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   
 13      - distance   The distance between two points in the feature space. 
 14      - weight     The importance given to each point for classification. 
 15   
 16   
 17  Classes: 
 18   
 19      - kNN           Holds information for a nearest neighbors classifier. 
 20   
 21   
 22  Functions: 
 23   
 24      - train        Train a new kNN classifier. 
 25      - calculate    Calculate the probabilities of each class, given an observation. 
 26      - classify     Classify an observation into a class. 
 27   
 28  Weighting Functions: 
 29   
 30      - equal_weight    Every example is given a weight of 1. 
 31   
 32  """ 
 33   
 34  import numpy 
 35   
 36   
37 -class kNN(object):
38 """Holds information necessary to do nearest neighbors classification. 39 40 Members: 41 42 - classes Set of the possible classes. 43 - xs List of the neighbors. 44 - ys List of the classes that the neighbors belong to. 45 - k Number of neighbors to look at. 46 47 """
48 - def __init__(self):
49 """kNN()""" 50 self.classes = set() 51 self.xs = [] 52 self.ys = [] 53 self.k = None
54 55
56 -def equal_weight(x, y):
57 """equal_weight(x, y) -> 1""" 58 # everything gets 1 vote 59 return 1
60 61
62 -def train(xs, ys, k, typecode=None):
63 """train(xs, ys, k) -> kNN 64 65 Train a k nearest neighbors classifier on a training set. xs is a 66 list of observations and ys is a list of the class assignments. 67 Thus, xs and ys should contain the same number of elements. k is 68 the number of neighbors that should be examined when doing the 69 classification. 70 """ 71 knn = kNN() 72 knn.classes = set(ys) 73 knn.xs = numpy.asarray(xs, typecode) 74 knn.ys = ys 75 knn.k = k 76 return knn
77 78
79 -def calculate(knn, x, weight_fn=equal_weight, distance_fn=None):
80 """calculate(knn, x[, weight_fn][, distance_fn]) -> weight dict 81 82 Calculate the probability for each class. knn is a kNN object. x 83 is the observed data. weight_fn is an optional function that 84 takes x and a training example, and returns a weight. distance_fn 85 is an optional function that takes two points and returns the 86 distance between them. If distance_fn is None (the default), the 87 Euclidean distance is used. Returns a dictionary of the class to 88 the weight given to the class. 89 """ 90 x = numpy.asarray(x) 91 92 order = [] # list of (distance, index) 93 if distance_fn: 94 for i in range(len(knn.xs)): 95 dist = distance_fn(x, knn.xs[i]) 96 order.append((dist, i)) 97 else: 98 # Default: Use a fast implementation of the Euclidean distance 99 temp = numpy.zeros(len(x)) 100 # Predefining temp allows reuse of this array, making this 101 # function about twice as fast. 102 for i in range(len(knn.xs)): 103 temp[:] = x - knn.xs[i] 104 dist = numpy.sqrt(numpy.dot(temp, temp)) 105 order.append((dist, i)) 106 order.sort() 107 108 # first 'k' are the ones I want. 109 weights = {} # class -> number of votes 110 for k in knn.classes: 111 weights[k] = 0.0 112 for dist, i in order[:knn.k]: 113 klass = knn.ys[i] 114 weights[klass] = weights[klass] + weight_fn(x, knn.xs[i]) 115 116 return weights
117 118
119 -def classify(knn, x, weight_fn=equal_weight, distance_fn=None):
120 """classify(knn, x[, weight_fn][, distance_fn]) -> class 121 122 Classify an observation into a class. If not specified, weight_fn will 123 give all neighbors equal weight. distance_fn is an optional function 124 that takes two points and returns the distance between them. If 125 distance_fn is None (the default), the Euclidean distance is used. 126 """ 127 weights = calculate( 128 knn, x, weight_fn=weight_fn, distance_fn=distance_fn) 129 130 most_class = None 131 most_weight = None 132 for klass, weight in weights.items(): 133 if most_class is None or weight > most_weight: 134 most_class = klass 135 most_weight = weight 136 return most_class
137