Classification of streaming big data with misses

Classification is a task of paramount importance for learning tasks involved in nowadays `Big Data´ applications. It is however challenged by the large volume of streaming and possibly incomplete data, and the need for real-time processing. The present paper advocates a novel approach that leverages the intrinsic low-dimensionality of (possibly large-scale) data to design a support-vector-machine (SVM) classifier from feature vectors with misses `on the fly.´ Towards this end, the max-margin cost function is regularized with the nuclear-norm to jointly impute the missing features and design the SVM hyperplane. Iterative batch and online algorithms are developed. Per iteration, a low-dimensional subspace is updated to enable imputation, and the SVM hyperplane is adjusted accordingly. Lightweight first-order iterations are also devised using stochastic alternating-minimization carried out via simple updates. Preliminary numerical tests corroborate the effectiveness of the novel approach.