Regularized multidimensional scaling with  radial basis functions

Sohana  Jahan; Hou-Duo  Qi

doi:10.3934/jimo.2016.12.543

Article Contents

2016, Volume 12, Issue 2: 543-563. Doi: 10.3934/jimo.2016.12.543

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Regularized multidimensional scaling with radial basis functions

Sohana Jahan^1, and
Hou-Duo Qi^1,

1.
School of Mathematics, University of Southampton

Received: July 31, 2014

Revised: December 31, 2014

Published: March 2016

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Abstract

The classical Multi-Dimensional Scaling (MDS) is an important method for data dimension reduction. Nonlinear variants have been developed to improve its performance. One of them is the MDS with Radial Basis Functions (RBF). A key issue that has not been well addressed in MDS-RBF is the effective selection of its centers. This paper treats this selection problem as a multi-task learning problem, which leads us to employ the $(2,1)$-norm to regularize the original MDS-RBF objective function. We then study its two reformulations: Diagonal and spectral reformulations. Both can be effectively solved through an iterative block-majorization method. Numerical experiments show that the regularized models can improve the original model significantly.

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Mathematics Subject Classification: Primary: 62H30, 68T10; Secondary: 90C25.

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