Open AccessKernel-based framework for spectral dimensionality reduction and clustering formulation: A theoretical study
Author(s) -
Xiomara Patricia Blanco Valencia,
Miguel A. Becerra,
Andrés Eduardo Castro-Ospina,
M. Ortega Adarme,
D. Viveros Melo,
Diego Ordóñez
Publication year - 2017
Publication title -
advances in distributed computing and artificial intelligence journal
Language(s) - English
Resource type - Journals
ISSN - 2255-2863
DOI - 10.14201/adcaij2017613140
Subject(s) - cluster analysis , dimensionality reduction , spectral clustering , kernel (algebra) , mathematics , kernel principal component analysis , kernel method , projection (relational algebra) , latent variable , principal component analysis , mathematical optimization , curse of dimensionality , clustering high dimensional data , matrix (chemical analysis) , algorithm , computer science , artificial intelligence , support vector machine , materials science , composite material , combinatorics
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.