Online Kernel Sliced Inverse Regression

TL;DR

This paper introduces an online kernel sliced inverse regression method for high-dimensional streaming data, addressing the challenge of increasing variable dimensions and enabling efficient online updates with performance comparable to batch methods.

Contribution

It proposes a novel online nonlinear dimension reduction technique using kernel sliced inverse regression with approximate linear dependence and dictionary variables.

Findings

Achieves performance close to batch kernel sliced inverse regression.

Effectively handles increasing variable dimensions in online settings.

Uses stochastic optimization for online updating of dimension reduction directions.

Abstract

Online dimension reduction is a common method for high-dimensional streaming data processing. Online principal component analysis, online sliced inverse regression, online kernel principal component analysis and other methods have been studied in depth, but as far as we know, online supervised nonlinear dimension reduction methods have not been fully studied. In this article, an online kernel sliced inverse regression method is proposed. By introducing the approximate linear dependence condition and dictionary variable sets, we address the problem of increasing variable dimensions with the sample size in the online kernel sliced inverse regression method, and propose a reduced-order method for updating variables online. We then transform the problem into an online generalized eigen-decomposition problem, and use the stochastic optimization method to update the centered dimension reduction directions. Simulations and the real data analysis show that our method can achieve close performance to batch processing kernel sliced inverse regression.