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Extended Box Clustering for Classification Problems

Extended Box Clustering for Classification Problems In this work we address a technique, based on elementary convex sets called box hulls, for effectively grouping finite point sets into non-convex objects, called box clusters. The proposed clustering approach is based on homogeneity conditions, not according to some distance measure, and it is situated inside the theoretical framework of Supervised clustering. This approach extends the so-called (convex) box clustering, originally developed in the context of the logical analysis of data, to non-convex geometry. We briefly discuss the topological properties of these clusters and introduce a family of hypergraphs, called incompatibility hypergraphs; the main aim for these hypergraphs is their role in clustering algorithms, even if they have strong theoretical properties as shown in other works in literature. We also discuss of supervised classification problems and generalized Voronoi diagrams are considered to define a classifier based on box clusters. Finally, computational experiments on real world data are used to show the efficacy of our methods both in terms of clustering and accuracy. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Classification Springer Journals

Extended Box Clustering for Classification Problems

Spinelli, Vincenzo
Journal of Classification , Volume 35 (1) – Mar 16, 2018
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References (48)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Classification Society of North America
Subject
Statistics; Statistical Theory and Methods; Pattern Recognition; Bioinformatics; Signal,Image and Speech Processing; Psychometrics; Marketing
ISSN
0176-4268
eISSN
1432-1343
DOI
10.1007/s00357-018-9253-2
Publisher site
See Article on Publisher Site

Abstract

In this work we address a technique, based on elementary convex sets called box hulls, for effectively grouping finite point sets into non-convex objects, called box clusters. The proposed clustering approach is based on homogeneity conditions, not according to some distance measure, and it is situated inside the theoretical framework of Supervised clustering. This approach extends the so-called (convex) box clustering, originally developed in the context of the logical analysis of data, to non-convex geometry. We briefly discuss the topological properties of these clusters and introduce a family of hypergraphs, called incompatibility hypergraphs; the main aim for these hypergraphs is their role in clustering algorithms, even if they have strong theoretical properties as shown in other works in literature. We also discuss of supervised classification problems and generalized Voronoi diagrams are considered to define a classifier based on box clusters. Finally, computational experiments on real world data are used to show the efficacy of our methods both in terms of clustering and accuracy.

Journal

Journal of Classification – Springer Journals

Published: Mar 16, 2018

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