Spectral clustering is a widely used clustering method with strong empirical performance and favorable computational scalability. Existing theory has established its consistency and risk guarantees under Gaussian and related mixture models, primarily in settings with relatively simple latent structure. In this paper, we study spectral clustering under a semiparametric Gaussian mixture model, where the observed data become Gaussian-mixture distributed only after unknown monotone coordinate-wise transformations. We derive non-asymptotic bounds for its cluster recovery error. As a byproduct of the theory, we show that spectral clustering provides a theoretically justified initialization for a broad class of high-dimensional mixture-based learning procedures.

翻译：暂无翻译