Laplacian normalization for deriving thematic fuzzy clusters with an additive spectral approach

Authors

  • Susana Nascimento,

    Corresponding author
    • Department of Computer Science and Centre for Artificial Intelligence (CENTRIA), Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal
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  • Rui Felizardo,

    1. Department of Computer Science and Centre for Artificial Intelligence (CENTRIA), Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa, Caparica, Portugal
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  • Boris Mirkin

    1. Department of Computer Science, Birkbeck University of London, London, UK
    2. School of Applied Mathematics and Informatics, National Research University Higher School of Economics, Moscow, Russian Federation
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Abstract

This paper presents a further investigation into computational properties of a novel fuzzy additive spectral clustering method, Fuzzy Additive Spectral clustering (FADDIS), recently introduced by authors. Specifically, we extend our analysis to ‘difficult’ data structures from the recent literature and develop two synthetic data generators simulating affinity data of Gaussian clusters and genuine additive similarity data, with a controlled level of noise. The FADDIS is experimentally verified on these data in comparison with two state-of-the-art fuzzy clustering methods. The claimed ability of FADDIS to help in determining the right number of clusters is experimentally tested, and the role of the pseudo-inverse Laplacian data transformation in this is highlighted. A potentially useful extension of the method to biclustering is introduced.

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