Cutoff for exact recovery of Gaussian mixture models
Abstract
We determine the information-theoretic cutoff value on separation of cluster centers for exact recovery of cluster labels in a $K$-component Gaussian mixture model with equal cluster sizes. Moreover, we show that a semidefinite programming (SDP) relaxation of the $K$-means clustering method achieves such sharp threshold for exact recovery without assuming the symmetry of cluster centers.
- Publication:
-
arXiv e-prints
- Pub Date:
- January 2020
- DOI:
- 10.48550/arXiv.2001.01194
- arXiv:
- arXiv:2001.01194
- Bibcode:
- 2020arXiv200101194C
- Keywords:
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- Mathematics - Statistics Theory;
- Computer Science - Data Structures and Algorithms;
- Computer Science - Information Theory;
- Mathematics - Probability;
- Statistics - Machine Learning