Package cluster

source code

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 dendogram - 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 dendogram 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()):

   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.KMeans(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.