Presentation 2-1, 13:10~13:35.
Speaker
Kohei Kawamoto (Kyushu University)
Title
Spectral Clustering Algorithm for the Gaussian Mixture Model
Abstract
The spectral clustering algorithm, often implemented through principal component analysis, has become a widely used method for binary clustering of unclassified data. While much of the existing theoretical analysis relies on the conditional homoscedasticity assumption, this condition is restrictive and often unrealistic in practical applications. In this paper, we investigate the spectral clustering algorithm under a general Gaussian mixture model without assuming conditional homoscedasticity or alignment between mean and covariance structures. We derive a non-asymptotic upper bound for the misclassification probability, which explicitly characterizes the effects of mean separation, covariance heterogeneity, and sample size. As a consequence, we establish the consistency of spectral clustering in high-dimensional regimes under mild and interpretable conditions.