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Abstract:
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Cluster analysis is a fundamental problem in statistics. It aims at categorizing the observations into different groups, called clusters, such that observations in the same cluster tend to be more similar to each other than those from different clusters. In this talk, I will introduce a new optimization-based clustering method called convex clustering over (weighted) undirected graph. The choice of both the graph and its weights is crucial to clustering performance as well as the algorithm's computational efficiency. Specifically, we consider two types of graphs: a minimum spanning tree and a so-called K-means bipartite graph. Computationally, both graphs make the associated optimization problems easier to solve compared to that with a complete graph; and statistically, both lead to better clustering results. Further numerical comparisons with the K-means clustering algorithm and a density-based algorithm demonstrate the superior performance of the proposed algorithms.
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