/**
* ICA function. Computes the W matrix from the
* preprocessed data.
*/
static mat ICA_compute(mat X, int rows, int cols)
{
mat TXp, GWX, W, Wd, W1, D, TU, TMP;
vect d, lim;
int i, it;
// matrix creation
TXp = mat_create(cols, rows);
GWX = mat_create(rows, cols);
W = mat_create(rows, rows);
Wd = mat_create(rows, rows);
D = mat_create(rows, rows);
TMP = mat_create(rows, rows);
TU = mat_create(rows, rows);
W1 = mat_create(rows, rows);
d = vect_create(rows);
// W rand init
mat_apply_fx(W, rows, rows, fx_rand, 0);
// sW <- La.svd(W)
mat_copy(W, rows, rows, Wd);
svdcmp(Wd, rows, rows, d, D);
// W <- sW$u %*% diag(1/sW$d) %*% t(sW$u) %*% W
mat_transpose(Wd, rows, rows, TU);
vect_apply_fx(d, rows, fx_inv, 0);
mat_diag(d, rows, D);
mat_mult(Wd, rows, rows, D, rows, rows, TMP);
mat_mult(TMP, rows, rows, TU, rows, rows, D);
mat_mult(D, rows, rows, W, rows, rows, Wd); // W = Wd
// W1 <- W
mat_copy(Wd, rows, rows, W1);
// lim <- rep(1000, maxit); it = 1
lim = vect_create(MAX_ITERATIONS);
for (i=0; i<MAX_ITERATIONS; i++)
lim[i] = 1000;
it = 0;
// t(X)/p
mat_transpose(X, rows, cols, TXp);
mat_apply_fx(TXp, cols, rows, fx_div_c, cols);
while (lim[it] > TOLERANCE && it < MAX_ITERATIONS) {
// wx <- W %*% X
mat_mult(Wd, rows, rows, X, rows, cols, GWX);
// gwx <- tanh(alpha * wx)
mat_apply_fx(GWX, rows, cols, fx_tanh, 0);
// v1 <- gwx %*% t(X)/p
mat_mult(GWX, rows, cols, TXp, cols, rows, TMP); // V1 = TMP
// g.wx <- alpha * (1 - (gwx)^2)
mat_apply_fx(GWX, rows, cols, fx_1sub_sqr, 0);
// v2 <- diag(apply(g.wx, 1, FUN = mean)) %*% W
mat_mean_rows(GWX, rows, cols, d);
mat_diag(d, rows, D);
mat_mult(D, rows, rows, Wd, rows, rows, TU); // V2 = TU
// W1 <- v1 - v2
mat_sub(TMP, TU, rows, rows, W1);
// sW1 <- La.svd(W1)
mat_copy(W1, rows, rows, W);
svdcmp(W, rows, rows, d, D);
// W1 <- sW1$u %*% diag(1/sW1$d) %*% t(sW1$u) %*% W1
mat_transpose(W, rows, rows, TU);
vect_apply_fx(d, rows, fx_inv, 0);
mat_diag(d, rows, D);
mat_mult(W, rows, rows, D, rows, rows, TMP);
mat_mult(TMP, rows, rows, TU, rows, rows, D);
mat_mult(D, rows, rows, W1, rows, rows, W); // W1 = W
// lim[it + 1] <- max(Mod(Mod(diag(W1 %*% t(W))) - 1))
mat_transpose(Wd, rows, rows, TU);
mat_mult(W, rows, rows, TU, rows, rows, TMP);
lim[it+1] = fabs(mat_max_diag(TMP, rows, rows) - 1);
// W <- W1
mat_copy(W, rows, rows, Wd);
it++;
}
// clean up
mat_delete(TXp, cols, rows);
mat_delete(GWX, rows, cols);
mat_delete(W, rows, rows);
mat_delete(D, rows, rows);
mat_delete(TMP, rows, rows);
mat_delete(TU, rows, rows);
mat_delete(W1, rows, rows);
vect_delete(d);
return Wd;
}
/**
* Main FastICA function. Centers and whitens the input
* matrix, calls the ICA computation function ICA_compute()
* and computes the output matrixes.
