Online Kernel Matrix Factorization

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Matrix factorization (MF) has shown to be a competitive machine learning strategy for many problems such as dimensionality reduction, latent topic modeling, clustering, dictionary learning and manifold learning, among others. In general, MF is a linear modeling method, so different strategies, most of them based on kernel methods, have been proposed to extend it to non-linear modeling. However, as with many other kernel methods, memory requirements and computing time limit the application of kernel-based MF methods in large-scale problems. In this paper, we present a new kernel MF (KMF). This method uses a budget, a set of representative points of size $$p\ll n$$ , where n is the size of the training data set, to tackle the memory problem, and uses stochastic gradient descent to tackle the computation time and memory problems. The experimental results show a performance, in particular tasks, comparable to other kernel matrix factorization and clustering methods, and a competitive computing time in large-scale problems.