Optimality of spectral clustering in the Gaussian Mixture Model


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Date

2020-08-05

Publication Type

Working Paper

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Abstract

Spectral clustering is one of the most popular algorithms to group high dimensional data. It is easy to implement and computationally efficient. Despite its popularity and successful applications, its theoretical properties have not been fully understood. In this paper, we show that spectral clustering is minimax optimal in the Gaussian Mixture Model with isotropic covariance matrix, when the number of clusters is fixed and the signal-to-noise ratio is large enough. Spectral gap conditions are widely assumed in the literature to analyze spectral clustering. On the contrary, these conditions are not needed to establish optimality of spectral clustering in this paper

Publication status

published

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Volume

Pages / Article No.

1911.00538

Publisher

Cornell University

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Subject

Clustering; High-dimensional estimation; PCA; Gaussian mixture model; k-means clustering

Organisational unit

02537 - Seminar für Statistik (SfS) / Seminar for Statistics (SfS)

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