Succinct Matrix Approximation and Efficient k-NN Classification

This work reveals that instead of the polynomial bounds in previous literatures there exists a sharper bound of exponential form for the L₂ norm of an arbitrary shaped random matrix. Based on the newly elaborated bound, a nonuniform sampling method is presented to succinctly approximate a matrix with a sparse binary one, and thus relieves the computation loads of k-NN classifier in both time and storage. The method is also pass-efficient because sampling and quantizing are combined together in a single step and the whole process can be completed within one pass over the input matrix. In the evaluations on compression ratio and reconstruction error, the sampling method exhibits impressive capability in providing succinct and tight approximations for the input matrices. The most significant finding in the classification experiment is that the k-NN classifier based on the approximation can even outperform the standard one. This provides another strong evidence for the claim that our method is especially capable in capturing intrinsic characteristics.