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9 """
10 This module contains a number of basic clustering algorithms. Clustering
11 describes the task of discovering groups of similar items with a large
12 collection. It is also describe as unsupervised machine learning, as the data
13 from which it learns is unannotated with class information, as is the case for
14 supervised learning. Annotated data is difficult and expensive to obtain in
15 the quantities required for the majority of supervised learning algorithms.
16 This problem, the knowledge acquisition bottleneck, is common to most natural
17 language processing tasks, thus fueling the need for quality unsupervised
18 approaches.
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20 This module contains a k-means clusterer, E-M clusterer and a group average
21 agglomerative clusterer (GAAC). All these clusterers involve finding good
22 cluster groupings for a set of vectors in multi-dimensional space.
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24 The K-means clusterer starts with k arbitrary chosen means then allocates each
25 vector to the cluster with the closest mean. It then recalculates the means of
26 each cluster as the centroid of the vectors in the cluster. This process
27 repeats until the cluster memberships stabilise. This is a hill-climbing
28 algorithm which may converge to a local maximum. Hence the clustering is
29 often repeated with random initial means and the most commonly occurring
30 output means are chosen.
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32 The GAAC clusterer starts with each of the M{N} vectors as singleton clusters.
33 It then iteratively merges pairs of clusters which have the closest centroids.
34 This continues until there is only one cluster. The order of merges gives rise
35 to a dendogram - a tree with the earlier merges lower than later merges. The
36 membership of a given number of clusters M{c}, M{1 <= c <= N}, can be found by
37 cutting the dendogram at depth M{c}.
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39 The Gaussian EM clusterer models the vectors as being produced by a mixture
40 of k Gaussian sources. The parameters of these sources (prior probability,
41 mean and covariance matrix) are then found to maximise the likelihood of the
42 given data. This is done with the expectation maximisation algorithm. It
43 starts with k arbitrarily chosen means, priors and covariance matrices. It
44 then calculates the membership probabilities for each vector in each of the
45 clusters - this is the 'E' step. The cluster parameters are then updated in
46 the 'M' step using the maximum likelihood estimate from the cluster membership
47 probabilities. This process continues until the likelihood of the data does
48 not significantly increase.
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50 They all extend the ClusterI interface which defines common operations
51 available with each clusterer. These operations include.
52 - cluster: clusters a sequence of vectors
53 - classify: assign a vector to a cluster
54 - classification_probdist: give the probability distribution over cluster memberships
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56 The current existing classifiers also extend cluster.VectorSpace, an
57 abstract class which allows for singular value decomposition (SVD) and vector
58 normalisation. SVD is used to reduce the dimensionality of the vector space in
59 such a manner as to preserve as much of the variation as possible, by
60 reparameterising the axes in order of variability and discarding all bar the
61 first d dimensions. Normalisation ensures that vectors fall in the unit
62 hypersphere.
63
64 Usage example (see also demo())::
65 vectors = [array(f) for f in [[3, 3], [1, 2], [4, 2], [4, 0]]]
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67 # initialise the clusterer (will also assign the vectors to clusters)
68 clusterer = cluster.KMeans(2, euclidean_distance)
69 clusterer.cluster(vectors, True)
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71 # classify a new vector
72 print clusterer.classify(array([3, 3]))
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74 Note that the vectors must use numpy array-like
75 objects. nltk_contrib.unimelb.tacohn.SparseArrays may be used for
76 efficiency when required.
77 """
78
79 from api import *
80 from util import *
81 from kmeans import *
82 from gaac import *
83 from em import *
84