Robust Factorization and Completion of Streaming Tensor Data via Variational Bayesian Inference

TL;DR

This paper introduces a Bayesian robust streaming tensor factorization model that automatically determines tensor rank, identifies outliers, and accurately captures low-rank structures in high-volume temporal data, outperforming existing methods.

Contribution

It is the first to develop a Bayesian approach for robust streaming tensor factorization with automatic rank determination and outlier detection.

Findings

Successfully identifies sparse outliers in streaming tensor data.

Automatically determines the tensor rank without prior knowledge.

Effectively factorizes and completes various real-world streaming tensors.

Abstract

Streaming tensor factorization is a powerful tool for processing high-volume and multi-way temporal data in Internet networks, recommender systems and image/video data analysis. In many applications the full tensor is not known, but instead received in a slice-by-slice manner over time. Streaming factorizations aim to take advantage of inherent temporal relationships in data analytics. Existing streaming tensor factorization algorithms rely on least-squares data fitting and they do not possess a mechanism for tensor rank determination. This leaves them susceptible to outliers and vulnerable to over-fitting. This paper presents the first Bayesian robust streaming tensor factorization model. Our model successfully identifies sparse outliers, automatically determines the underlying tensor rank and accurately fits low-rank structure. We implement our model in Matlab and compare it to existing algorithms. Our algorithm is applied to factorize and complete various streaming tensors including synthetic data, dynamic MRI, video sequences, and Internet traffic data.