Spectral clustering in the Gaussian mixture block model

[2305.00979] Spectral clustering in the Gaussian mixture block model Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Statistics > Machine Learning arXiv:2305.00979 (stat) [Submitted on 29 Apr 2023 ( v1 ), last revised 14 Aug 2026 (this version, v4)] Title: Spectral clustering in the Gaussian mixture block model Authors: Shuangping Li , Tselil Schramm View a PDF of the paper titled Spectral clustering in the Gaussian mixture block model, by Shuangping Li and 1 other authors View PDF HTML (experimental) Abstract: Gaussian mixture block models are distributions over graphs that strive to model modern networks: to generate a graph from such a model, we associate each vertex $i$ with a latent feature vector $u_i \in \mathbb{R}^d$ sampled from a mixture of Gaussians, and we add edge $(i,j)$ if and only if the feature vectors are sufficiently similar, in that $\langle u_i,u_j \rangle \ge \tau$ for a pre-specified threshold $\tau$. The different components of the Gaussian mixture represent the fact that there may be different types of nodes with different distributions over features -- for example, in a social network each component represents the different attributes of a distinct community. Natural algorithmic tasks associated with these networks are embedding (recovering the latent feature vectors) and clustering (grouping nodes by their mixture component). In this paper we initiate the study of clustering and embedding graphs sampled from high-dimensional Gaussian mixture block models, where the dimension of the latent feature vectors $d\to \infty$ as the size of the network $n \to \infty$. This high-dimensional setting is most appropriate in the context of modern networks, in which we think of the latent feature space as being high-dimensional. We analyze the performance of canonical spectral clustering and embedding algorithms for such graphs in the case of 2-component spherical Gaussian mixtures, and begin to sketch out the information-computation landscape for clustering and embedding in these models. Comments: 54 pages. Accepted for publication in the Annals of Applied Probability Subjects: Machine Learning (stat.ML) ; Data Structures and Algorithms (cs.DS); Social and Information Networks (cs.SI); Probability (math.PR); Statistics Theory (math.ST) Cite as: arXiv:2305.00979 [stat.ML] (or arXiv:2305.00979v4 [stat.ML] for this version) https://doi.org/10.48550/arXiv.2305.00979 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Shuangping Li [ view email ] [v1] Sat, 29 Apr 2023 23:56:55 UTC (47 KB) [v2] Mon, 25 Mar 2024 07:47:57 UTC (56 KB) [v3] Wed, 10 Apr 2024 23:06:38 UTC (58 KB) [v4] Fri, 14 Aug 2026 18:25:28 UTC (57 KB) Full-text links: Access Paper: View a PDF of the paper titled Spectral clustering in the Gaussian mixture block model, by Shuangping Li and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: stat.ML < prev | next > new | recent | 2023-05 Change to browse by: cs cs.DS cs.SI math math.PR math.ST stat stat.TH References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... 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