Data may have multiple modalities, known as multi-view data. With the assumption that multi-view data often lie on a latent subspace, multi-view subspace clustering finds the underlying subspace by leveraging multiple views and clusters the data accordingly. Due to inevitable system errors, multi-view data may contain outliers and it may not therefore strictly follow subspace structure. Besides, prior information such as pairwise constraints describing relations between data instances is often available. These constraints provide a valuable guide on learning. Unfortunately, standard multi-view subspace clustering methods do not simultaneously exploit high order correlations among views and prior constraints with low computational complexity. In this paper, we propose a novel Robust Multi-View Subspace Clustering method, named as RMVSC, which is capable of taking advantage of high order correlations among views and prior constraints for outlier-robust multi-view subspace clustering with low computational complexity. The key idea is to use a low-rank tensor along with a constraint to integrate information from views and prior constraints for more comprehensive learning. We regard underlying clean subspace of singular vectors of views (leveraging views) which also represent projection coefficient of cluster membership vectors in data space (utilizing prior constraints) as a tensor. By decomposing singular vector of each view into its underlying clean subspace and a structured-sparse error (outlier) term, we characterize outliers explicitly. To solve the challenging optimization problem, we develop an algorithm based on Augmented Lagrangian Multiplier. Experimental results on real-world datasets show the superiority of the proposed method and its robustness against outliers.

With the increasing popularity of streaming tensor data such as videos and audios, tensor factorization and completion have attracted much attention recently in this area. Existing work usually assume that streaming tensors only grow in one mode. However, in many real-world scenarios, tensors may grow in multiple modes (or dimensions), i.e., multi-aspect streaming tensors. Standard streaming methods cannot directly handle this type of data elegantly. Moreover, due to inevitable system errors, data may be contaminated by outliers, which cause significant deviations from real data values and make such research particularly challenging. In this paper, we propose a novel method for Outlier-Robust Multi-Aspect Streaming Tensor Completion and Factorization (OR-MSTC), which is a technique capable of dealing with missing values and outliers in multi-aspect streaming tensor data. The key idea is to decompose the tensor structure into an underlying low-rank clean tensor and a structured-sparse error (outlier) tensor, along with a weighting tensor to mask missing data. We also develop an efficient algorithm to solve the non-convex and non-smooth optimization problem of OR-MSTC. Experimental results on various real-world datasets show the superiority of the proposed method over the baselines and its robustness against outliers.

In the era of big data, data may come from multiple sources, known as multi-view data. Multi-view clustering aims at generating better clusters by exploiting complementary and consistent information from multiple views rather than relying on the individual view. Due to inevitable system errors caused by data-captured sensors or others, the data in each view may be erroneous. Various types of errors behave differently and inconsistently in each view. More precisely, error could exhibit as noise and corruptions in reality. Unfortunately, none of the existing multi-view clustering approaches handle all of these error types. Consequently, their clustering performance is dramatically degraded. In this paper, we propose a novel Markov chain method for Error-Robust Multi-View Clustering (EMVC). By decomposing each view into a shared transition probability matrix and error matrix and imposing structured sparsity-inducing norms on error matrices, we characterize and handle typical types of errors explicitly. To solve the challenging optimization problem, we propose a new efficient algorithm based on Augmented Lagrangian Multipliers and prove its convergence rigorously. Experimental results on various synthetic and real-world datasets show the superiority of the proposed EMVC method over the baseline methods and its robustness against different types of errors.