Title: A distance scaling method to improve spectral clustering of data with different densities

Authors: Hassan Motallebi; Mina Jamshidi

Addresses: Department of Electrical and Computer Engineering, Graduate University of Advanced Technology, Kerman, Iran ' Department of Applied Mathematics, Graduate University of Advanced Technology, Kerman, Iran

Abstract: Despite its advantages over other types of clustering, most spectral clustering algorithms have challenges in finding clusters with varied densities. Another challenge of these algorithms is discovering poorly separated clusters. Both issues are due to the fact that the distance between two points is not always a good measure of their similarity; a point can be closer to a dissimilar point in another cluster than to points in its own cluster. To overcome this, we propose a distance scaling method, which rescales the distance between two points according to their local densities and the shared neighbourhood information. Based on the scaling method, we propose a fuzzy spectral clustering algorithm. We propose a recursive notion of membership degree and design an iterative algorithm for approximating membership degrees. The results of our experiments shows that the proposed distance scaling method improves clustering performance for poorly separated clusters and clusters with varied densities.

Keywords: spectral clustering; distance scaling; density-based measure; fuzzy membership degree; shared neighbours.

DOI: 10.1504/IJDS.2021.122778

International Journal of Data Science, 2021 Vol.6 No.4, pp.328 - 347

Received: 04 Aug 2021
Accepted: 29 Dec 2021
Published online: 10 May 2022 *

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