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cs345-cl

cs345-cl - Clustering DistanceMeasures kMeansAlgorithms 1 x...

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1 Clustering Distance Measures Hierarchical Clustering k  -Means Algorithms

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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

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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. High-dimensional spaces look different:  almost all pairs of points are at about  the same distance. Assuming random points within a bounding  box, e.g., values between 0 and 1 in each  dimension.

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6 Example : SkyCat A catalog of 2 billion “sky objects”  represented objects by their radiation in  9 dimensions (frequency bands). Problem : cluster into similar objects,  e.g., galaxies, nearby stars, quasars,  etc. Sloan Sky Survey is a newer, better  version.
7 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 vice-versa.

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8 The Space of CD’s Think of a space with one dimension for  each customer. Values in a dimension may be 0 or 1 only. A CD’s point in this space is             ( x 1 x 2 ,…,  x k ), where  x i  = 1 iff the  th   customer bought the CD. Compare with the “correlated items” matrix:  rows = customers; cols. = CD’s.
9 Example : Clustering Documents Represent a document by a vector    ( x 1 x 2 ,…,  x k ), where  x i  = 1 iff the  th  word (in  some order) appears in the document. It actually doesn’t matter if  k   is infinite; i.e.,  we don’t limit the set of words. Documents with similar sets of words  may be about the same topic.

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

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cs345-cl - Clustering DistanceMeasures kMeansAlgorithms 1 x...

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