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#include "mp.h"
#include <algorithm>
#include <cmath>
static const double ETA = 500;
static const double MIN_GAIN = 1e-2;
static const double EPSILON = 1e-12;
static const double INITIAL_MOMENTUM = 0.5;
static const double FINAL_MOMENTUM = 0.8;
static const double EARLY_EXAGGERATION = 4.;
static const double GAIN_FRACTION = 0.2;
static const int MOMENTUM_THRESHOLD_ITER = 20;
static const int EXAGGERATION_THRESHOLD_ITER = 100;
static const int MAX_BINSEARCH_TRIES = 50;
static void calcP(const arma::mat &X, arma::mat &P, double perplexity, double tol = 1e-5);
static double hBeta(const arma::rowvec &Di, double beta, arma::rowvec &Pi);
arma::mat mp::tSNE(const arma::mat &X, arma::uword k, double perplexity, arma::uword nIter)
{
arma::mat Y(X.n_rows, k);
mp::tSNE(X, Y, perplexity, nIter);
return Y;
}
void mp::tSNE(const arma::mat &X, arma::mat &Y, double perplexity, arma::uword nIter)
{
double momentum;
arma::uword n = X.n_rows;
arma::uword k = Y.n_cols;
arma::mat Q(n, n);
arma::mat dY(n, k),
gains(n, k, arma::fill::ones),
iY(n, k, arma::fill::zeros);
arma::mat P(n, n, arma::fill::zeros);
calcP(X, P, perplexity);
P = (P + P.t());
P /= arma::accu(P);
P *= EARLY_EXAGGERATION;
P.transform([](double v) { return std::max(v, EPSILON); });
for (arma::uword iter = 0; iter < nIter; iter++) {
arma::vec sumY = arma::sum(Y % Y, 1);
arma::mat num = -2. * (Y * Y.t());
num.each_col() += sumY;
arma::inplace_trans(num);
num.each_col() += sumY;
num = 1. / (1. + num);
num.diag() *= 0;
Q = num / arma::accu(num);
Q.transform([](double v) { return std::max(v, EPSILON); });
for (arma::uword i = 0; i < n; i++) {
arma::mat tmp = -Y;
tmp.each_row() += Y.row(i);
tmp.each_col() %= (P.col(i) - Q.col(i)) % num.col(i);
dY.row(i) = arma::sum(tmp, 0);
}
momentum = (iter < MOMENTUM_THRESHOLD_ITER) ? INITIAL_MOMENTUM : FINAL_MOMENTUM;
gains = (gains + GAIN_FRACTION) % ((dY > 0) != (iY > 0))
+ (gains * (1 - GAIN_FRACTION)) % ((dY > 0) == (iY > 0));
gains.transform([](double v) { return std::max(v, MIN_GAIN); });
iY = momentum * iY - ETA * (gains % dY);
Y += iY;
Y.each_row() -= mean(Y, 0);
if (iter == EXAGGERATION_THRESHOLD_ITER)
P /= EARLY_EXAGGERATION; // remove early exaggeration
}
}
static void calcP(const arma::mat &X, arma::mat &P, double perplexity, double tol) {
arma::colvec sumX = arma::sum(X % X, 1);
arma::mat D = -2 * (X * X.t());
D.each_col() += sumX;
arma::inplace_trans(D);
D.each_col() += sumX;
D.diag() *= 0;
double logU = log(perplexity);
arma::rowvec beta(X.n_rows, arma::fill::ones);
arma::rowvec Pi(X.n_rows);
for (arma::uword i = 0; i < X.n_rows; i++) {
double betaMin = -arma::datum::inf;
double betaMax = arma::datum::inf;
arma::rowvec Di = D.row(i);
double h = hBeta(Di, beta[i], Pi);
double hDiff = h - logU;
for (int tries = 0; fabs(hDiff) > tol && tries < MAX_BINSEARCH_TRIES; tries++) {
if (hDiff > 0) {
betaMin = beta[i];
if (betaMax == arma::datum::inf || betaMax == -arma::datum::inf)
beta[i] *= 2;
else
beta[i] = (beta[i] + betaMax) / 2.;
} else {
betaMax = beta[i];
if (betaMin == arma::datum::inf || betaMin == -arma::datum::inf)
beta[i] /= 2;
else
beta[i] = (beta[i] + betaMin) / 2.;
}
h = hBeta(Di, beta[i], Pi);
hDiff = h - logU;
}
P.row(i) = Pi;
}
}
static inline double hBeta(const arma::rowvec &Di, double beta, arma::rowvec &Pi) {
Pi = arma::exp(-Di * beta);
double sumPi = arma::accu(Pi);
double h = log(sumPi) + beta * arma::accu(Di % Pi) / sumPi;
Pi /= sumPi;
return h;
}
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