# import Libraries of other lib packages import bob.math import bob.io.base from ._library import * from . import version from .version import module as __version__ from . import plot from . import load from . import calibration from . import openbr import numpy def mse (estimation, target): """mse(estimation, target) -> error Calculates the mean square error between a set of outputs and target values using the following formula: .. math:: MSE(\hat{\Theta}) = E[(\hat{\Theta} - \Theta)^2] Estimation (:math:\hat{\Theta}) and target (:math:\Theta) are supposed to have 2 dimensions. Different examples are organized as rows while different features in the estimated values or targets are organized as different columns. """ return numpy.mean((estimation - target)**2, 0) def rmse (estimation, target): """rmse(estimation, target) -> error Calculates the root mean square error between a set of outputs and target values using the following formula: .. math:: RMSE(\hat{\Theta}) = \sqrt(E[(\hat{\Theta} - \Theta)^2]) Estimation (:math:\hat{\Theta}) and target (:math:\Theta) are supposed to have 2 dimensions. Different examples are organized as rows while different features in the estimated values or targets are organized as different columns. """ return numpy.sqrt(mse(estimation, target)) def relevance (input, machine): """relevance (input, machine) -> relevances Calculates the relevance of every input feature to the estimation process using the following definition from: Neural Triggering System Operating on High Resolution Calorimetry Information, Anjos et al, April 2006, Nuclear Instruments and Methods in Physics Research, volume 559, pages 134-138 .. math:: R(x_{i}) = |E[(o(x) - o(x|x_{i}=E[x_{i}]))^2]| In other words, the relevance of a certain input feature **i** is the change on the machine output value when such feature is replaced by its mean for all input vectors. For this to work, the input parameter has to be a 2D array with features arranged column-wise while different examples are arranged row-wise. """ o = machine(input) i2 = input.copy() retval = numpy.ndarray((input.shape[1],), 'float64') retval.fill(0) for k in range(input.shape[1]): i2[:,:] = input #reset i2[:,k] = numpy.mean(input[:,k]) retval[k] = (mse(machine(i2), o).sum())**0.5 return retval def recognition_rate(cmc_scores, threshold=None): """recognition_rate(cmc_scores, threshold) -> RR Calculates the recognition rate from the given input, which is identical to the rank 1 (C)MC value. The input has a specific format, which is a list of two-element tuples. Each of the tuples contains the negative and the positive scores for one test item. To read the lists from score files in 4 or 5 column format, please use the :py:func:bob.measure.load.cmc_four_column or :py:func:bob.measure.load.cmc_five_column function. If **threshold** is set to None, the recognition rate is defined as the number of test items, for which the positive score is greater than or equal to all negative scores, divided by the number of all test items. If several positive scores for one test item exist, the **highest** score is taken. If **threshold** assumes one value, the recognition rate is defined as the number of test items, for which the positive score is greater than or equal to all negative scores and the threshold divided by the number of all test items. If several positive scores for one test item exist, the **highest** score is taken. **Parameters:** cmc_scores : CMC scores loaded with one of the functions (:py:func:bob.measure.load.cmc_four_column or :py:func:bob.measure.load.cmc_five_column) threshold : Decision threshold. If None, the decision threshold will be the **highest** positive score. **Returns:** RR : float The rank 1 recognition rate, i.e., the relative number of correctly identified identities """ # If no scores are given, the recognition rate is exactly 0. if not cmc_scores: return 0. correct = 0. for neg, pos in cmc_scores: #If threshold is none, let's use the highest positive score as the decision threshold if(threshold is None): # get the maximum positive score for the current probe item # (usually, there is only one positive score, but just in case...) max_pos = numpy.max(pos) # check if the positive score is smaller than all negative scores if (neg < max_pos).all(): correct += 1. else: #If threshold is NOT None, we have an openset identification max_pos = numpy.max(pos) if((threshold < max_pos) and (neg < max_pos).all()): correct += 1. # return relative number of correctly matched scores return correct / float(len(cmc_scores)) def cmc(cmc_scores): """cmc(cmc_scores) -> curve Calculates the cumulative match characteristic (CMC) from the given input. The input has a specific format, which is a list of two-element tuples. Each of the tuples contains the negative and the positive scores for one test item. To read the lists from score files in 4 or 5 column format, please use the :py:func:bob.measure.load.cmc_four_column or :py:func:bob.measure.load.cmc_five_column function. For each test item the probability that the rank r of the positive score is calculated. The rank is computed as the number of negative scores that are higher than the positive score. If several positive scores for one test item exist, the **highest** positive score is taken. The CMC finally computes how many test items have rank r or higher. **Parameters:** cmc_scores : [(array_like(1D, float), array_like(1D, float))] A list of tuples, where each tuple contains the negative and positive scores for one probe of the database threshold : Decision threshold. If None, the decision threshold will be the **highest** positive score. **Returns:** curve : array_like(2D, float) The CMC curve, with the Rank in the first column and the number of correctly classified clients (in this rank) in the second column. """ # If no scores are given, we cannot plot anything probe_count = float(len(cmc_scores)) if not probe_count: raise ValueError("The given set of scores is empty") # compute MC match_characteristic = numpy.zeros((max([len(neg) for (neg,pos) in cmc_scores])+1,), numpy.int) for neg, pos in cmc_scores: if((type(pos)!=float) and (len(pos) == 0)): raise ValueError("For the CMC computation at least one positive score is necessary. Please review who you are loading the scores. You must set load_only_negatives=False in the :py:func:bob.measure.load.cmc_four_column or :py:func:bob.measure.load.cmc_five_column` methods.") # get the maximum positive score for the current probe item # (usually, there is only one positive score, but just in case...) max_pos = numpy.max(pos) # count the number of negative scores that are higher than the best positive score index = numpy.sum(neg >= max_pos) match_characteristic[index] += 1 # cumulate cumulative_match_characteristic = numpy.ndarray(match_characteristic.shape, numpy.float64) count = 0. for i in range(match_characteristic.shape[0]): count += match_characteristic[i] cumulative_match_characteristic[i] = count / probe_count return cumulative_match_characteristic def get_config(): """Returns a string containing the configuration information. """ import bob.extension return bob.extension.get_config(__name__, version.externals) # gets sphinx autodoc done right - don't remove it __all__ = [_ for _ in dir() if not _.startswith('_')]