/* 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); }