Bayesian Robust Tensor Factorization for Incomplete Multiway Data

Abstract

We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CANDECOMP/PARAFAC (CP)-rank tensor capturing the global information and a sparse tensor capturing the local information (also considered as outliers), thus providing the robust predictive distribution over missing entries. The low-CP-rank tensor is modeled by multilinear interactions between multiple latent factors on which the column sparsity is enforced by a hierarchical prior, while the sparse tensor is modeled by a hierarchical view of Student-t distribution that associates an individual hyperparameter with each element independently. For model learning, we develop an efficient variational inference under a fully Bayesian treatment, which can effectively prevent the overfitting problem and scales linearly with data size. In contrast to existing related works, our method can perform model selection automatically and implicitly without the need of tuning parameters. More specifically, it can discover the groundtruth of CP rank and automatically adapt the sparsity inducing priors to various types of outliers. In addition, the tradeoff between the low-rank approximation and the sparse representation can be optimized in the sense of maximum model evidence. The extensive experiments and comparisons with many state-of-the-art algorithms on both synthetic and real-world data sets demonstrate the superiorities of our method from several perspectives.

Optimizing spatial patterns with sparse filter bands for motor-imagery based brain–computer interface

“…In recent years, multiway learning algorithms have shown their promising potentials for the collaborative optimization in the spatial, temporal and spectral dimensions of brain signals [46,47,48,49,50,51,52,53]. A combination of collaborative multiway optimization and regularization for filter band selection could further benefit to improve the effectiveness of CSP for MI-based BCI.…”

Unsupervised deep context prediction for background estimation and foreground segmentation

“…Although this method performs well for background estimation problem but global optimality is still the challenging issue in this approach. Qibin Zhao et al [53] presented a method called Bayesian Robust Tensor Factorization for Incomplete Multiway Data (BRTF). This method is a generative model for robust tensor factorization in the presence of missing data and outliers.…”

Survey on Probabilistic Models of Low-Rank Matrix Factorizations

“…A zero-truncated Poisson tensor factorization for binary tensors was proposed in [46]. A Bayesian robust tensor factorization [47] was proposed and it is the extension of probabilistic stable robust PCA. And in [48], the CP factorization was formulated by a hierarchical probabilistic model.…”

“…Among them, the TT format is a special case of the HT and the tensor tree structure [33]. The probabilistic models of the Tucker were presented in [34][35][36] and that of the CP were developed in [37][38][39][40][41][42][43][44][45][46][47][48].…”