Abstract
Suppose κ centers are fit to m points by heuristically minimizing the κ-means cost; what is the corresponding fit over the source distribution? This question is resolved here for distributions with p ≥ 4 bounded moments; in particular, the difference between the sample cost and distribution cost decays with m and p as mmin{-1/4,-1/2+2/p}. The essential technical contribution is a mechanism to uniformly control deviations in the face of unbounded parameter sets, cost functions, and source distributions. To further demonstrate this mechanism, a soft clustering variant of κ-means cost is also considered, namely the log likelihood of a Gaussian mixture, subject to the constraint that all covariance matrices have bounded spectrum. Lastly, a rate with refined constants is provided for κ-means instances possessing some cluster structure.
Original language | English (US) |
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Journal | Advances in Neural Information Processing Systems |
State | Published - 2013 |
Event | 27th Annual Conference on Neural Information Processing Systems, NIPS 2013 - Lake Tahoe, NV, United States Duration: Dec 5 2013 → Dec 10 2013 |
ASJC Scopus subject areas
- Computer Networks and Communications
- Information Systems
- Signal Processing