Manifold regularization based on Nystr{\"o}m type subsampling

TL;DR

This paper introduces a Nyström-based subsampling method for large-scale kernel learning, providing a theoretical framework and demonstrating its effectiveness in image classification and intrusion detection tasks.

Contribution

It develops a multi-penalty regularization scheme with theoretical analysis and optimal convergence rates, tailored for Nyström subsampling in large-scale kernel methods.

Findings

Achieves optimal minimax convergence rates.

Demonstrates effectiveness on Caltech-101 and NSL-KDD datasets.

Proposes an aggregation approach for combining Nyström approximants.

Abstract

In this paper, we study the Nystr{\"o}m type subsampling for large scale kernel methods to reduce the computational complexities of big data. We discuss the multi-penalty regularization scheme based on Nystr{\"o}m type subsampling which is motivated from well-studied manifold regularization schemes. We develop a theoretical analysis of multi-penalty least-square regularization scheme under the general source condition in vector-valued function setting, therefore the results can also be applied to multi-task learning problems. We achieve the optimal minimax convergence rates of multi-penalty regularization using the concept of effective dimension for the appropriate subsampling size. We discuss an aggregation approach based on linear function strategy to combine various Nystr{\"o}m approximants. Finally, we demonstrate the performance of multi-penalty regularization based on Nystr{\"o}m type subsampling on Caltech-101 data set for multi-class image classification and NSL-KDD benchmark data set for intrusion detection problem.