This preview shows pages 1–13. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 1 Clustering Distance Measures Hierarchical Clustering kMeans 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 Highdimensional 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 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 , 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. NonEuclidean r A E u c l i d e a n s p a c e has some number of realvalued dimensions and “dense” points. R There is a notion of “average” of two points....
View
Full
Document
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.
 Fall '07
 Dunbar,A
 Algorithms

Click to edit the document details