# Clustering - Clustering in Networks(Spectral Clustering...

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Clustering in Networks (Spectral Clustering with the Graph Laplacian . . . a brief introduction) Tom Carter Computer Science CSU Stanislaus http://csustan.csustan.edu/˜ tom/Clustering March 2, 2011 1

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Our general topics: What is Clustering? 3 An Example 8 Spectral Clustering (a general outline) 11 Graph Laplacian(s) 13 References 18 2
What is Clustering? Many real-world data sets consist of (or refer to) collections of entities of some general type. Some example data sets might be: Points in space (e.g., a set of ( x,y ) coordinates) Populations of people (e.g., census data . . . ) Financial instruments (e.g., stocks, with data set the daily closing prices) Collections of texts (e.g., a set of emails, or blog posts, or . . . ) A social network (e.g., Facebook, or phone contacts) 3

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Our data sets give us views into collections of entities, and we would like to use the data sets to better understand the entities . . . Often we can think of our data set as telling us something about the ”relatedness” of our collection of entities. In some cases, the ”relatedness” might be very simply and directly represented in the data set. For example, on Facebook, two members might be related if they are ”friends” of each other. Two emails might be related if they are from the same person. In the census, two people might be ”related” if they live in the same town, or if they have the same job, or etc. Two web pages might be related if one contains a link to the other. More generally, we may be able to develop a ”relatedness” metric associated with the data set. For example, the 4
relatedness between two stocks might be the degree to which their prices are correlated with each other over time. The relatedness between two texts might be the number of distinct words they have in common. One useful starting point to understanding such data sets is

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Clustering - Clustering in Networks(Spectral Clustering...

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