Regularizaed extraction of non-negative latent factors from high-dimensional sparse matrices

With the exploration of the World Wide Web, more and more entities are involved in various online applications, e.g., recommender systems and social network services. In such context, high-dimensional sparse matrices describing the relationships among them are frequently encountered. It is highly important to develop efficient non-negative latent factor (NLF) models for these high-dimensional sparse relationships because of a) their ability to extract useful knowledge from them; b) their fulfillment of the non-negativity constraints for representing most non-negative industrial data; and c) their high computational and storage efficiency on high-dimensional sparse matrices. However, due to the imbalanced distribution of known data in such a matrix, it is necessary to investigate the regularization effect in NLF models. We first review the NLF model briefly. Then we propose to integrate the frequency-weight on each involved entity into its Tikhonov regularization terms, for representing the imbalanced data from a high-dimensional sparse matrix. Experimental results on industrial-size matrices indicate that the proposed scheme is effective in improving the performance of the NLF model in missing-data-estimation.