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 Document
Unformatted text preview: 1 Clustering Preliminaries Applications Euclidean/NonEuclidean Spaces Distance Measures 2 The Problem of Clustering ◆ Given a set of points, with a notion of distance between points, group the points into some number of clusters , 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 ◆ Clustering in two dimensions looks easy. ◆ Clustering small amounts of data looks easy. ◆ And in most cases, looks are not deceiving. 5 The Curse of Dimensionality ◆ Many applications involve not 2, but 10 or 10,000 dimensions. ◆ Highdimensional spaces look different: almost all pairs of points are at about the same distance. 6 Example : Curse of Dimensionality ◆ Assume random points within a bounding box, e.g., values between 0 and 1 in each dimension. ◆ In 2 dimensions: a variety of distances between 0 and 1.41. ◆ In 10,000 dimensions, the difference in any one dimension is distributed as a triangle. 7 Example – Continued ◆ The law of large numbers applies. ◆ Actual distance between two random points is the sqrt of the sum of squares of essentially the same set of differences. 8 Example HighDimension Application: SkyCat ◆ A catalog of 2 billion “sky objects” represents objects by their radiation in 7 dimensions (frequency bands). ◆ Problem : cluster into similar objects, e.g., galaxies, nearby stars, quasars, etc. ◆ Sloan Sky Survey is a newer, better version. 9 Example : Clustering CD’s (Collaborative Filtering) ◆ Intuitively : music divides into categories, and customers prefer a few categories. ◗ But what are categories really? ◆ Represent a CD by the customers who bought it. ◆ Similar CD’s have similar sets of customers, and viceversa. 10 The Space of CD’s ◆ Think of a space with one dimension for each customer....
View
Full
Document
This document was uploaded on 03/04/2012.
 Fall '09

Click to edit the document details