SUBSPACE LEARNING AND IMPUTATION FOR STREAMING BIG DATA MATRICES AND TENSORS
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The document discusses a method for extracting low-dimensional structure from high-dimensional data in the context of streaming big data analytics. It introduces algorithms based on rank minimization for scaling imputation of missing data while tracking subspaces, utilizing techniques like exponentially weighted least-squares and nuclear norm regularization. Simulations demonstrate the effectiveness of the proposed approaches compared to existing solutions, particularly in handling low-rank matrix and tensor data with missing entries.
SUBSPACE LEARNING AND IMPUTATION FOR STREAMING BIG DATA MATRICES AND TENSORS
- 1. SUBSPACE LEARNING AND IMPUTATION FOR STREAMING BIG DATA MATRICES AND TENSORS ABSTRACT Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with “Big Data” analytics. However, increasingly noisy, heterogeneous, and incomplete datasets, as well as the need for real-time processing of streaming data, posemmajor challenges to this end. In this context, the present paper permeates benefits from rank minimization to scalable imputation of missing data, via tracking low-dimensional subspaces and unraveling latent (possibly multi-way) structure from incomplete streaming data. For low-rank matrix data, a subspace estimator is proposed based on an exponentially weighted least-squares criterion regularized with the nuclear norm. After recasting the nonseparable nuclear norm into a form amenable to online optimization, real-time algorithms with complementary strengths are developed, and their convergence is established under simplifying technical assumptions. In a stationary setting, the asymptotic estimates obtained offer the well-documented performance guarantees of the batch nuclear-norm regularized estimator. Under the same unifying framework, a novel online (adaptive) algorithm is developed to obtain multi-way decompositions of low-rank tensors with missing entries and perform imputation as a byproduct. Simulated tests with both synthetic as well as real Internet and cardiac magnetic resonance imagery (MRI) data confirm the efficacy of the proposed algorithms, and their superior performance relative to state-of-the-art alternatives.