#!/usr/bin/env python # Ivana Chingovska # Fri Dec 7 12:33:37 CET 2012 """Utility functions for computation of EPSC curve and related measurement""" import bob.measure import numpy def calc_pass_rate(threshold, attacks): """Calculates the rate of successful spoofing attacks Parameters ---------- threshold : the threshold used for classification scores : numpy with the scores of the spoofing attacks Returns ------- float rate of successful spoofing attacks """ return (attacks >= threshold).mean() def weighted_neg_error_rate_criteria(data, weight, thres, beta=0.5, criteria='eer'): """Given the single value for the weight parameter balancing between impostors and spoofing attacks and a threshold, calculates the error rates and their relationship depending on the criteria (difference in case of 'eer', hter in case of 'min-hter' criteria) Keyword parameters: - data - the development data used to determine the threshold. List on 4 numpy.arrays containing: negatives (licit), positives (licit), negatives (spoof), positivies (spoof) - weight - the weight parameter balancing between impostors and spoofing attacks - thres - the given threshold - beta - the weight parameter balancing between real accesses and all the negative samples (impostors and spoofing attacks). Note that this parameter will be overriden and not considered if the selected criteria is 'min-hter'. - criteria - 'eer', 'wer' or 'min-hter' criteria for decision threshold """ licit_neg = data[0] licit_pos = data[1] spoof_neg = data[2] spoof_pos = data[3] # unpacking the data farfrr_licit = bob.measure.farfrr(licit_neg, licit_pos, thres) farfrr_spoof = bob.measure.farfrr(spoof_neg, spoof_pos, thres) frr = farfrr_licit[1] # farfrr_spoof[1] should have the same value far_i = farfrr_licit[0] far_s = farfrr_spoof[0] far_w = (1 - weight) * far_i + weight * far_s if criteria == 'eer': if beta == 0.5: return abs(far_w - frr) else: # return abs(far_w - frr) return abs((1 - beta) * frr - beta * far_w) elif criteria == 'min-hter': return (far_w + frr) / 2 else: return (1 - beta) * frr + beta * far_w def recursive_thr_search(data, span_min, span_max, weight, beta=0.5, criteria='eer'): """Recursive search for the optimal threshold given a criteria. It evaluates the full range of thresholds at 100 points, and computes the one which optimizes the threshold. In the next search iteration, it examines the region around the point that optimizes the threshold. The procedure stops when the search range is smaller then 1e-10. Keyword arguments: - data - the development data used to determine the threshold. List on 4 numpy.arrays containing: negatives (licit), positives (licit), negatives (spoof), positivies (spoof) - span_min - the minimum of the search range - span_max - the maximum of the search range - weight - the weight parameter balancing between impostors and spoofing attacks - beta - the weight parameter balancing between real accesses and all the negative samples (impostors and spoofing attacks). Note that methods called within this function will override this parameter and not considered if the selected criteria is 'min-hter'. - criteria - the decision threshold criteria ('eer' for EER, 'wer' for Minimum WER or 'min-hter' for Minimum HTER criteria). """ quit_thr = 1e-10 steps = 100 if abs((span_max - span_min) / span_max) < quit_thr: return span_max # or span_min, it doesn't matter else: step_size = (span_max - span_min) / steps thresholds = numpy.array( [(i * step_size) + span_min for i in range(steps + 1)]) weighted_error_rates = numpy.array([ weighted_neg_error_rate_criteria(data, weight, thr, beta, criteria) for thr in thresholds ]) selected_thres = thresholds[numpy.where( weighted_error_rates == min(weighted_error_rates) )] # all the thresholds which have minimum weighted error rate thr = selected_thres[int( selected_thres.size / 2 )] # choose the centrally positioned threshold return recursive_thr_search(data, thr - step_size, thr + step_size, weight, beta, criteria) def weighted_negatives_threshold(licit_neg, licit_pos, spoof_neg, spoof_pos, weight, beta=0.5, criteria='eer'): """Calculates the threshold for achieving the given criteria between the FAR_w and the FRR, given the single value for the weight parameter balancing between impostors and spoofing attacks and a single value for the parameter beta balancing between the real accesses and the negatives (impostors and spoofing attacks) Keyword parameters: - licit_neg - numpy.array of scores for the negatives (licit scenario) - licit_pos - numpy.array of scores for the positives (licit scenario) - spoof_neg - numpy.array of scores for the negatives (spoof scenario) - spoof_pos - numpy.array of scores for the positives (spoof scenario) - weight - the weight parameter balancing between impostors and spoofing attacks - beta - the weight parameter balancing between real accesses and all the