Coverage for nltk.cluster : 100%

# Natural Language Toolkit: Clusterers 

# 

# Copyright (C) 2001-2012 NLTK Project 

# Author: Trevor Cohn <tacohn@cs.mu.oz.au> 

# URL: <http://www.nltk.org/> 

# For license information, see LICENSE.TXT 

""" 

This module contains a number of basic clustering algorithms. Clustering 

describes the task of discovering groups of similar items with a large 

collection. It is also describe as unsupervised machine learning, as the data 

from which it learns is unannotated with class information, as is the case for 

supervised learning.  Annotated data is difficult and expensive to obtain in 

the quantities required for the majority of supervised learning algorithms. 

This problem, the knowledge acquisition bottleneck, is common to most natural 

language processing tasks, thus fueling the need for quality unsupervised 

approaches. 

This module contains a k-means clusterer, E-M clusterer and a group average 

agglomerative clusterer (GAAC). All these clusterers involve finding good 

cluster groupings for a set of vectors in multi-dimensional space. 

The K-means clusterer starts with k arbitrary chosen means then allocates each 

vector to the cluster with the closest mean. It then recalculates the means of 

each cluster as the centroid of the vectors in the cluster. This process 

repeats until the cluster memberships stabilise. This is a hill-climbing 

algorithm which may converge to a local maximum. Hence the clustering is 

often repeated with random initial means and the most commonly occurring 

output means are chosen. 

The GAAC clusterer starts with each of the *N* vectors as singleton clusters. 

It then iteratively merges pairs of clusters which have the closest centroids. 

This continues until there is only one cluster. The order of merges gives rise 

to a dendrogram - a tree with the earlier merges lower than later merges. The 

membership of a given number of clusters *c*, *1 <= c <= N*, can be found by 

cutting the dendrogram at depth *c*. 

The Gaussian EM clusterer models the vectors as being produced by a mixture 

of k Gaussian sources. The parameters of these sources (prior probability, 

mean and covariance matrix) are then found to maximise the likelihood of the 

given data. This is done with the expectation maximisation algorithm. It 

starts with k arbitrarily chosen means, priors and covariance matrices. It 

then calculates the membership probabilities for each vector in each of the 

clusters - this is the 'E' step. The cluster parameters are then updated in 

the 'M' step using the maximum likelihood estimate from the cluster membership 

probabilities. This process continues until the likelihood of the data does 

not significantly increase. 

They all extend the ClusterI interface which defines common operations 

available with each clusterer. These operations include. 

   - cluster: clusters a sequence of vectors 

   - classify: assign a vector to a cluster 

   - classification_probdist: give the probability distribution over cluster memberships 

The current existing classifiers also extend cluster.VectorSpace, an 

abstract class which allows for singular value decomposition (SVD) and vector 

normalisation. SVD is used to reduce the dimensionality of the vector space in 

such a manner as to preserve as much of the variation as possible, by 

reparameterising the axes in order of variability and discarding all bar the 

first d dimensions. Normalisation ensures that vectors fall in the unit 

hypersphere. 

Usage example (see also demo()):: 

    from nltk import cluster 

    from nltk.cluster import euclidean_distance 

    from numpy import array 

    vectors = [array(f) for f in [[3, 3], [1, 2], [4, 2], [4, 0]]] 

    # initialise the clusterer (will also assign the vectors to clusters) 

    clusterer = cluster.KMeansClusterer(2, euclidean_distance) 

    clusterer.cluster(vectors, True) 

    # classify a new vector 

    print clusterer.classify(array([3, 3])) 

Note that the vectors must use numpy array-like 

objects. nltk_contrib.unimelb.tacohn.SparseArrays may be used for 

efficiency when required. 

""" 

from nltk.cluster.util import (VectorSpaceClusterer, Dendrogram, 

                               euclidean_distance, cosine_distance) 

from nltk.cluster.kmeans import KMeansClusterer 

from nltk.cluster.gaac import GAAClusterer 

from nltk.cluster.em import EMClusterer