/* File name: cda.c Created by: Ljubomir Buturovic Created: 02/12/2003 Purpose: principal components analysis and Fisher's linear discriminant. */ /* Copyright 2004 Ljubomir J. Buturovic Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. */ #include #include #include #include "lerr.h" #include "cda.h" #include "pcp.h" #include "pau.h" #include "lau.h" #include "lmat.h" static char rcsid[] = "$Id: cda.c,v 1.23 2005/02/11 19:35:54 ljubomir Exp $"; /* Calculate principal components transformation matrix on 'dset'. Return -1 in case of error and set 'errc'. Errors are malloc() errors and LERR_ITMAX in eigen(). */ float **pca(struct dataset *dset, int *errc) { int i; int j; int nv; int status; float **sigma; float **pcamx; pcamx = (float **) 0; /* Calculate Sw matrix, which is the overall covariance matrix estimate times (nv-1). */ sigma = cest(dset->x, dset->d, dset->nv, COVARIANCE_MATRIX); nv = dset->nv; for (i = 0; i < dset->d; i++) for (j = 0; j < dset->d; j++) sigma[i][j] = (nv-1)*sigma[i][j]; /* Peform eigenanalysis. */ status = eigsn(sigma, dset->d, (float **) 0, &pcamx, errc); mx_free((void **) sigma, dset->d); if (status == -1) pcamx = (float **) 0; return pcamx; } /* Calculate Fisher's linear discriminant (transformation matrix) on 'dset'. Return -1 in case of error and set 'errc'. Errors are malloc() errors and LERR_ITMAX in eigen(). */ float **fld(struct dataset *dset, int *errc) { int i; int j; int m; int d; int status; int offset; int nv; float dsign; float dexp; float *mean; /* data set mean */ float *diff; float **xmean; /* class means */ float **sigma; float **sw; /* scatter matrix */ float **swi; /* inverse of scatter matrix */ float **sb; /* general between-class scatter matrix */ float **mx; /* inv(Sw)*Sb */ float **tmx; /* the transformation matrix */ float *evl; /* TESTING */ /* Calculate Sw. */ status = 0; tmx = (float **) 0; d = dset->d; evl = malloc(d*sizeof(float)); /* TESTING */ mean = mest(dset->x, d, dset->nv); xmean = malloc(dset->c*sizeof(float *)); offset = 0; for (i = 0; i < dset->c; i++) { xmean[i] = mest(&dset->x[offset], d, dset->nd[i]); offset += dset->nd[i]; } sw = fmx_alloc(d, d); if (sw) { fmx_set(sw, d, d, 0.0); offset = 0; for (m = 0; (m < dset->c) && !status; m++) { sigma = cest(&dset->x[offset], d, dset->nd[m], COVARIANCE_MATRIX); if (sigma) { nv = dset->nd[m]-1; for (i = 0; i < d; i++) for (j = 0; j < d; j++) sw[i][j] += nv*sigma[i][j]; mx_free((void **) sigma, d); offset += dset->nd[m]; } else status = -1; } if (!status) { /* Invert Sw. */ swi = fmx_inv(sw, d, &dsign, &dexp, errc); mx_free((void **) sw, d); if (!(*errc)) { diff = malloc(d*sizeof(float)); if (diff) { /* Calculate Sb. */ sb = fmx_alloc(d, d); if (sb) { fmx_set(sb, d, d, 0.0); for (m = 0; m < dset->c; m++) { nv = dset->nd[m]; for (j = 0; j < d; j++) diff[j] = xmean[m][j]-mean[j]; for (i = 0; i < d; i++) for (j = 0; j < d; j++) sb[i][j] += nv*diff[i]*diff[j]; } /* Multiply inv(Sw)*Sb. */ mx = fmx_mult(swi, d, d, sb, d, 0); /* Calculate eigenvectors of the product. */ status = eigen(mx, d, &evl, &tmx, errc); if (status == -1) tmx = (float **) mx_free((void **) tmx, d); mx_free((void **) sb, d); mx_free((void **) mx, d); } vx_free(diff); } } mx_free((void **) swi, d); } } vx_free(mean); mx_free((void **) xmean, dset->c); return tmx; } /* Collect user input and call Principal Component Analysis linear feature extractor pca() (type == PDR_PCA) or calculate Fisher's linear discriminant(s) (type == PDR_FISHER), using the training data set. */ void p_cda(int type, int *errc, char **xname) { int status; int itd; int max_value; int default_value; char *fname; float **tmx; max_value = -1; default_value = -1; tmx = (float **) 0; if (tds) { /* This transformation is only defined if dimension is less than the number of vectors. */ if (tds->d >= tds->nv) { status = -1; *errc = PERR_INCONSISTENT_FE; } else { clear_screen(); inverse_video(); cursor_on(); if (type == PDR_PCA) { default_value = 2; max_value = tds->d; } else if (type == PDR_FISHER) { if (tds->c-1 < tds->d) default_value = tds->c-1; else default_value = tds->d; max_value = default_value; } itd = input_d(stdin, stdout, max_value, default_value); fname = input_filename(PMSG_LIN_OUTPUT_FNAME, PCP_LIN, stdout); cursor_off(); print_line(stdout, PCA_MSG, PCP_QLEN); reset_video(); if (type == PDR_PCA) tmx = pca(tds, errc); else if (type == PDR_FISHER) tmx = fld(tds, errc); if (tmx) { status = fmx_save(tmx, itd, tds->d, fname, 0); mx_free((void **) tmx, tds->d); if (status == -1) { *errc = errno; *xname = strdup(fname); } } else status = -1; } } else *errc = PERR_UNDEFINED_TDS; }