// Evaluate t-SNE cost function (approximately)
double TSNE::evaluateError(int* row_P, int* col_P, double* val_P, double* Y, int N, double theta)
{
// Get estimate of normalization term
const int QT_NO_DIMS = 2;
QuadTree* tree = new QuadTree(Y, N);
double buff[QT_NO_DIMS] = {.0, .0};
double sum_Q = .0;
for(int n = 0; n < N; n++) tree->computeNonEdgeForces(n, theta, buff, &sum_Q);
// Loop over all edges to compute t-SNE error
int ind1, ind2;
double C = .0, Q;
for(int n = 0; n < N; n++) {
ind1 = n * QT_NO_DIMS;
for(int i = row_P[n]; i < row_P[n + 1]; i++) {
Q = .0;
ind2 = col_P[i] * QT_NO_DIMS;
for(int d = 0; d < QT_NO_DIMS; d++) buff[d] = Y[ind1 + d];
for(int d = 0; d < QT_NO_DIMS; d++) buff[d] -= Y[ind2 + d];
for(int d = 0; d < QT_NO_DIMS; 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));
}
}
return C;
}
// Compute gradient of the t-SNE cost function (using Barnes-Hut algorithm)
void TSNE::computeGradient(double* P, int* inp_row_P, int* inp_col_P, double* inp_val_P, double* Y, int N, int D, double* dC, double theta)
{
// Construct quadtree on current map
QuadTree* tree = new QuadTree(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;
}