluateError(unsigned int* row_P, unsigned int* col_P, double* val_P, double* Y, int N, int D, double theta, bool save_cost_per_point)
{
// Get estimate of normalization term
SPTree* tree = new SPTree(D, Y, N);
double* buff = (double*) calloc(D, sizeof(double));
double sum_Q = .0;
for(int n = 0; n < N; n++) tree->computeNonEdgeForces(n, theta, buff, &sum_Q);
double* cost_per_point = new double[N];
// Loop over all edges to compute t-SNE error
int ind1, ind2;
double C = .0, Q, c;
for(int n = 0; n < N; n++) {
cost_per_point[n] = .0;
ind1 = n * D;
for(int i = row_P[n]; i < row_P[n + 1]; i++) {
Q = .0;
ind2 = col_P[i] * D;
for(int d = 0; d < D; d++) buff[d] = Y[ind1 + d];
for(int d = 0; d < D; d++) buff[d] -= Y[ind2 + d];
for(int d = 0; d < D; d++) Q += buff[d] * buff[d];
Q = (1.0 / (1.0 + Q)) / sum_Q;
c = val_P[i] * log((val_P[i] + FLT_MIN) / (Q + FLT_MIN));
cost_per_point[n] += c;
C += c;
}
}
if (save_cost_per_point)
save_1D_array(cost_per_point, N, "cost_per_point.txt");
// Clean up memory
free(buff);
delete tree;
delete[] cost_per_point;
return C;
}
// Compute input similarities with a fixed perplexity
static void computeGaussianPerplexity(double* X, int N, int D, double* P, double perplexity) {
// Compute the squared Euclidean distance matrix
double* DD = (double*) malloc(N * N * sizeof(double));
if(DD == NULL) { printf("Memory allocation failed!\n"); exit(1); }
computeSquaredEuclideanDistance(X, N, D, DD);
// Compute the Gaussian kernel row by row
int nN = 0;
for(int n = 0; n < N; n++) {
// Initialize some variables
bool found = false;
double beta = 1.0;
double min_beta = -DBL_MAX;
double max_beta = DBL_MAX;
double tol = 1e-5;
double sum_P;
// Iterate until we found a good perplexity
int iter = 0;
while(!found && iter < 200) {
// Compute Gaussian kernel row
for(int m = 0; m < N; m++) P[nN + m] = exp(-beta * DD[nN + m]);
P[nN + n] = DBL_MIN;
// Compute entropy of current row
sum_P = DBL_MIN;
for(int m = 0; m < N; m++) sum_P += P[nN + m];
double H = 0.0;
for(int m = 0; m < N; m++) H += beta * (DD[nN + m] * P[nN + m]);
H = (H / sum_P) + log(sum_P);
// Evaluate whether the entropy is within the tolerance level
double Hdiff = H - log(perplexity);
if(Hdiff < tol && -Hdiff < tol) {
found = true;
}
else {
if(Hdiff > 0) {
min_beta = beta;
if(max_beta == DBL_MAX || max_beta == -DBL_MAX)
beta *= 2.0;
else
beta = (beta + max_beta) / 2.0;
}
else {
max_beta = beta;
if(min_beta == -DBL_MAX || min_beta == DBL_MAX)
beta /= 2.0;
else
beta = (beta + min_beta) / 2.0;
}
}
// Update iteration counter
iter++;
}
// Row normalize P
for(int m = 0; m < N; m++) P[nN + m] /= sum_P;
nN += N;
}
// Clean up memory
free(DD); DD = NULL;
}
// Compute input similarities with a fixed perplexity using ball trees (this function allocates memory another function should free)
static void computeGaussianPerplexity(double* X, int N, int D, unsigned int** _row_P, unsigned int** _col_P, double** _val_P, double perplexity, int K) {
if(perplexity > K) printf("Perplexity should be lower than K!\n");
// Allocate the memory we need
