cs345-cl

cs345-cl - 1 Clustering Distance Measures Hierarchical...

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Unformatted text preview: 1 Clustering Distance Measures Hierarchical Clustering k-Means Algorithms 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 High-dimensional spaces look different: almost all pairs of points are at about the same distance. R Assuming 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” represented 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 vice-versa. 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 , x 2 ,…, x k ), where x i = 1 iff the i th customer bought the CD. R Compare with the “correlated items” matrix: rows = customers; cols. = CD’s. 9 Example : Clustering Documents r Represent a document by a vector ( x 1 , x 2 ,…, x k ), where x i = 1 iff the i th word (in some order) appears in the document. R It actually doesn’t matter if k is infinite; i.e., we don’t limit the set of words. r Documents with similar sets of words may be about the same topic. 10 Example : Protein Sequences r Objects are sequences of {C,A,T,G}. r Distance between sequences is e d i t d i s t a n c e , the minimum number of inserts and deletes needed to turn one into the other. r Note there is a “distance,” but no convenient space in which points “live.” 11 Distance Measures r Each clustering problem is based on some kind of “distance” between points. r Two major classes of distance measure: 1 . E u c l i d e a n 2 . N o n - E u c l i d e a n 12 Euclidean Vs. Non-Euclidean r A E u c l i d e a n s p a c e has some number of real-valued dimensions and “dense” points. R There is a notion of “average” of two points....
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This note was uploaded on 01/31/2011 for the course CS 345 taught by Professor Dunbar,a during the Fall '07 term at UC Davis.

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cs345-cl - 1 Clustering Distance Measures Hierarchical...

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