Nonnegative matrix factorization with local similarity learning

摘要

High-dimensional data are ubiquitous in the learning community and it has become increasingly challenging to learn from such data [1]. For example, as one of the most important tasks in multimedia and data mining, information retrieval has drawn considerable attentions in recent years [2-4], where there is often a need to handle high-dimensional data. Often times, it is desirable and demanding to seek a data representation to reveal latent data structures of high-dimensional data, which is usually helpful for further data processing. It is thus a critical problem to find a suitable representation of the data in many learning tasks, such as image clustering and classification [5,1], foreground-background separation in surveillance video [6,7], matrix completion [8], community detection [9], link prediction [10], etc. To this end, a number of methods have been developed to seek proper representations of data, among which matrix factorization technique has been widely used to handle high-dimensional data. Matrix factorization seeks two or more low-dimensional matrices to approximate the original data such that the high-dimensional data can be represented with reduced dimensions [11,12]. For some types of data, such as images and documents, the entries are naturally nonnegative. For such data, nonnegative