Robust Tensor CUR Decompositions: Rapid Low-Tucker-Rank Tensor Recovery with Sparse Corruption

We study the tensor robust principal component analysis (TRPCA) problem, a tensorial extension of matrix robust principal component analysis (RPCA), that aims to split the given tensor into an underlying low-rank component and a sparse outlier component. This work proposes a fast algorithm, called Robust Tensor CUR Decompositions (RTCUR), for large-scale non-convex TRPCA problems under the Tucker rank setting. RTCUR is developed within a framework of alternating projections that projects between the set of low-rank tensors and the set of sparse tensors. We utilize the recently developed tensor CUR decomposition to substantially reduce the computational complexity in each projection. In addition, we develop four variants of RTCUR for different application settings. We demonstrate the effectiveness and computational advantages of RTCUR against state-of-the-art methods on both synthetic and real-world datasets.

Inference of Media Bias and Content Quality Using Natural-Language Processing

Media bias can significantly impact the formation and development of opinions and sentiments in a population. It is thus important to study the emergence and development of partisan media and political polarization. However, it is challenging to quantitatively infer the ideological positions of media outlets. In this paper, we present a quantitative framework to infer both political bias and content quality of media outlets from text, and we illustrate this framework with empirical experiments with real-world data. We apply a bidirectional long short-term memory (LSTM) neural network to a data set of more than 1 million tweets to generate a two-dimensional ideological-bias and content-quality measurement for each tweet. We then infer a ``media-bias chart'' of (bias, quality) coordinates for the media outlets by integrating the (bias, quality) measurements of the tweets of the media outlets. We also apply a variety of baseline machine-learning methods, such as a naive-Bayes method and a support-vector machine (SVM), to infer the bias and quality values for each tweet. All of these baseline approaches are based on a bag-of-words approach. We find that the LSTM-network approach has the best performance of the examined methods. Our results illustrate the importance of leveraging word order into machine-learning methods in text analysis.

Fast Robust Tensor Principal Component Analysis via Fiber CUR Decomposition

We study the problem of tensor robust principal component analysis (TRPCA), which aims to separate an underlying low-multilinear-rank tensor and a sparse outlier tensor from their sum. In this work, we propose a fast non-convex algorithm, coined Robust Tensor CUR (RTCUR), for large-scale TRPCA problems. RTCUR considers a framework of alternating projections and utilizes the recently developed tensor Fiber CUR decomposition to dramatically lower the computational complexity. The performance advantage of RTCUR is empirically verified against the state-of-the-arts on the synthetic datasets and is further demonstrated on the real-world application such as color video background subtraction.