Cost-based Reweighting for Principal Lq Support Vector Machines for Sufficient Dimension Reduction

Andreas Artemiou

doi:10.3844/jmssp.2019.218.224

Abstract

In this work we try to address the imbalance of the number of points which naturally occurs when slicing the response in Sufficient Dimension Reduction methods (SDR). Specifically, some recently proposed support vector machine based (SVM-based) methodology suffers a lot more due to the properties of the SVM algorithm. We target a recently proposed algorithm called Principal LqSVM and we propose the reweighting based on a different cost. We demonstrate that our reweighted proposal works better than the original algorithm in simulated and real data.

Highlights

Sufficient Dimension Reduction (SDR) is a class of supervised linear and nonlinear feature extraction methods which are being developed mainly in a regression as well as in classification settings
The linearity condition is very common in linear feature extraction in the SDR literature
We note that the imbalance in the SDR framework is artificial as it depends on the way we select the number of slices, with higher number of slices leading to a more imbalance between the slices

Summary

Introduction

Sufficient Dimension Reduction (SDR) is a class of supervised linear and nonlinear feature extraction methods which are being developed mainly in a regression as well as in classification settings. Since there are many β’s that satisfy model (1) we focus on estimating the one which gives the minimum d If such a space exists, we call it the Central Dimension Reduction Subspace (CDRS) or the Central Subspace (CS), which is denoted by SY|X. The interested reader is referred to Cook (1998) for more details on the existence of the subspace Some methods under this model include Sliced Inverse Regression (SIR) by Li (1991), Sliced Average Variance Estimation (SAVE) by Cook and Weisberg (1991), Contour Regression (CR) by Li et al (2005), Directional Regression (DR) by Li and Wang (2007) and Sliced Inverse Mean Difference (SIMD) by Artemiou and Tian (2015). Most of the methods discussed here use inverse moments to perform feature extraction

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Conclusion