Mode-Finding for Mixtures of Gaussian Distributions
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean Shift: A Robust Approach Toward Feature Space Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean Shift, Mode Seeking, and Clustering
IEEE Transactions on Pattern Analysis and Machine Intelligence
Convex Optimization
Mathematical Programming: Series A and B
A statistical approach to rule learning
ICML '06 Proceedings of the 23rd international conference on Machine learning
Clustering with Bregman Divergences
The Journal of Machine Learning Research
Fast Global Kernel Density Mode Seeking: Applications to Localization and Tracking
IEEE Transactions on Image Processing
Input space versus feature space in kernel-based methods
IEEE Transactions on Neural Networks
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
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A recent trend in exemplar based unsupervised learning is to formulate the learning problem as a convex optimization problem. Convexity is achieved by restricting the set of possible prototypes to training exemplars. In particular, this has been done for clustering, vector quantization and mixture model density estimation. In this paper we propose a novel algorithm that is theoretically and practically superior to these convex formulations. This is possible by posing the unsupervised learning problem as a single convex "master problem" with non-convex subproblems. We show that for the above learning tasks the subproblems are extremely well-behaved and can be solved efficiently.