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Greedy clustering methods

Greedy clustering methods. Prof. Ramin Zabih http://cs100r.cs.cornell.edu. Administrivia. Guest lecture on Tuesday Prof. Charlie van Loan, on ellipse fitting Prelim 3: Thursday 11/29 (last lecture) Review session the day before A6 is due Friday 11/30 (LDOC) Final projects due Friday 12/7

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Greedy clustering methods

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  1. Greedy clustering methods Prof. Ramin Zabih http://cs100r.cs.cornell.edu

  2. Administrivia • Guest lecture on Tuesday • Prof. Charlie van Loan, on ellipse fitting • Prelim 3: Thursday 11/29 (last lecture) • Review session the day before • A6 is due Friday 11/30 (LDOC) • Final projects due Friday 12/7 • Course evals! http://www.engineering.cornell.edu/courseeval/

  3. Clustering • Generally speaking, the goal is to maximize similarity within a cluster, and to minimize similarity between clusters • We will assume that the space and the number of clusters are known • Usually (but not always) a safe assumption • Sometimes you only know distances between pairs of points • May not be embeddable in a space • Often assume a known number of clusters

  4. Example Figure from Johan Everts

  5. Applications of clustering • Economics or politics • Finding similar-minded or similar behaving groups of people (market segmentation) • Find stocks that behave similarly • Spatial clustering • Earthquake centers cluster along faults • Find epidemics (famous example: cholera) • Classify documents for web search • Automatic directory construction (like Yahoo!) • Find more documents “like this one”

  6. Clustering algorithms • There are many types of methods • How is a cluster is represented? • Is a cluster represented by a data point, or by a point in the middle of the cluster? • This is similar to an argument we saw before… • An interesting class of methods uses graph partitioning • Edge weights are distances • There are many classes of algorithms

  7. Greedy methods • Many CS problems can be solved by repeatedly doing whatever seems best at the moment • I.e., without needing a long-term plan • These are called greedy algorithms • Example: hill climbing for convex function minimization • Example: sorting by swapping out-of-order pairs

  8. K-center clustering • Find K cluster centers that minimize the maximum distance between any point and its nearest center • We want the worst point in the worst cluster to still be good (i.e., close to its center) • This is a nice optimization problem • Given a clustering, we can describe how good it is, so we have a figure of merit • But to find the optimal clustering we have to try every one!

  9. A greedy method • Pick a random point to start with, this is your first cluster center • Find the farthest point from the cluster center, this is a new cluster center • Find the farthest point from any cluster center and add it

  10. Example Figure from Jia Li

  11. An amazing property • This algorithm gives you a figure of merit that is no worse than twice the optimum • Such results are very difficult to achieve, and the subject of much research • Mostly in CS681, a bit in CS482 • You can’t find the optimum, yet you can prove something about it!

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