Splitting Methods for Convex Clustering

Clustering is a fundamental problem in many scientific applications. Standard methods such as k-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal. Recently introduced convex relaxations of k-means and hierarchi...

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Vydáno v:Journal of computational and graphical statistics Ročník 24; číslo 4; s. 994 - 1013
Hlavní autoři: Chi, Eric C., Lange, Kenneth
Médium: Journal Article
Jazyk:angličtina
Vydáno: United States Taylor & Francis 02.10.2015
American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America
Taylor & Francis Ltd
Témata:
Algorithms
Alternating direction method of multipliers
Alternating minimization algorithm
Cluster analysis
Clustering and Pattern Detection
Convex analysis
Convex optimization
Hierarchical clustering
k-means
Mathematical problems
Norms
Numerical analysis
Regularization paths
Studies
Regularization paths
k-means
Alternating direction method of multipliers
Hierarchical clustering
Convex optimization
Alternating minimization algorithm
ISSN:1061-8600, 1537-2715
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Popis
Shrnutí:Clustering is a fundamental problem in many scientific applications. Standard methods such as k-means, Gaussian mixture models, and hierarchical clustering, however, are beset by local minima, which are sometimes drastically suboptimal. Recently introduced convex relaxations of k-means and hierarchical clustering shrink cluster centroids toward one another and ensure a unique global minimizer. In this work, we present two splitting methods for solving the convex clustering problem. The first is an instance of the alternating direction method of multipliers (ADMM); the second is an instance of the alternating minimization algorithm (AMA). In contrast to previously considered algorithms, our ADMM and AMA formulations provide simple and unified frameworks for solving the convex clustering problem under the previously studied norms and open the door to potentially novel norms. We demonstrate the performance of our algorithm on both simulated and real data examples. While the differences between the two algorithms appear to be minor on the surface, complexity analysis and numerical experiments show AMA to be significantly more efficient. This article has supplementary materials available online.
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ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2014.948181