*_row_P = (unsigned int*) malloc((N + 1) * sizeof(unsigned int));
*_col_P = (unsigned int*) calloc(N * K, sizeof(unsigned int));
*_val_P = (double*) calloc(N * K, sizeof(double));
if(*_row_P == NULL || *_col_P == NULL || *_val_P == NULL) { printf("Memory allocation failed!\n"); exit(1); }
unsigned int* row_P = *_row_P;
unsigned int* col_P = *_col_P;
double* val_P = *_val_P;
double* cur_P = (double*) malloc((N - 1) * sizeof(double));
if(cur_P == NULL) { printf("Memory allocation failed!\n"); exit(1); }
row_P[0] = 0;
for(int n = 0; n < N; n++) row_P[n + 1] = row_P[n] + (unsigned int) K;
// Build ball tree on data set
VpTree<DataPoint, euclidean_distance>* tree = new VpTree<DataPoint, euclidean_distance>();
vector<DataPoint> obj_X(N, DataPoint(D, -1, X));
for(int n = 0; n < N; n++) obj_X[n] = DataPoint(D, n, X + n * D);
tree->create(obj_X);
// Loop over all points to find nearest neighbors
printf("Building tree...\n");
vector<DataPoint> indices;
vector<double> distances;
double* betas = new double[N];
for(int n = 0; n < N; n++) {
if(n % 10000 == 0) printf(" - point %d of %d\n", n, N);
// Find nearest neighbors
indices.clear();
distances.clear();
tree->search(obj_X[n], K + 1, &indices, &distances);
// Initialize some variables for binary search
bool found = false;
double beta = 1.0;
double min_beta = -DBL_MAX;
double max_beta = DBL_MAX;
double tol = 1e-5;
// Iterate until we found a good perplexity
int iter = 0; double sum_P;
while(!found && iter < 200) {
// Compute Gaussian kernel row
for(int m = 0; m < K; m++) cur_P[m] = exp(-beta * distances[m + 1] * distances[m + 1]);
// Compute entropy of current row
sum_P = DBL_MIN;
for(int m = 0; m < K; m++) sum_P += cur_P[m];
double H = .0;
for(int m = 0; m < K; m++) H += beta * (distances[m + 1] * distances[m + 1] * cur_P[m]);
H = (H / sum_P) + log(sum_P);
// Evaluate whether the entropy is within the tolerance level
double Hdiff = H - log(perplexity);
if(Hdiff < tol && -Hdiff < tol) {
found = true;
}
else {
if(Hdiff > 0) {
min_beta = beta;
if(max_beta == DBL_MAX || max_beta == -DBL_MAX)
beta *= 2.0;
else
beta = (beta + max_beta) / 2.0;
}
else {
max_beta = beta;
if(min_beta == -DBL_MAX || min_beta == DBL_MAX)
beta /= 2.0;
else
beta = (beta + min_beta) / 2.0;
}
}
// Update iteration counter
iter++;
}
// Save the found beta to a vector of all betas
betas[n] = beta;
// Row-normalize current row of P and store in matrix
for(unsigned int m = 0; m < K; m++) cur_P[m] /= sum_P;
for(unsigned int m = 0; m < K; m++) {
col_P[row_P[n] + m] = (unsigned int) indices[m + 1].index();
val_P[row_P[n] + m] = cur_P[m];
}
}
// Save the betas to disk, so we can recover them later
save_1D_array(betas, N, "betas.txt");
// Clean up memory
obj_X.clear();
free(cur_P);
delete tree;
delete[] betas;
}
// Symmetrizes a sparse matrix
static void symmetrizeMatrix(unsigned int** _row_P, unsigned int** _col_P, double** _val_P, int N) {
// Get sparse matrix
unsigned int* row_P = *_row_P;
unsigned int* col_P = *_col_P;
double* val_P = *_val_P;