negative samples (impostors and spoofing attacks). Note that methods called within this function will override this parameter and not considered if the selected criteria is 'min-hter'. - criteria - the decision threshold criteria ('eer' for EER, 'wer' for Minimum WER or 'min-hter' for Minimum HTER criteria). """ span_min = min( numpy.append(licit_neg, spoof_neg) ) # the min of the span where we will search for the threshold span_max = max( numpy.append(licit_pos, spoof_pos) ) # the max of the span where we will search for the threshold data = (licit_neg, licit_pos, spoof_neg, spoof_pos) # pack the data into a single list return recursive_thr_search(data, span_min, span_max, weight, beta, criteria) def epsc_weights(licit_neg, licit_pos, spoof_neg, spoof_pos, points=100): """Returns the weights for EPSC Keyword arguments: - points - number of points to calculate EPSC """ step_size = 1 / float(points) weights = numpy.array([(i * step_size) for i in range(points + 1)]) return weights def epsc_thresholds(licit_neg, licit_pos, spoof_neg, spoof_pos, points=100, criteria='eer', omega=None, beta=None): """Calculates the optimal thresholds for EPSC, for a range of the weight parameter balancing between impostors and spoofing attacks, and for a range of the beta parameter balancing between real accesses and all the negatives (impostors and spoofing attacks) Keyword arguments: - licit_neg - numpy.array of scores for the negatives (licit scenario) - licit_pos - numpy.array of scores for the positives (licit scenario) - spoof_neg - numpy.array of scores for the negatives (spoof scenario) - spoof_pos - numpy.array of scores for the positives (spoof scenario) - points - number of points to calculate EPSC - criteria - the decision threshold criteria ('eer', 'wer' or 'min-hter') - omega - the value of the parameter omega, balancing between impostors and spoofing attacks. If None, it is going to span the full range [0,1]. Otherwise, can be set to a fixed value or a list of values. - beta - the value of the parameter beta, balancing between real accesses and all the negatives (zero-effort impostors and spoofing attacks). If None, it is going to span the full range [0,1]. Otherwise, can be set to a fixed value or a list of values. """ step_size = 1 / float(points) if omega is None: omega = numpy.array([(i * step_size) for i in range(points + 1)]) elif not isinstance(omega, list) and not isinstance( omega, tuple) and not isinstance(omega, numpy.ndarray): omega = numpy.array([omega]) else: omega = numpy.array(omega) if beta is None: beta = numpy.array([(i * step_size) for i in range(points + 1)]) elif not isinstance(beta, list) and not isinstance( beta, tuple) and not isinstance(beta, numpy.ndarray): beta = numpy.array([beta]) else: beta = numpy.array(beta) thresholds = numpy.ndarray([beta.size, omega.size], 'float64') for bindex, b in enumerate(beta): thresholds[bindex, :] = numpy.array([ weighted_negatives_threshold( licit_neg, licit_pos, spoof_neg, spoof_pos, w, b, criteria=criteria) for w in omega ], 'float64') return omega, beta, thresholds def weighted_err(error_1, error_2, weight): """Calculates the weighted error rate between the two input parameters Keyword arguments: - error_1 - the first input error rate (FAR for zero effort impostors usually) - error_2 - the second input error rate (SFAR) - weight - the given weight """ return (1 - weight) * error_1 + weight * error_2 def error_rates_at_weight(licit_neg, licit_pos, spoof_neg, spoof_pos, omega, threshold, beta=0.5): """Calculates several error rates: FRR, FAR (zero-effort impostors), SFAR, FAR_w, HTER_w for a given value of w. It returns the calculated threshold as a last argument Keyword arguments: - licit_neg - numpy.array of scores for the negatives (licit scenario) - licit_pos - numpy.array of scores for the positives (licit scenario) - spoof_neg - numpy.array of scores for the negatives (spoof scenario) - spoof_pos - numpy.array of scores for the positives (spoof scenario) - threshold - the given threshold - omega - the omega parameter balancing between impostors and spoofing attacks - beta - the weight parameter balancing between real accesses and all the negative samples (impostors and spoofing attacks). """ farfrr_licit = bob.measure.farfrr( licit_neg, licit_pos, threshold) # calculate test frr @ threshold (licit scenario) farfrr_spoof = bob.measure.farfrr( spoof_neg, spoof_pos, threshold) # calculate test frr @ threshold (spoof scenario) # we can take this value from farfrr_spoof as well, it doesn't matter frr = farfrr_licit[1] far = farfrr_licit[0] sfar = farfrr_spoof[0] far_w = weighted_err(far, sfar, omega) hter_w = (far_w + frr) / 2 wer_wb = weighted_err(frr, far_w, beta) return (frr, far, sfar, far_w, wer_wb, hter_w, threshold) def epsc_error_rates(licit_neg, licit_pos, spoof_neg, spoof_pos, thresholds, omega, beta): """Calculates several error