clustering1-1

clustering1-1 - Clustering Preliminaries Applications...

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1 Clustering Preliminaries Applications Euclidean/Non-Euclidean Spaces Distance Measures
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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 clusters , so that members of a cluster are in some sense as close to each other as possible.
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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
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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 not deceiving.
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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.
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6 Example : Curse of Dimensionality r Assume random points within a bounding box, e.g., values between 0 and 1 in each dimension. r In 2 dimensions: a variety of distances between 0 and 1.41. r In 10,000 dimensions, the difference in any one dimension is distributed as a triangle.
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7 Example – Continued r The law of large numbers applies. r Actual distance between two random points is the sqrt of the sum of squares of essentially the same set of differences.
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8 Example High-Dimension Application: SkyCat r A catalog of 2 billion “sky objects” represents objects by their radiation in 7 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.
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9 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.
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10 The Space of CD’s r Think of a space with one dimension for each customer.
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This document was uploaded on 03/04/2012.

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clustering1-1 - Clustering Preliminaries Applications...

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