Sparse and online null proximal discriminant analysis for one class learning in large-scale datasets

Recently, null proximal discriminant analysis (NPDA) has been introduced in [1] to identify anomalies in a target data set. However, the proposed algorithm involves high computational burden and memory requirement which limit its use to moderate sized static datasets. The goal of this paper is to propose an incremental and sparse NPDA which is able both to process sequentially a large volume of data and remove the redundant information. More precisely, our solution lies in computing the null projection direction by a recursive singular value decomposition in the kernel induced feature space. Sparsity of the solution is achieved by thresholding the null score between the already processed data and newly injected data. The combined action of these two steps introduces a significant gain in terms of time complexity and memory burden while offering comparable classification performance as the batch method. Experimental results on large-scale data sets confirm the effectiveness of the proposed algorithm.