// Count number of elements and row counts of symmetric matrix
int* row_counts = (int*) calloc(N, sizeof(int));
if(row_counts == NULL) { printf("Memory allocation failed!\n"); exit(1); }
for(int n = 0; n < N; n++) {
for(int i = row_P[n]; i < row_P[n + 1]; i++) {
// Check whether element (col_P[i], n) is present
bool present = false;
for(int m = row_P[col_P[i]]; m < row_P[col_P[i] + 1]; m++) {
if(col_P[m] == n) present = true;
}
if(present) row_counts[n]++;
else {
row_counts[n]++;
row_counts[col_P[i]]++;
}
}
}
int no_elem = 0;
for(int n = 0; n < N; n++) no_elem += row_counts[n];
// Allocate memory for symmetrized matrix
unsigned int* sym_row_P = (unsigned int*) malloc((N + 1) * sizeof(unsigned int));
unsigned int* sym_col_P = (unsigned int*) malloc(no_elem * sizeof(unsigned int));
double* sym_val_P = (double*) malloc(no_elem * sizeof(double));
if(sym_row_P == NULL || sym_col_P == NULL || sym_val_P == NULL) { printf("Memory allocation failed!\n"); exit(1); }
// Construct new row indices for symmetric matrix
sym_row_P[0] = 0;
for(int n = 0; n < N; n++) sym_row_P[n + 1] = sym_row_P[n] + (unsigned int) row_counts[n];
// Fill the result matrix
int* offset = (int*) calloc(N, sizeof(int));
if(offset == NULL) { printf("Memory allocation failed!\n"); exit(1); }
for(int n = 0; n < N; n++) {
for(unsigned int i = row_P[n]; i < row_P[n + 1]; i++) { // considering element(n, col_P[i])
// Check whether element (col_P[i], n) is present
bool present = false;
for(unsigned int m = row_P[col_P[i]]; m < row_P[col_P[i] + 1]; m++) {
if(col_P[m] == n) {
present = true;
if(n <= col_P[i]) { // make sure we do not add elements twice
sym_col_P[sym_row_P[n] + offset[n]] = col_P[i];
sym_col_P[sym_row_P[col_P[i]] + offset[col_P[i]]] = n;
sym_val_P[sym_row_P[n] + offset[n]] = val_P[i] + val_P[m];
sym_val_P[sym_row_P[col_P[i]] + offset[col_P[i]]] = val_P[i] + val_P[m];
}
}
}
// If (col_P[i], n) is not present, there is no addition involved
if(!present) {
sym_col_P[sym_row_P[n] + offset[n]] = col_P[i];
sym_col_P[sym_row_P[col_P[i]] + offset[col_P[i]]] = n;
sym_val_P[sym_row_P[n] + offset[n]] = val_P[i];
sym_val_P[sym_row_P[col_P[i]] + offset[col_P[i]]] = val_P[i];
}
// Update offsets
if(!present || (present && n <= col_P[i])) {
offset[n]++;
if(col_P[i] != n) offset[col_P[i]]++;
}
}
}
// Divide the result by two
for(int i = 0; i < no_elem; i++) sym_val_P[i] /= 2.0;
// Return symmetrized matrices
free(*_row_P); *_row_P = sym_row_P;
free(*_col_P); *_col_P = sym_col_P;
free(*_val_P); *_val_P = sym_val_P;
// Free up some memery
free(offset); offset = NULL;
free(row_counts); row_counts = NULL;
}
// Compute squared Euclidean distance matrix
static void computeSquaredEuclideanDistance(double* X, int N, int D, double* DD) {
const double* XnD = X;
for(int n = 0; n < N; ++n, XnD += D) {
const double* XmD = XnD + D;
double* curr_elem = &DD[n*N + n];
*curr_elem = 0.0;
double* curr_elem_sym = curr_elem + N;
for(int m = n + 1; m < N; ++m, XmD+=D, curr_elem_sym+=N) {
*(++curr_elem) = 0.0;
for(int d = 0; d < D; ++d) {
*curr_elem += (XnD[d] - XmD[d]) * (XnD[d] - XmD[d]);
