cs345-cl

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

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1 Clustering Distance Measures Hierarchical Clustering k -Means Algorithms

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2 The Problem of Clustering rhombus6 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

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4 Problems With Clustering rhombus6 Clustering in two dimensions looks easy. rhombus6 Clustering small amounts of data looks easy. rhombus6 And in most cases, looks are not deceiving.
5 The Curse of Dimensionality rhombus6 Many applications involve not 2, but 10 or 10,000 dimensions. rhombus6 High-dimensional spaces look different: almost all pairs of points are at about the same distance. rhombus4 Assuming random points within a bounding box, e.g., values between 0 and 1 in each dimension.

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6 Example : SkyCat rhombus6 A catalog of 2 billion “sky objects” represented objects by their radiation in 9 dimensions (frequency bands). rhombus6 Problem : cluster into similar objects, e.g., galaxies, nearby stars, quasars, etc. rhombus6 Sloan Sky Survey is a newer, better version.
7 Example : Clustering CD’s (Collaborative Filtering) rhombus6 Intuitively: music divides into categories, and customers prefer a few categories. rhombus4 But what are categories really? rhombus6 Represent a CD by the customers who bought it. rhombus6 Similar CD’s have similar sets of customers, and vice-versa.

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8 The Space of CD’s rhombus6 Think of a space with one dimension for each customer. rhombus4 Values in a dimension may be 0 or 1 only. rhombus6 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. rhombus4 Compare with the “correlated items” matrix: rows = customers; cols. = CD’s.
9 Example : Clustering Documents rhombus6 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. rhombus4 It actually doesn’t matter if k is infinite; i.e., we don’t limit the set of words. rhombus6 Documents with similar sets of words may be about the same topic.

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10 Example : Protein Sequences rhombus6 Objects are sequences of {C,A,T,G}. rhombus6 Distance between sequences is edit distance , the minimum number of inserts and deletes needed to turn one into the other. rhombus6 Note there is a “distance,” but no convenient space in which points “live.”
11 Distance Measures rhombus6 Each clustering problem is based on some kind of “distance” between points. rhombus6 Two major classes of distance measure: 1. Euclidean 2. Non-Euclidean

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12 Euclidean Vs. Non-Euclidean rhombus6 A Euclidean space has some number of real-valued dimensions and “dense” points. rhombus4 There is a notion of “average” of two points.
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