A More Efficient and Practical Modified Nyström Method

Wei Zhang (), Zhe Sun, Jian Liu and Suisheng Chen
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Wei Zhang: Fair Friend Institute of Intelligent Manufacturing, Hangzhou Vocational & Technical College, Hangzhou 310018, China
Zhe Sun: Post Industry Technology Research and Development Center of the State Posts Bureau (Internet of Things Technology), Nanjing University of Posts and Telecommunications, Nanjing 210023, China
Jian Liu: College of Information Engineering, Nanjing University of Finance and Economics, Nanjing 210023, China
Suisheng Chen: Fair Friend Institute of Intelligent Manufacturing, Hangzhou Vocational & Technical College, Hangzhou 310018, China

Mathematics, 2023, vol. 11, issue 11, 1-13

Abstract: In this paper, we propose an efficient Nyström method with theoretical and empirical guarantees. In parallel computing environments and for sparse input kernel matrices, our algorithm can have computation efficiency comparable to the conventional Nyström method, theoretically. Additionally, we derive an important theoretical result with a compacter sketching matrix and faster speed, at the cost of some accuracy loss compared to the existing state-of-the-art results. Faster randomized SVD and more efficient adaptive sampling methods are also proposed, which have wide application in many machine-learning and data-mining tasks.

Keywords: kernel method; Nyström method; low-rank approximation; machine learning (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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