*/
void fastICA(mat X, int rows, int cols, int compc, mat K, mat W, mat A, mat S) {
mat XT, V, TU, D, X1, _A;
vect scale, d;
clock_t clock1, clock2;
float time;
//char ascii_path[512];
//strcpy(ascii_path, "/storage/sdcard0/NickGun/EEG/Log.txt");
//FILE *Log;
//chu thich voi truong hop 14 kenh, 2s (256mau) du lieu, 14 thanh phan doc lap>>> cols = 14, rows = 256, compc = 14
// matrix creation
XT = mat_create(cols, rows); //14x256
X1 = mat_create(compc, rows); //14x256
V = mat_create(cols, cols); //14x14
D = mat_create(cols, cols); //14x14
TU = mat_create(cols, cols); //14x14
scale = vect_create(cols); //14
d = vect_create(cols); //14
clock1 = clock();
/*
* CENTERING
*/
mat_center(X, rows, cols, scale); //tru di gia tri trung binh cua moi cot
clock2 = clock();
time = (clock2 - clock1) / CLOCKS_PER_SEC;
//Log = fopen(ascii_path, "wb");
//fprintf(Log, "CENTERING %f \n", time);
//fclose(Log);
clock1 = clock();
/*
* WHITENING
*/
// X <- t(X); V <- X %*% t(X)/rows
mat_transpose(X, rows, cols, XT); //XT la chuyen vi cua ma tran X[256][14] >>> XT[14][256]
mat_apply_fx(X, rows, cols, fx_div_c, rows); //lay tung gia tri cua X[i][j] chia cho 14
mat_mult(XT, cols, rows, X, rows, cols, V); //V=XT*X >>>V[14][14]
// La.svd(V)
svdcmp(V, cols, cols, d, D); // V = s$u, d = s$d, D = s$v
// D <- diag(c(1/sqrt(d))
vect_apply_fx(d, cols, fx_inv_sqrt, 0);
mat_diag(d, cols, D);
// K <- D %*% t(U)
mat_transpose(V, cols, cols, TU);
mat_mult(D, cols, cols, TU, cols, cols, V); // K = V
// X1 <- K %*% X
mat_mult(V, compc, cols, XT, cols, rows, X1);
clock2 = clock();
time = (clock2 - clock1) / CLOCKS_PER_SEC;
//Log = fopen(ascii_path, "at");
//fprintf(Log, "WHITENING %f \n", time);
//fclose(Log);
clock1 = clock();
/*
* FAST ICA
*/
_A = ICA_compute(X1, compc, rows);
clock2 = clock();
time = (clock2 - clock1) / CLOCKS_PER_SEC;
//Log = fopen(ascii_path, "at");
//fprintf(Log, "FASTICA %f \n", time);
//fclose(Log);
clock1 = clock();
/*
* OUTPUT
*/
// X <- t(x)
mat_transpose(XT, cols, rows, X);
mat_decenter(X, rows, cols, scale);
// K
mat_transpose(V, compc, cols, K);
// w <- a %*% K; S <- w %*% X
mat_mult(_A, compc, compc, V, compc, cols, D);
mat_mult(D, compc, cols, XT, cols, rows, X1);
// S
mat_transpose(X1, compc, rows, S);
// A <- t(w) %*% solve(w * t(w))
mat_transpose(D, compc, compc, TU);
mat_mult(D, compc, compc, TU, compc, compc, V);
mat_inverse(V, compc, D); //ham nay tinh mat tran ngich dao
mat_mult(TU, compc, compc, D, compc, compc, V);
// A
mat_transpose(V, compc, compc, A);
// W
mat_transpose(_A, compc, compc, W);
// cleanup
mat_delete(XT, cols, rows);
mat_delete(X1, compc, rows);
mat_delete(V, cols, cols);
mat_delete(D, cols, cols);
mat_delete(TU, cols, cols);
vect_delete(scale);
vect_delete(d);
clock2 = clock();
time = (clock2 - clock1) / CLOCKS_PER_SEC;
//Log = fopen(ascii_path, "at");
//fprintf(Log, "OUTPUT %f \n", time);
//fclose(Log);
}
/**
* Main FastICA function. Centers and whitens the input
* matrix, calls the ICA computation function ICA_compute()
* and computes the output matrixes.
*/
void fastICA(mat X, int rows, int cols, int compc, mat K, mat W, mat A, mat S)
{
mat XT, V, TU, D, X1, _A;
vect scale, d;
// matrix creation
XT = mat_create(cols, rows);
X1 = mat_create(compc, rows);
V = mat_create(cols, cols);
D = mat_create(cols, cols);
TU = mat_create(cols, cols);
scale = vect_create(cols);
d = vect_create(cols);
/*
* CENTERING
*/
mat_center(X, rows, cols, scale);
/*
* WHITENING
*/
// X <- t(X); V <- X %*% t(X)/rows
mat_transpose(X, rows, cols, XT);
mat_apply_fx(X, rows, cols, fx_div_c, rows);
mat_mult(XT, cols, rows, X, rows, cols, V);
// La.svd(V)
svdcmp(V, cols, cols, d, D); // V = s$u, d = s$d, D = s$v
// D <- diag(c(1/sqrt(d))
vect_apply_fx(d, cols, fx_inv_sqrt, 0);
mat_diag(d, cols, D);
// K <- D %*% t(U)
mat_transpose(V, cols, cols, TU);
mat_mult(D, cols, cols, TU, cols, cols, V); // K = V
// X1 <- K %*% X
mat_mult(V, compc, cols, XT, cols, rows, X1);
/*
* FAST ICA
*/
_A = ICA_compute(X1, compc, rows);
/*
* OUTPUT
*/
// X <- t(x)
mat_transpose(XT, cols, rows, X);
mat_decenter(X, rows, cols, scale);
// K
mat_transpose(V, compc, cols, K);
// w <- a %*% K; S <- w %*% X
mat_mult(_A, compc, compc, V, compc, cols, D);
mat_mult(D, compc, cols, XT, cols, rows, X1);
// S
mat_transpose(X1, compc, rows, S);
// A <- t(w) %*% solve(w * t(w))
mat_transpose(D, compc, compc, TU);
mat_mult(D, compc, compc, TU, compc, compc, V);
mat_inverse(V, compc, D);
mat_mult(TU, compc, compc, D, compc, compc, V);
// A
mat_transpose(V, compc, compc, A);
// W
mat_transpose(_A, compc, compc, W);
// cleanup
mat_delete(XT, cols, rows);
mat_delete(X1, compc, rows);
mat_delete(V, cols, cols);
mat_delete(D, cols, cols);
mat_delete(TU,cols, cols);
vect_delete(scale);
vect_delete(d);
}
/**
* ICA function. Computes the W matrix from the
* preprocessed data.
