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arXiv · 1710.04872

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

Abhishake Rastogi·Sivananthan Sampath
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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.

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Abhishake Rastogi, Sivananthan Sampath. 2017-10-13. Manifold regularization based on Nystr{\"o}m type subsampling. https://doi.org/10.1016/j.acha.2018.12.002

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