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