On the Consistency of Spectral Clustering under Generalized Gaussian Mixture Models
Abstract
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.
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BibTeX
@misc{zhang2026consistency,
title = {{On the Consistency of Spectral Clustering under Generalized Gaussian Mixture Models}},
author = {Lyuou Zhang and Boxiang Wang and Wen Zhou and Hui Zou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33944},
eprint = {2610.33944},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33944},
note = {CC0},
}
RIS
TY - UNPB
TI - On the Consistency of Spectral Clustering under Generalized Gaussian Mixture Models
AU - Lyuou Zhang
AU - Boxiang Wang
AU - Wen Zhou
AU - Hui Zou
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33944
UR - https://arxiv.org/abs/2610.33944
AB - 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.
ER -