Kernel-based framework for spectral dimensionality reduction and clustering formulation: A theoretical study

Author:

Blanco Valencia Xiomara Patricia,Becerra M. A.,Castro Ospina A. E.,Ortega Adarme M.,Viveros Melo D.,Peluffo Ordóñez D. H.

Abstract

This work outlines a unified formulation to represent spectral approaches for both dimensionality reduction and clustering. Proposed formulation starts with a generic latent variable model in terms of the projected input data matrix.Particularly, such a projection maps data onto a unknown high-dimensional space. Regarding this model, a generalized optimization problem is stated using quadratic formulations and a least-squares support vector machine.The solution of the optimization is addressed through a primal-dual scheme.Once latent variables and parameters are determined, the resultant model outputs a versatile projected matrix able to represent data in a low-dimensional space, as well as to provide information about clusters. Particularly, proposedformulation yields solutions for kernel spectral clustering and weighted-kernel principal component analysis.

Publisher

Ediciones Universidad de Salamanca

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