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Unformatted text preview: CS573: Homework 4 Due date: Tuesday November 16, start of class 1 Between cluster distances (4 pts) Let cluster C i contain n i samples, and let d ij be some measure of distance between two clusters C i and C j . In general, one might expect that if C i and C j are merged to form a new cluster C k , then the distance from C k to some other cluster C h is not simply related to d hi and d hj . However, consider the equation: d hk = α i d hi + α j d hj + βd ij + γ  d hi d hj  Show that the following choices for the coefficients α i ,α j ,β,γ lead to the distance functions indicated. 1. Singlelink: α i = α j = 0 . 5 ,β = 0 ,γ = . 5 2. Completelink: α i = α j = 0 . 5 ,β = 0 ,γ = +0 . 5 3. Averagelink: α i = n i n i + n j ,α j = n j n i + n j ,β = γ = 0 4. Betweencluster distance (i.e., squared Euclidean distance between centroids): α i = n i n i + n j ,α j = n j n i + n j ,β = α i α j ,γ = 0 2 Clustering theorem (4 pts) Read the paper: J. Kleinberg (2002). An Impossibility Theorem for Clustering. In Pro ceedings of the 16th conference on Neural Information Processing Systems. Explain its main result. Is there a hope for providing a good clustering framework/algorithm? 3 Spectral Clustering (8 pts) In this problem we will analyze the operation of a variant of spectral clustering methods on two datasets shown in Figure 1. For each of the datasets (unless directed otherwise) please answer the following questions....
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This note was uploaded on 03/13/2012 for the course CS 573 taught by Professor Staff during the Fall '08 term at Purdue.
 Fall '08
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