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Unformatted text preview: 1 Clustering Preliminaries Applications Euclidean/NonEuclidean Spaces Distance Measures 2 The Problem of Clustering r Given a set of points, with a notion of distance between points, group the points into some number of c l u s t e r s , so that members of a cluster are in some sense as close to each other as possible. 3 Example x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x 4 Problems With Clustering r Clustering in two dimensions looks easy. r Clustering small amounts of data looks easy. r And in most cases, looks are n o t deceiving. 5 The Curse of Dimensionality r Many applications involve not 2, but 10 or 10,000 dimensions. r Highdimensional spaces look different: almost all pairs of points are at about the same distance. R Example : assume random points within a bounding box, e.g., values between 0 and 1 in each dimension. 6 Example : SkyCat r A catalog of 2 billion “sky objects” represents objects by their radiation in 9 dimensions (frequency bands). r Problem : cluster into similar objects, e.g., galaxies, nearby stars, quasars, etc. r Sloan Sky Survey is a newer, better version. 7 Example : Clustering CD’s (Collaborative Filtering) r Intuitively: music divides into categories, and customers prefer a few categories. R But what are categories really? r Represent a CD by the customers who bought it. r Similar CD’s have similar sets of customers, and viceversa. 8 The Space of CD’s r Think of a space with one dimension for each customer. R Values in a dimension may be 0 or 1 only. r A CD’s point in this space is ( x 1 , 2 ,…, k ), where i = 1 iff the i th customer bought the CD....
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This document was uploaded on 03/04/2012.
 Fall '09

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