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Computation of the similarity matrix for the spectral clustering method: numerical experiments

Spectral clustering is a powerful method for finding structure in adataset through the eigenvectors of a similarity matrix. It often outperformstraditional clustering algorithms such as k-means when thestructure of the individual clusters is highly non-convex. Its accuracydepends on how the similarity between pairs of data points is defined.Two important items contribute to the construction of the similaritymatrix: the sparsity of the underlying weighted graph, which dependsmainly on the distances among data points, and the similarity function.When a Gaussian similarity function is used, the choice of thescale parameter σ can be critical. In this paper we examine both items,the sparsity and the selection of suitable σ’s, based either directly onthe graph associated to the dataset or on the minimal spanning tree(MST) of the graph. An extensive numerical experimentation on artificialand real-world datasets has been carried out to compare theperformances of the methods.

2017

Autori esterni: Grazia Lotti (Dipartimento di matematica, Universita' di Parma, Italia), Ornella Menchi (Dipartimento di informatica, Universita' di Pisa, Italia), Francesco Romani (Dipartimento di informatica, Universita' di Pisa, Italia)
Autori IIT:

Tipo: Rapporto Tecnico
Area di disciplina: Mathematics
IIT TR-09/2017

File: IIT-09-2017.pdf

Attività: Metodi numerici per problemi di grandi dimensioni