Package Bio :: Module kNN
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Source Code for Module Bio.kNN

  1  #!/usr/bin/env python 
  2  # This code is part of the Biopython distribution and governed by its 
  3  # license.  Please see the LICENSE file that should have been included 
  4  # as part of this package. 
  5  """ 
  6  This module provides code for doing k-nearest-neighbors classification. 
  7   
  8  k Nearest Neighbors is a supervised learning algorithm that classifies 
  9  a new observation based the classes in its surrounding neighborhood. 
 10   
 11  Glossary: 
 12  distance   The distance between two points in the feature space. 
 13  weight     The importance given to each point for classification. 
 14   
 15   
 16  Classes: 
 17  kNN           Holds information for a nearest neighbors classifier. 
 18   
 19   
 20  Functions: 
 21  train        Train a new kNN classifier. 
 22  calculate    Calculate the probabilities of each class, given an observation. 
 23  classify     Classify an observation into a class. 
 24   
 25      Weighting Functions: 
 26  equal_weight    Every example is given a weight of 1. 
 27   
 28  """ 
 29   
 30  import numpy 
 31   
 32   
33 -class kNN(object):
34 """Holds information necessary to do nearest neighbors classification. 35 36 Members: 37 classes Set of the possible classes. 38 xs List of the neighbors. 39 ys List of the classes that the neighbors belong to. 40 k Number of neighbors to look at. 41 42 """
43 - def __init__(self):
44 """kNN()""" 45 self.classes = set() 46 self.xs = [] 47 self.ys = [] 48 self.k = None
49 50
51 -def equal_weight(x, y):
52 """equal_weight(x, y) -> 1""" 53 # everything gets 1 vote 54 return 1
55 56
57 -def train(xs, ys, k, typecode=None):
58 """train(xs, ys, k) -> kNN 59 60 Train a k nearest neighbors classifier on a training set. xs is a 61 list of observations and ys is a list of the class assignments. 62 Thus, xs and ys should contain the same number of elements. k is 63 the number of neighbors that should be examined when doing the 64 classification. 65 """ 66 knn = kNN() 67 knn.classes = set(ys) 68 knn.xs = numpy.asarray(xs, typecode) 69 knn.ys = ys 70 knn.k = k 71 return knn
72 73
74 -def calculate(knn, x, weight_fn=equal_weight, distance_fn=None):
75 """calculate(knn, x[, weight_fn][, distance_fn]) -> weight dict 76 77 Calculate the probability for each class. knn is a kNN object. x 78 is the observed data. weight_fn is an optional function that 79 takes x and a training example, and returns a weight. distance_fn 80 is an optional function that takes two points and returns the 81 distance between them. If distance_fn is None (the default), the 82 Euclidean distance is used. Returns a dictionary of the class to 83 the weight given to the class. 84 """ 85 x = numpy.asarray(x) 86 87 order = [] # list of (distance, index) 88 if distance_fn: 89 for i in range(len(knn.xs)): 90 dist = distance_fn(x, knn.xs[i]) 91 order.append((dist, i)) 92 else: 93 # Default: Use a fast implementation of the Euclidean distance 94 temp = numpy.zeros(len(x)) 95 # Predefining temp allows reuse of this array, making this 96 # function about twice as fast. 97 for i in range(len(knn.xs)): 98 temp[:] = x - knn.xs[i] 99 dist = numpy.sqrt(numpy.dot(temp, temp)) 100 order.append((dist, i)) 101 order.sort() 102 103 # first 'k' are the ones I want. 104 weights = {} # class -> number of votes 105 for k in knn.classes: 106 weights[k] = 0.0 107 for dist, i in order[:knn.k]: 108 klass = knn.ys[i] 109 weights[klass] = weights[klass] + weight_fn(x, knn.xs[i]) 110 111 return weights
112 113
114 -def classify(knn, x, weight_fn=equal_weight, distance_fn=None):
115 """classify(knn, x[, weight_fn][, distance_fn]) -> class 116 117 Classify an observation into a class. If not specified, weight_fn will 118 give all neighbors equal weight. distance_fn is an optional function 119 that takes two points and returns the distance between them. If 120 distance_fn is None (the default), the Euclidean distance is used. 121 """ 122 weights = calculate( 123 knn, x, weight_fn=weight_fn, distance_fn=distance_fn) 124 125 most_class = None 126 most_weight = None 127 for klass, weight in weights.items(): 128 if most_class is None or weight > most_weight: 129 most_class = klass 130 most_weight = weight 131 return most_class
132