Embedding of the Hamming space into a sphere with weighted quadrance metric and c-means clustering of nominal-continuous data

Article type: Research Article

Authors: Denisiuk, Aleksander^{a; *} | Grabowski, Michał^b

Affiliations: [a] Department of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, Olsztyn, Poland | [b] Warsaw School of Computer Science, Warsaw, Poland

Correspondence: [*] Corresponding author: Aleksander Denisiuk, Department of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn, ul. Słoneczna 54, 10-710 Olsztyn, Poland. E-mail: [email protected].

Abstract: In this paper we present a new c-means clustering algorithm for combined continuous-nominal data. We use spherical representation of nominal data. The impact of specific features is modeled with corresponding weights in metric definition. To solve constrained minimization problem we transfer the methodology of reformulation functions to the considered context. As a result we obtain a clustering algorithm with adaptation of weights. Series of numerical experiments on real and synthetic data show that the algorithm can successfully cluster raw, non-normalized data.

Keywords: C-means clustering, weighted metric, nominal-continuous data, low-distortion embedding, quadrance, reformulation

DOI: 10.3233/IDA-173645

Journal: Intelligent Data Analysis, vol. 22, no. 6, pp. 1297-1314, 2018