Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Clustering with Bregman Divergences
The Journal of Machine Learning Research
A method for initialising the K-means clustering algorithm using kd-trees
Pattern Recognition Letters
A Unified Continuous Optimization Framework for Center-Based Clustering Methods
The Journal of Machine Learning Research
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On the Fermat--Weber center of a convex object
Computational Geometry: Theory and Applications
You are what you consume: a bayesian method for personalized recommendations
Proceedings of the 7th ACM conference on Recommender systems
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In this paper, we consider the task of clustering multivariate normal distributions with respect to the relative entropy into a prescribed number, k , of clusters using a generalization of Lloyd's k -means algorithm [1]. We revisit this information-theoretic clustering problem under the auspices of mixed-type Bregman divergences, and show that the approach of Davis and Dhillon [2] (NIPS*06) can also be derived directly, by applying the Bregman k -means algorithm, once the proper vector/matrix Legendre transformations are defined. We further explain the dualistic structure of the sided k -means clustering, and present a novel k -means algorithm for clustering with respect to the symmetrical relative entropy, the J -divergence.Our approach extends to differential entropic clustering of arbitrary members of the same exponential families in statistics.