}
*curr_elem_sym = *curr_elem;
}
}
}
// Makes data zero-mean
static void zeroMean(double* X, int N, int D) {
// Compute data mean
double* mean = (double*) calloc(D, sizeof(double));
if(mean == NULL) { printf("Memory allocation failed!\n"); exit(1); }
int nD = 0;
for(int n = 0; n < N; n++) {
for(int d = 0; d < D; d++) {
mean[d] += X[nD + d];
}
nD += D;
}
for(int d = 0; d < D; d++) {
mean[d] /= (double) N;
}
// Subtract data mean
nD = 0;
for(int n = 0; n < N; n++) {
for(int d = 0; d < D; d++) {
X[nD + d] -= mean[d];
}
nD += D;
}
free(mean); mean = NULL;
}
// Generates a Gaussian random number
static double randn() {
double x, y, radius;
do {
x = 2 * (rand() / ((double) RAND_MAX + 1)) - 1;
y = 2 * (rand() / ((double) RAND_MAX + 1)) - 1;
radius = (x * x) + (y * y);
} while((radius >= 1.0) || (radius == 0.0));
radius = sqrt(-2 * log(radius) / radius);
x *= radius;
y *= radius;
return x;
}
// Function that loads data from a t-SNE file
// Note: this function does a malloc that should be freed elsewhere
bool TSNE::load_data(double** data, int* n, int* d, int* no_dims, double* theta, double* perplexity, int* rand_seed, int* max_iter) {
// Open file, read first 2 integers, allocate memory, and read the data
FILE *h;
if((h = fopen("data.dat", "r+b")) == NULL) {
printf("Error: could not open data file.\n");
return false;
}
fread(n, sizeof(int), 1, h); // number of datapoints
fread(d, sizeof(int), 1, h); // original dimensionality
fread(theta, sizeof(double), 1, h); // gradient accuracy
fread(perplexity, sizeof(double), 1, h); // perplexity
fread(no_dims, sizeof(int), 1, h); // output dimensionality
fread(max_iter, sizeof(int),1,h); // maximum number of iterations
*data = (double*) malloc(*d * *n * sizeof(double));
if(*data == NULL) { printf("Memory allocation failed!\n"); exit(1); }
fread(*data, sizeof(double), *n * *d, h); // the data
if(!feof(h)) fread(rand_seed, sizeof(int), 1, h); // random seed
fclose(h);
printf("Read the %i x %i data matrix successfully!\n", *n, *d);
return true;
}
// Function that saves map to a t-SNE file
void TSNE::save_data(double* data, int* landmarks, double* costs, int n, int d) {
// Open file, write first 2 integers and then the data
FILE *h;
if((h = fopen("result.dat", "w+b")) == NULL) {
printf("Error: could not open data file.\n");
return;
}
fwrite(&n, sizeof(int), 1, h);
fwrite(&d, sizeof(int), 1, h);
fwrite(data, sizeof(double), n * d, h);
fwrite(landmarks, sizeof(int), n, h);
fwrite(costs, sizeof(double), n, h);
fclose(h);
printf("Wrote the %i x %i data matrix successfully!\n", n, d);
}
// Function that saves a 1D array in the numpy.savetxt format
void save_1D_array(double* array, int n, const char* filename) {
// Open file, write first 2 integers and then the data
FILE *h;
if((h = fopen(filename, "w")) == NULL) {
printf("Error: could not open [%s] for writing.\n", filename);
return;
}
//fprintf(h, "%d\n", n);
for (int i = 0; i < n; ++i)
fprintf(h, "%f\n", array[i]);
fclose(h);
printf("Wrote [%s] successfully, with %i rows!\n", filename, n);
}