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Convex Clustering with Exemplar-Based Models
Danial Lashkari · Polina Golland

Mon Dec 03 08:10 PM -- 08:25 PM (PST) @
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Clustering is often formulated as the maximum likelihood estimation of a mixture model that explains the data. The EM algorithm widely used to solve the resulting optimization problem is inherently a gradient-descent method and is sensitive to initialization. The resulting solution is a local optimum in the neighborhood of the initial guess. This sensitivity to initialization presents a significant challenge in clustering large data sets into many clusters. In this paper, we present a different approach to approximate mixture fitting for clustering. We introduce an exemplar-based likelihood function that approximates the exact likelihood. This formulation leads to a convex minimization problem and an efficient algorithm with \emph{guaranteed convergence to the globally optimal solution}. The resulting clustering can be thought of as a probabilistic mapping of the data points to the set of exemplars that minimizes the average distance and the information-theoretic cost of mapping. We present experimental results illustrating the performance of our algorithm and its comparison with the conventional approach to mixture model clustering.

Author Information

Danial Lashkari (Massachusetts Institute of Technology)
Polina Golland (Massachusetts Institute of Technology)

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