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.