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Making nonlinear manifold learning models interpretable: The manifold grand tour

Lisboa, P and Martín-Guerrero, JD and Vellido, A (2015) Making nonlinear manifold learning models interpretable: The manifold grand tour. Expert Systems with Applications, 42 (22). pp. 8982-8988. ISSN 0957-4174

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Abstract

Dimensionality reduction is required to produce visualisations of high dimensional data. In this framework, one of the most straightforward approaches to visualising high dimensional data is based on reducing complexity and applying linear projections while tumbling the projection axes in a defined sequence which generates a Grand Tour of the data. We propose using smooth nonlinear topographic maps of the data distribution to guide the Grand Tour, increasing the effectiveness of this approach by prioritising the linear views of the data that are most consistent with global data structure in these maps. A further consequence of this approach is to enable direct visualisation of the topographic map onto projective spaces that discern structure in the data. The experimental results on standard databases reported in this paper, using self-organising maps and generative topographic mapping, illustrate the practical value of the proposed approach. The main novelty of our proposal is the definition of a systematic way to guide the search of data views in the grand tour, selecting and prioritizing some of them, based on nonlinear manifold models.

Item Type: Article
Uncontrolled Keywords: 01 Mathematical Sciences, 08 Information And Computing Sciences
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Applied Mathematics
Publisher: Elsevier
Date Deposited: 30 Oct 2015 13:50
Last Modified: 07 Oct 2016 11:00
DOI or Identification number: 10.1016/j.eswa.2015.07.054
URI: http://researchonline.ljmu.ac.uk/id/eprint/2266

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