# Copyright 2000 by Jeffrey Chang. All rights reserved. # This code is part of the Biopython distribution and governed by its # license. Please see the LICENSE file that should have been included # as part of this package. """This provides code for a general Naive Bayes learner. Naive Bayes is a supervised classification algorithm that uses Bayes rule to compute the fit between a new observation and some previously observed data. The observations are discrete feature vectors, with the Bayes assumption that the features are independent. Although this is hardly ever true, the classifier works well enough in practice. Glossary: observation A feature vector of discrete data. class A possible classification for an observation. Classes: NaiveBayes Holds information for a naive Bayes classifier. Functions: train Train a new naive Bayes classifier. calculate Calculate the probabilities of each class, given an observation. classify Classify an observation into a class. """ import numpy def _contents(items): term = 1.0/len(items) counts = {} for item in items: counts[item] = counts.get(item,0) + term return counts 00038 class NaiveBayes: """Holds information for a NaiveBayes classifier. Members: classes List of the possible classes of data. p_conditional CLASS x DIM array of dicts of value -> P(value|class,dim) p_prior List of the prior probabilities for every class. dimensionality Dimensionality of the data. """ def __init__(self): self.classes = [] self.p_conditional = None self.p_prior = [] self.dimensionality = None def calculate(nb, observation, scale=0): """calculate(nb, observation[, scale]) -> probability dict Calculate log P(class|observation) for each class. nb is a NaiveBayes classifier that has been trained. observation is a list representing the observed data. scale is whether the probability should be scaled by P(observation). By default, no scaling is done. The return value is a dictionary where the keys is the class and the value is the log probability of the class. """ # P(class|observation) = P(observation|class)*P(class)/P(observation) # Taking the log: # lP(class|observation) = lP(observation|class)+lP(class)-lP(observation) # Make sure the observation has the right dimensionality. if len(observation) != nb.dimensionality: raise ValueError("observation in %d dimension, but classifier in %d" \ % (len(observation), nb.dimensionality)) # Calculate log P(observation|class) for every class. n = len(nb.classes) lp_observation_class = numpy.zeros(n) # array of log P(observation|class) for i in range(n): # log P(observation|class) = SUM_i log P(observation_i|class) probs = [None] * len(observation) for j in range(len(observation)): probs[j] = nb.p_conditional[i][j].get(observation[j], 0) lprobs = numpy.log(numpy.clip(probs, 1.e-300, 1.e+300)) lp_observation_class[i] = sum(lprobs) # Calculate log P(class). lp_prior = numpy.log(nb.p_prior) # Calculate log P(observation). lp_observation = 0.0 # P(observation) if scale: # Only calculate this if requested. # log P(observation) = log SUM_i P(observation|class_i)P(class_i) obs = numpy.exp(numpy.clip(lp_prior+lp_observation_class,-700,+700)) lp_observation = numpy.log(sum(obs)) # Calculate log P(class|observation). lp_class_observation = {} # Dict of class : log P(class|observation) for i in range(len(nb.classes)): lp_class_observation[nb.classes[i]] = \ lp_observation_class[i] + lp_prior[i] - lp_observation return lp_class_observation def classify(nb, observation): """classify(nb, observation) -> class Classify an observation into a class. """ # The class is the one with the highest probability. probs = calculate(nb, observation, scale=0) max_prob = max_class = None for klass in nb.classes: if max_prob is None or probs[klass] > max_prob: max_prob, max_class = probs[klass], klass return max_class def train(training_set, results, priors=None, typecode=None): """train(training_set, results[, priors]) -> NaiveBayes Train a naive bayes classifier on a training set. training_set is a list of observations. results is a list of the class assignments for each observation. Thus, training_set and results must be the same length. priors is an optional dictionary specifying the prior probabilities for each type of result. If not specified, the priors will be estimated from the training results. """ if not len(training_set): raise ValueError("No data in the training set.") if len(training_set) != len(results): raise ValueError("training_set and results should be parallel lists.") # If no typecode is specified, try to pick a reasonable one. If # training_set is a Numeric array, then use that typecode. # Otherwise, choose a reasonable default. # XXX NOT IMPLEMENTED # Check to make sure each vector in the training set has the same # dimensionality. dimensions = [len(x) for x in training_set] if min(dimensions) != max(dimensions): raise ValueError("observations have different dimensionality") nb = NaiveBayes() nb.dimensionality = dimensions[0] # Get a list of all the classes, and # estimate the prior probabilities for the classes. if priors is not None: percs = priors nb.classes = list(set(results)) else: class_freq = _contents(results) nb.classes = class_freq.keys() percs = class_freq nb.classes.sort() # keep it tidy nb.p_prior = numpy.zeros(len(nb.classes)) for i in range(len(nb.classes)): nb.p_prior[i] = percs[nb.classes[i]] # Collect all the observations in class. For each class, make a # matrix of training instances versus dimensions. I might be able # to optimize this with Numeric, if the training_set parameter # were guaranteed to be a matrix. However, this may not be the # case, because the client may be hacking up a sparse matrix or # something. c2i = {} # class to index of class for index, key in enumerate(nb.classes): c2i[key] = index observations = [[] for c in nb.classes] # separate observations by class for i in range(len(results)): klass, obs = results[i], training_set[i] observations[c2i[klass]].append(obs) # Now make the observations Numeric matrics. for i in range(len(observations)): # XXX typecode must be specified! observations[i] = numpy.asarray(observations[i], typecode) # Calculate P(value|class,dim) for every class. # This is a good loop to optimize. nb.p_conditional = [] for i in range(len(nb.classes)): class_observations = observations[i] # observations for this class nb.p_conditional.append([None] * nb.dimensionality) for j in range(nb.dimensionality): # Collect all the values in this dimension. values = class_observations[:, j] # Add pseudocounts here. This needs to be parameterized. #values = list(values) + range(len(nb.classes)) # XXX add 1 # Estimate P(value|class,dim) nb.p_conditional[i][j] = _contents(values) return nb if __name__ == "__main__": # Car data from example 'Naive Bayes Classifier example' by Eric Meisner November 22, 2003 # http://www.inf.u-szeged.hu/~ormandi/teaching/mi2/02-naiveBayes-example.pdf xcar=[ ['Red', 'Sports', 'Domestic'], ['Red', 'Sports', 'Domestic'], ['Red', 'Sports', 'Domestic'], ['Yellow', 'Sports', 'Domestic'], ['Yellow', 'Sports', 'Imported'], ['Yellow', 'SUV', 'Imported'], ['Yellow', 'SUV', 'Imported'], ['Yellow', 'SUV', 'Domestic'], ['Red', 'SUV', 'Imported'], ['Red', 'Sports', 'Imported'] ] ycar=[ 'Yes', 'No', 'Yes', 'No', 'Yes', 'No', 'Yes', 'No', 'No', 'Yes' ] carmodel = train(xcar, ycar) carresult = classify(carmodel, ['Red', 'Sports', 'Domestic']) print 'Is Yes?', carresult carresult = classify(carmodel, ['Red', 'SUV', 'Domestic']) print 'Is No?', carresult

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