Learning a Partial Graph and the Nyström Extension for Spectral Clustering

Gurugubelli, S and Kadambari, SK and Prabhakar Chepuri, S (2021) Learning a Partial Graph and the Nyström Extension for Spectral Clustering. In: 55th Asilomar Conference on Signals, Systems and Computers, ACSSC 2021, 31 October 2021 - 3 November 2021, Virtual, Pacific Grove, pp. 1531-1535.

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Abstract

We focus on partial graph learning for spectral clustering based on the Nyström method, which uses only a subset of the columns of a positive semi-definite matrix to approximate its eigenvectors. We propose an algorithm to learn only those graph edges that are required by the Nyström method instead of learning the entire graph. Assuming a smoothness data model, we learn a multi-component subgraph and the cluster affiliations of the remaining nodes in the graph to the nodes in the subgraph. We propose an efficient solver based on alternating minimization that solves for the node embeddings of the partial graph via the Nyström method and learns the partial graph in an alternating manner. Experiments performed on real datasets demonstrate that the proposed method outperforms the standard Nyström based spectral clustering technique that uses Gaussian similarity kernel to construct the partial graph in terms of both run time and clustering performance, and achieves clustering performance comparable to that achieved by learning a complete multicomponent graph and its node embeddings in approximately half its run time. © 2021 IEEE.

Item Type:	Conference Proceedings
Publication:	Conference Record - Asilomar Conference on Signals, Systems and Computers
Publisher:	IEEE Computer Society
Additional Information:	The copyright for this article belongs to IEEE Computer Society
Keywords:	Computer vision; Embeddings; Graph theory, Embeddings; Graph learning; Learn+; Multicomponents; Nystrom approximation; Nystrom method; Representation learning; Sketchings; Spectral clustering; Subgraphs, Clustering algorithms
Department/Centre:	Division of Electrical Sciences > Electronic Systems Engineering (Formerly Centre for Electronic Design & Technology) Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited:	19 May 2022 10:55
Last Modified:	19 May 2022 10:55
URI:	https://eprints.iisc.ac.in/id/eprint/71913

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