Subspace Learning and Imputation for Streaming Big Data Matrices and Tensors - 2015
Extracting latent low-dimensional structure from high-dimensional information is of paramount importance in timely inference tasks encountered with “Huge Information” analytics. However, increasingly noisy, heterogeneous, and incomplete datasets, and the requirement for real-time processing of streaming information, create major challenges to the current end. In this context, the present paper permeates edges from rank minimization to scalable imputation of missing data, via tracking low-dimensional subspaces and unraveling latent (probably multi-means) structure from incomplete streaming information. For low-rank matrix knowledge, a subspace estimator is proposed primarily based on an exponentially weighted least-squares criterion regularized with the nuclear norm. After recasting the nonseparable nuclear norm into a kind amenable to online optimization, real-time algorithms with complementary strengths are developed, and their convergence is established under simplifying technical assumptions. During a stationary setting, the asymptotic estimates obtained supply the well-documented performance guarantees of the batch nuclear-norm regularized estimator. Underneath the same unifying framework, a unique online (adaptive) algorithm is developed to get multi-manner decompositions of low-rank tensors with missing entries and perform imputation as a byproduct. Simulated tests with each artificial plus real Internet and cardiac magnetic resonance imagery (MRI) information confirm the efficacy of the proposed algorithms, and their superior performance relative to state-of-the-art alternatives.
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