Exploratory Data Analysis and Searching Cliques in Graphs

Hubai, András and Szabó, Sándor and Zaválnij, Bogdán (2024) Exploratory Data Analysis and Searching Cliques in Graphs. ALGORITHMS, 17 (3). ISSN 1999-4893

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Abstract

The principal component analysis is a well-known and widely used technique to determine the essential dimension of a data set. Broadly speaking, it aims to find a low-dimensional linear manifold that retains a large part of the information contained in the original data set. It may be the case that one cannot approximate the entirety of the original data set using a single low-dimensional linear manifold even though large subsets of it are amenable to such approximations. For these cases we raise the related but different challenge (problem) of locating subsets of a high dimensional data set that are approximately 1-dimensional. Naturally, we are interested in the largest of such subsets. We propose a method for finding these 1-dimensional manifolds by finding cliques in a purpose-built auxiliary graph.

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