*/
static mat ICA_compute(mat X, int rows, int cols) {
mat TXp, GWX, W, Wd, W1, D, TU, TMP;
vect d, lim;
int i, it;
FILE *OutputFile;
clock_t clock1, clock2;
float time;
//char ascii_path[512];
//strcpy(ascii_path, "/storage/sdcard0/NickGun/EEG/Log.txt");
//FILE *Log;
// matrix creation
TXp = mat_create(cols, rows);
GWX = mat_create(rows, cols);
W = mat_create(rows, rows);
Wd = mat_create(rows, rows);
D = mat_create(rows, rows);
TMP = mat_create(rows, rows);
TU = mat_create(rows, rows);
W1 = mat_create(rows, rows);
d = vect_create(rows);
// W rand init
mat_apply_fx(W, rows, rows, fx_rand, 0);
// sW <- La.svd(W)
mat_copy(W, rows, rows, Wd);
svdcmp(Wd, rows, rows, d, D);
// W <- sW$u %*% diag(1/sW$d) %*% t(sW$u) %*% W
mat_transpose(Wd, rows, rows, TU);
vect_apply_fx(d, rows, fx_inv, 0);
mat_diag(d, rows, D);
mat_mult(Wd, rows, rows, D, rows, rows, TMP);
mat_mult(TMP, rows, rows, TU, rows, rows, D);
mat_mult(D, rows, rows, W, rows, rows, Wd); // W = Wd
// W1 <- W
mat_copy(Wd, rows, rows, W1);
// lim <- rep(1000, maxit); it = 1
lim = vect_create(MAX_ITERATIONS);
for (i = 0; i < MAX_ITERATIONS; i++)
lim[i] = 1000;
it = 0;
// t(X)/p
mat_transpose(X, rows, cols, TXp);
mat_apply_fx(TXp, cols, rows, fx_div_c, cols);
while (lim[it] > TOLERANCE && it < MAX_ITERATIONS) {
// wx <- W %*% X
mat_mult(Wd, rows, rows, X, rows, cols, GWX);
// gwx <- tanh(alpha * wx)
mat_apply_fx(GWX, rows, cols, fx_tanh, 0);
// v1 <- gwx %*% t(X)/p
mat_mult(GWX, rows, cols, TXp, cols, rows, TMP); // V1 = TMP
// g.wx <- alpha * (1 - (gwx)^2)
mat_apply_fx(GWX, rows, cols, fx_1sub_sqr, 0);
// v2 <- diag(apply(g.wx, 1, FUN = mean)) %*% W
mat_mean_rows(GWX, rows, cols, d);
mat_diag(d, rows, D);
mat_mult(D, rows, rows, Wd, rows, rows, TU); // V2 = TU
// W1 <- v1 - v2
mat_sub(TMP, TU, rows, rows, W1);
// sW1 <- La.svd(W1)
mat_copy(W1, rows, rows, W);
svdcmp(W, rows, rows, d, D);
// W1 <- sW1$u %*% diag(1/sW1$d) %*% t(sW1$u) %*% W1
mat_transpose(W, rows, rows, TU);
vect_apply_fx(d, rows, fx_inv, 0);
mat_diag(d, rows, D);
mat_mult(W, rows, rows, D, rows, rows, TMP);
mat_mult(TMP, rows, rows, TU, rows, rows, D);
mat_mult(D, rows, rows, W1, rows, rows, W); // W1 = W
// lim[it + 1] <- max(Mod(Mod(diag(W1 %*% t(W))) - 1))
mat_transpose(Wd, rows, rows, TU); //chuyen vi
mat_mult(W, rows, rows, TU, rows, rows, TMP); //TMP=WxTU
lim[it + 1] = fabs(mat_max_diag(TMP, rows, rows) - 1);
if(lim[it+1]<0.1)
break;
/*
OutputFile = fopen("/storage/sdcard0/Nickgun/EEG/data/lim",
"at");
fprintf(OutputFile, "%f \n", lim[it+1]);
fclose(OutputFile);
// W <- W1
*/
mat_copy(W, rows, rows, Wd);
it++;
}
// clean up
mat_delete(TXp, cols, rows);
mat_delete(GWX, rows, cols);
mat_delete(W, rows, rows);
mat_delete(D, rows, rows);
mat_delete(TMP, rows, rows);
mat_delete(TU, rows, rows);
mat_delete(W1, rows, rows);
vect_delete(d);
return Wd;
}