Online low-rank subspace learning from incomplete data using rank revealing ℓ2/ℓ1 regularization

Massive amounts of data (also called big data) generated by a wealth of sources such as social networks, satellite sensors etc., necessitate the deployment of efficient processing tools. In this context, online subspace learning algorithms that aim at retrieving low-rank representations of data constitute a mainstay in many applications. Working with incomplete (partially observed) data has recently become commonplace. Moreover, the knowledge of the real rank of the sought subspace is rarely at our disposal a priori. Herein, a novel low-rank subspace learning algorithm from incomplete data is presented. Its main premise is the online processing of incomplete data along with the imposition of low-rankness on the sought subspace via a sophisticated utilization of the group sparsity inducing ℓ2/ℓ1 norm. As is experimentally shown, the resulting scheme is efficient in accurately learning the subspace as well as in unveiling its real rank.