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Unsupervised learning: Clustering

Unsupervised learning: Clustering. Ata Kaban The University of Birmingham http://www.cs.bham.ac.uk/~axk. The Clustering Problem. Unsupervised Learning. Data (input). ‘Interesting structure’ (output). Should contain essential traits discard unessential details

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Unsupervised learning: Clustering

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  1. Unsupervised learning: Clustering Ata Kaban The University of Birmingham http://www.cs.bham.ac.uk/~axk

  2. The Clustering Problem Unsupervised Learning Data (input) ‘Interesting structure’ (output) • Should contain essential traits • discard unessential details • provide a compact summary the data • interpretable for humans • … Objective function that expresses our notion of interestingness for this data

  3. Here is some data…

  4. Formalising • Data points xnn=1,2,… N • Assume K clusters • Binary indicator variables zkn associated with each data point and cluster: 1 if xn is in cluster k and 0 otherwise • Define a measure of cluster compactness as the total distance from the cluster mean:

  5. Cluster quality objective (the smaller the better): • Two sets of parameters - the cluster mean values mkand the cluster allocation indicator variables zkn • Minimise the above objective over each set of variables while holding one set fixed  This is exactly what the K-means algorithm is doing! (can you prove it?)

  6. Pseudo-code of K-means algorithm: Begin initialize 1, 2, …,K (randomly selected) do classify n samples according to nearest i recompute i until no change in i return 1, 2, …, K End

  7. Other forms of clustering • Many times, clusters are not disjoint, but a cluster may have subclusters, in turn having sub-subclusters. • Hierarchical clustering

  8. Given any two samples x and x’, they will be grouped together at some level, and if they are grouped a level k, they remain grouped for all higher levels • Hierarchical clustering  tree representation called dendrogram

  9. The similarity values may help to determine if the grouping are natural or forced, but if they are evenly distributed no information can be gained • Another representation is based on set, e.g., on the Venn diagrams

  10. Hierarchical clustering can be divided in agglomerative and divisive. • Agglomerative (bottom up, clumping): start with n singleton cluster and form the sequence by merging clusters • Divisive (top down, splitting): start with all of the samples in one cluster and form the sequence by successively splitting clusters

  11. Agglomerative hierarchical clustering • The procedure terminates when the specified number of cluster has been obtained, and returns the cluster as sets of points, rather than the mean or a representative vector for each cluster

  12. Application to image segmentation

  13. Application to clustering face images Cluster centres = face prototypes

  14. The problem of the number of clusters • Typically, the number of clusters is known. • When it’s not, that is a hard problem called model selection. There are several ways of proceed. • A common approach is to repeat the clustering with K=1, K=2, K=3, etc.

  15. What did we learn today? • Data clustering • K-means algorithm in detail • How K-means can get stuck and how to take care of that • The outline of Hierarchical clustering methods

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