Efficient Nystrom method for low rank approximation and error analysis

Abstract

Kernel methods suffer from the high time and space complexity because kernel methods having large kernel matrix for training data. So we have to speed up the kernel method. That problem is solved by the low rank approximation. In this paper, we compare the two sampling based low rank approximation techniques implement for the large kernel matrix. First one is standard Nystrom method and the second is our proposed efficient Nystrom method. In the proposed approach we extract the low dimension form the high dimensional data using low rank approximation. We have shown the quality of low rank approximation based on Frobenius norm and spectral norm. Our experimental results show efficient Nystrom method is superior as compared to standard Nystrom method. We show the comparison based on the various error bounds. We perform the efficient Nystrom method on variety of data sets.