Robust Tensor Tracking With Missing Data and Outliers: Novel Adaptive CP Decomposition and Convergence Analysis

Abstract

Canonical Polyadic (CP) decomposition is a powerful multilinear algebra tool for analyzing multiway (a.k.a. tensor) data and has been used for various signal processing and machine learning applications. When the underlying tensor is derived from data streams, adaptive CP decomposition is required. In this paper, we propose a novel method called robust adaptive CP decomposition (RACP) for dealing with high-order incomplete streaming tensors that are corrupted by outliers. At each time instant, RACP first performs online outlier rejection to accurately detect and remove sparse outliers, and then performs tensor factor tracking to efficiently update the tensor basis. A unified convergence analysis of RACP is also established in that the sequence of generated solutions converges asymptotically to a stationary point of the objective function. Extensive experiments were conducted on both synthetic and real data to demonstrate the effectiveness of RACP in comparison with state-of-the-art adaptive CP algorithms.