Optimal Clustering in Anisotropic Gaussian Mixture Models
Statistics Theory
2021-01-19 v2 Machine Learning
Machine Learning
Statistics Theory
Abstract
We study the clustering task under anisotropic Gaussian Mixture Models where the covariance matrices from different clusters are unknown and are not necessarily the identical matrix. We characterize the dependence of signal-to-noise ratios on the cluster centers and covariance matrices and obtain the minimax lower bound for the clustering problem. In addition, we propose a computationally feasible procedure and prove it achieves the optimal rate within a few iterations. The proposed procedure is a hard EM type algorithm, and it can also be seen as a variant of the Lloyd's algorithm that is adjusted to the anisotropic covariance matrices.
Cite
@article{arxiv.2101.05402,
title = {Optimal Clustering in Anisotropic Gaussian Mixture Models},
author = {Xin Chen and Anderson Y. Zhang},
journal= {arXiv preprint arXiv:2101.05402},
year = {2021}
}