Online sketching for big data subspace learning

Sketching (a.k.a. subsampling) high-dimensional data is a crucial task to facilitate data acquisition process e.g., in magnetic resonance imaging, and to render affordable `Big Data' analytics. Multidimensional nature and the need for realtime processing of data however pose major obstacles. To cope with these challenges, the present paper brings forth a novel real-time sketching scheme that exploits the correlations across data stream to learn a latent subspace based upon tensor PARAFAC decomposition `on the fly.' Leveraging the online subspace updates, we introduce a notion of importance score, which is subsequently adapted into a randomization scheme to predict a minimal subset of important features to acquire in the next time instant. Preliminary tests with synthetic data corroborate the effectiveness of the novel scheme relative to uniform sampling.