/* compute the mean, the covariance matrix, and the eigenvectors.
They are stored in the structure itself */
void pca_online_complete (struct pca_online_s * pca)
{
int d = pca->d;
int n = pca->n;
fvec_div_by (pca->mu, d, n);
fvec_div_by (pca->cov, d * d, n);
float * mumut = fvec_new (d*d);
fmat_mul_tr (pca->mu, pca->mu, d, d, 1, mumut);
fvec_sub (pca->cov, mumut, d*d);
free (mumut);
assert(fvec_all_finite(pca->cov,d*d));
pca->eigvec = fmat_new_pca_from_covariance (d, pca->cov, pca->eigval);
}
/* compute the mean and covariance matrix */
void pca_online_cov (struct pca_online_s * pca)
{
int d = pca->d;
int n = pca->n;
fvec_div_by (pca->mu, d, n);
fvec_div_by (pca->cov, d * (long)d, n);
float * mumut = fvec_new (d*(long)d);
fmat_mul_tr (pca->mu, pca->mu, d, d, 1, mumut);
fvec_sub (pca->cov, mumut, d*(long)d);
free (mumut);
fvec_mul_by (pca->cov, d * (long)d, n / (double) (n-1));
assert(fvec_all_finite(pca->cov,d*(long)d));
pca->n = -pca->n;
}
/* Accumulate information for PCA for n input vectors */
void pca_online_accu (struct pca_online_s * pca, const float * v, long n)
{
int d = pca->d;
float * cov = fvec_new (d*(long)d);
float * mu = fvec_new (d);
fmat_sum_rows (v, d, n, mu);
fmat_mul_tr (v, v, d, d, n, cov);
fvec_add (pca->mu, mu, d);
fvec_add (pca->cov, cov, d*(long)d);
pca->n += n;
free (cov);
free (mu);
}
void gmm_fisher_save_soft_assgn(int n, const float *v, const gmm_t * g, int flags,
float *dp_dlambda,
float *word_total_soft_assignment) {
long d=g->d, k=g->k;
float *p = fvec_new(n * k);
long i,j,l;
long ii=0;
float * vp = NULL; /* v*p */
float * sum_pj = NULL; /* sum of p's for a given j */
gmm_compute_p(n,v,g,p,flags | GMM_FLAGS_W);
#define P(j,i) p[(i)*k+(j)]
#define V(l,i) v[(i)*d+(l)]
#define MU(l,j) g->mu[(j)*d+(l)]
#define SIGMA(l,j) g->sigma[(j)*d+(l)]
#define VP(l,j) vp[(j)*d+(l)]
// Save total soft assignment per centroid
if (word_total_soft_assignment != NULL) {
for (j=0; j<k; j++) {
double sum=0;
for (i=0; i<n; i++) {
sum += P(j,i);
}
if (n != 0) {
word_total_soft_assignment[j] = (float)(sum/n);
} else {
word_total_soft_assignment[j] = 0.0;
}
}
}
if(flags & GMM_FLAGS_W) {
for(j=1; j<k; j++) {
double accu=0;
for(i=0; i<n; i++)
accu+= P(j,i)/g->w[j] - P(0,i)/g->w[0];
/* normalization */
double f=n*(1/g->w[j]+1/g->w[0]);
dp_dlambda[ii++]=accu/sqrt(f);
}
}
if(flags & GMM_FLAGS_MU) {
float *dp_dmu=dp_dlambda+ii;
#define DP_DMU(l,j) dp_dmu[(j)*d+(l)]
if(0) { /* simple and slow */
for(j=0; j<k; j++) {
for(l=0; l<d; l++) {
double accu=0;
for(i=0; i<n; i++)
accu += P(j,i) * (V(l,i)-MU(l,j)) / SIGMA(l,j);
DP_DMU(l,j)=accu;
}
}
} else { /* complicated and fast */
/* precompute tables that may be useful for sigma too */
vp = fvec_new(k * d);
fmat_mul_tr(v,p,d,k,n,vp);
sum_pj = fvec_new(k);
for(j=0; j<k; j++) {
double sum=0;
for(i=0; i<n; i++) sum += P(j,i);
sum_pj[j] = sum;
}
for(j=0; j<k; j++) {
for(l=0; l<d; l++)
DP_DMU(l,j) = (VP(l,j) - MU(l,j) * sum_pj[j]) / SIGMA(l,j);
}
}
/* normalization */
if(!(flags & GMM_FLAGS_NO_NORM)) {
for(j=0; j<k; j++)
for(l=0; l<d; l++) {
float nf = sqrt(n*g->w[j]/SIGMA(l,j));
if(nf > 0) DP_DMU(l,j) /= nf;
}
}
#undef DP_DMU
ii+=d*k;
}
if(flags & (GMM_FLAGS_SIGMA | GMM_FLAGS_1SIGMA)) {
if(flags & GMM_FLAGS_1SIGMA) { /* fast not implemented for 1 sigma */
for(j=0; j<k; j++) {
double accu2=0;
for(l=0; l<d; l++) {
double accu=0;
for(i=0; i<n; i++)
accu += P(j,i) * (sqr(V(l,i)-MU(l,j)) / SIGMA(l,j) - 1) / sqrt(SIGMA(l,j));
if(flags & GMM_FLAGS_SIGMA) {
double f=flags & GMM_FLAGS_NO_NORM ? 1.0 : 2*n*g->w[j]/SIGMA(l,j);
dp_dlambda[ii++]=accu/sqrt(f);
}
accu2+=accu;
}
if(flags & GMM_FLAGS_1SIGMA) {
double f=flags & GMM_FLAGS_NO_NORM ? 1.0 : 2*d*n*g->w[j]/SIGMA(0,j);
dp_dlambda[ii++]=accu2/sqrt(f);
}
}
} else { /* fast and complicated */
assert(flags & GMM_FLAGS_SIGMA);
float *dp_dsigma = dp_dlambda + ii;
if(!vp) {
vp = fvec_new(k * d);
fmat_mul_tr(v,p,d,k,n,vp);
}
if(!sum_pj) {
sum_pj = fvec_new(k);
for(j=0; j<k; j++) {
double sum=0;
for(i=0; i<n; i++) sum += P(j,i);
sum_pj[j] = sum;
}
}
float *v2 = fvec_new(n * d);
for(i = n*d-1 ; i >= 0; i--) v2[i] = v[i] * v[i];
float *v2p = fvec_new(k * d);
fmat_mul_tr(v2,p,d,k,n,v2p);
free(v2);
#define V2P(l,j) v2p[(j)*d+(l)]
#define DP_DSIGMA(i,j) dp_dsigma[(i)+(j)*d]
for(j=0; j<k; j++) {
for(l=0; l<d; l++) {
double accu;
accu = V2P(l, j);
accu += VP(l, j) * (- 2 * MU(l,j));
accu += sum_pj[j] * (sqr(MU(l,j)) - SIGMA(l,j));
/* normalization */
double f;
if(flags & GMM_FLAGS_NO_NORM) {
f = pow(SIGMA(l,j), -1.5);
} else {
f = 1 / (SIGMA(l,j) * sqrt(2*n*g->w[j]));
}
DP_DSIGMA(l,j) = accu * f;
}
}
free(v2p);
#undef DP_DSIGMA
#undef V2P
ii += d * k;
}
}
assert(ii==gmm_fisher_sizeof(g,flags));
#undef P
#undef V
#undef MU
#undef SIGMA
free(p);
free(sum_pj);
free(vp);
}
