1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
|
#include "mp.h"
#include <algorithm>
#include "utils.h"
static const double EPSILON = 1e-6;
arma::mat mp::lamp(const arma::mat &X, const arma::uvec &sampleIndices, const arma::mat &Ys)
{
arma::mat projection(X.n_rows, 2);
lamp(X, sampleIndices, Ys, projection);
return projection;
}
void mp::lamp(const arma::mat &X, const arma::uvec &sampleIndices, const arma::mat &Ys, arma::mat &Y)
{
int n = uintToInt<arma::uword, int>(X.n_rows);
const arma::mat &Xs = X.rows(sampleIndices);
arma::uword sampleSize = sampleIndices.n_elem;
#pragma omp parallel for shared(X, Xs, Ys, Y, n)
for (int i = 0; i < n; i++) {
const arma::rowvec &point = X.row(i);
// calculate alphas
arma::rowvec alphas(sampleSize);
for (arma::uword j = 0; j < sampleSize; j++) {
double dist = arma::accu(arma::square(Xs.row(j) - point));
alphas[j] = 1. / std::max(dist, EPSILON);
}
double alphas_sum = arma::accu(alphas);
// calculate \tilde{X} and \tilde{Y}
arma::rowvec Xtil = arma::sum(alphas * Xs, 0) / alphas_sum;
arma::rowvec Ytil = arma::sum(alphas * Ys, 0) / alphas_sum;
// calculate \hat{X} and \hat{Y}
arma::mat Xhat = Xs;
Xhat.each_row() -= Xtil;
arma::mat Yhat = Ys;
Yhat.each_row() -= Ytil;
// calculate A and B
alphas = arma::sqrt(alphas);
arma::mat &At = Xhat;
inplace_trans(At);
At.each_row() %= alphas;
arma::mat &B = Yhat;
B.each_col() %= alphas.t();
arma::mat U, V;
arma::vec s(Ys.n_cols);
arma::svd(U, s, V, At * B);
arma::mat M = U.head_cols(Ys.n_cols) * V.t();
Y.row(i) = (point - Xtil) * M + Ytil;
}
for (arma::uword i = 0; i < sampleSize; i++) {
Y.row(sampleIndices[i]) = Ys.row(i);
}
}
|
