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

Expert Systems: The Journal of Knowledge Engineering. 2013. Vol. 30. No. 4. P. 294–305.

Mirkin B., Nascimento S., Felizardo R.

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.

Keywords: spectral fuzzy clustering, number of clusters, спектральный кластер, Laplacian normalization, число кластеров, нормализация Лапласа

Publication based on the results of: An investigation of new methods of mathematical modelling and mechanism design in the social, economic and political sciences (2013)