rates: FAR_w and WER_wb for the given weights (omega and beta) and thresholds (the thresholds need to be computed first using the method: epsc_thresholds() before passing to this method) Parameters ---------- licit_neg : array_like array of scores for the negatives (licit scenario) licit_pos : array_like array of scores for the positives (licit scenario) spoof_neg : array_like array of scores for the negatives (spoof scenario) spoof_pos : array_like array of scores for the positives (spoof scenario) thresholds : array_like ndarray with threshold values omega : array_like array of the omega parameter balancing between impostors and spoofing attacks beta : array_like array of the beta parameter balancing between real accesses and all negatives (impostors and spoofing attacks) Returns ------- far_w_errors: array_like FAR_w wer_wb_errors: array_like WER_wb """ far_w_errors = numpy.ndarray((beta.size, omega.size), 'float64') wer_wb_errors = numpy.ndarray((beta.size, omega.size), 'float64') for bindex, b in enumerate(beta): errors = [ error_rates_at_weight(licit_neg, licit_pos, spoof_neg, spoof_pos, w, thresholds[bindex, windex], b) for windex, w in enumerate(omega) ] far_w_errors[bindex, :] = [errors[i][3] for i in range(len(errors))] wer_wb_errors[bindex, :] = [errors[i][4] for i in range(len(errors))] return far_w_errors, wer_wb_errors def all_error_rates(licit_neg, licit_pos, spoof_neg, spoof_pos, thresholds, omega, beta): """Calculates several error rates: FAR_w and WER_wb for the given weights (omega and beta) and thresholds (the thresholds need to be computed first using the method: epsc_thresholds() before passing to this method) Parameters ---------- licit_neg : array_like array of scores for the negatives (licit scenario) licit_pos : array_like array of scores for the positives (licit scenario) spoof_neg : array_like array of scores for the negatives (spoof scenario) spoof_pos : array_like array of scores for the positives (spoof scenario) thresholds : array_like ndarray with threshold values omega : array_like array of the omega parameter balancing between impostors and spoofing attacks beta : array_like array of the beta parameter balancing between real accesses and all negatives (impostors and spoofing attacks) Returns ------- far_w_errors: array_like FAR_w wer_wb_errors: array_like WER_wb """ frr_errors = numpy.ndarray((beta.size, omega.size), 'float64') far_errors = numpy.ndarray((beta.size, omega.size), 'float64') sfar_errors = numpy.ndarray((beta.size, omega.size), 'float64') far_w_errors = numpy.ndarray((beta.size, omega.size), 'float64') wer_wb_errors = numpy.ndarray((beta.size, omega.size), 'float64') hter_wb_errors = numpy.ndarray((beta.size, omega.size), 'float64') for bindex, b in enumerate(beta): errors = [ error_rates_at_weight(licit_neg, licit_pos, spoof_neg, spoof_pos, w, thresholds[bindex, windex], b) for windex, w in enumerate(omega) ] frr_errors[bindex, :] = [errors[i][0] for i in range(len(errors))] far_errors[bindex, :] = [errors[i][1] for i in range(len(errors))] sfar_errors[bindex, :] = [errors[i][2] for i in range(len(errors))] far_w_errors[bindex, :] = [errors[i][3] for i in range(len(errors))] wer_wb_errors[bindex, :] = [errors[i][4] for i in range(len(errors))] hter_wb_errors[bindex, :] = [errors[i][5] for i in range(len(errors))] return (frr_errors, far_errors, sfar_errors, far_w_errors, wer_wb_errors, hter_wb_errors) def calc_aue(licit_neg, licit_pos, spoof_neg, spoof_pos, thresholds, omega, beta, l_bound=0, h_bound=1, var_param='omega'): """Calculates AUE of EPSC for the given thresholds and weights Keyword arguments: - licit_neg - numpy.array of scores for the negatives (licit scenario) - licit_pos - numpy.array of scores for the positives (licit scenario) - spoof_neg - numpy.array of scores for the negatives (spoof scenario) - spoof_pos - numpy.array of scores for the positives (spoof scenario) - l_bound - lower bound of integration - h_bound - higher bound of integration - points - number of points to calculate EPSC - criteria - the decision threshold criteria ('eer', 'wer' or 'min-hter') - var_param - name of the parameter which is varied on the abscissa ('omega' or 'beta') """ from scipy import integrate if var_param == 'omega': errors = all_error_rates(licit_neg, licit_pos, spoof_neg, spoof_pos, thresholds, omega, beta) weights = omega # setting the weights to the varying parameter else: errors = all_error_rates(licit_neg, licit_pos, spoof_neg, spoof_pos, thresholds, omega, beta) weights = beta # setting the weights to the varying parameter wer_errors = errors[4].reshape(1, errors[4].size) l_ind = numpy.where(weights >= l_bound)[0][0] h_ind = numpy.where(weights <= h_bound)[0][-1] aue = integrate.cumtrapz(wer_errors, weights) aue = numpy.append( [0], aue) # for indexing purposes, aue is cumulative integration aue = aue[h_ind] - aue[l_ind] return aue