On some spectral properties of stochastic similarity matrices for data clustering

2019/10/03 by Denis Gaidashev, Gaidashev, Denis, Ralf Pihlström +3
Computer Science · Mathematics · #60B20 #65C50 #91C20 #Bayesian Methods and Mixture Models #FOS: Mathematics #Image Retrieval and Classification Techniques #Morphological variations and asymmetry #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1910.01392

openalex publication_date 2019/10/03 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for Gaussian mixture distributions, and in particular, provide conditions for the existence of a spectral gap between the leading and remaining eigenvalues for matrices with entries from a Gaussian mixture with two real univariate components. Furthermore, we describe an algorithm in which a collection of image elements is treated as a dynamical system in which the existence of the mentioned spectral gap results in an efficient clustering.

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