Online Tensor Decomposition and Imputation for Count Data

摘要

Unveiling low-dimensional latent structure by means of multilinear decompositions of tensor data is central to data analytics tasks at the confluence of signal processing, machine learning and data mining. However, increasingly noisy, incomplete, and heterogeneous datasets (that deviate from e.g., Gaussian distributional assumptions) as well as the need for real-time processing of streaming data pose major challenges to this end. In this context, the present paper develops a novel online (adaptive) algorithm to obtain three-way decompositions of low-rank, Poisson-distributed tensors. Such (possibly incomplete) streams of count data arise with various applications including traffic engineering, computer network monitoring, genomics, photonics and satellite imaging. The proposed estimator minimizes a Poisson log-likelihood cost along with a separable regularizer of the PARAFAC decomposition factors, to trade-off fidelity for complexity of the approximation captured by the decomposition's rank. Leveraging stochastic gradient descent iterations, a scalable, online algorithm is developed to learn the decomposition factors on-the-fly and perform data imputation as a byproduct. Preliminary numerical tests with simulated data and solar flare video confirm the efficacy of the proposed tensor imputation algorithm, as well as its convergence to the batch estimator benchmark.