Related papers: Low Rank Tensor Completion via Adaptive ADMM

Recovering a low-rank tensor from incomplete information is a recurring problem in signal processing and machine learning. The most popular convex relaxation of this problem minimizes the sum of the nuclear norms of the unfoldings of the…

Minimization of the nuclear norm is often used as a surrogate, convex relaxation, for finding the minimum rank completion (recovery) of a partial matrix. The minimum nuclear norm problem can be solved as a trace minimization semidefinite…

Modern technological advances have enabled an unprecedented amount of structured data with complex temporal dependence, urging the need for new methods to efficiently model and forecast high-dimensional tensor-valued time series. This paper…

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank…

Recently, numerous tensor singular value decomposition (t-SVD)-based tensor recovery methods have shown promise in processing visual data, such as color images and videos. However, these methods often suffer from severe performance…

The recent proposed Tensor Nuclear Norm (TNN) [Lu et al., 2016; 2018a] is an interesting convex penalty induced by the tensor SVD [Kilmer and Martin, 2011]. It plays a similar role as the matrix nuclear norm which is the convex surrogate of…

We study extensions of compressive sensing and low rank matrix recovery (matrix completion) to the recovery of low rank tensors of higher order from a small number of linear measurements. While the theoretical understanding of low rank…

With the advancement of the data acquisition techniques, multi-view learning has become a hot topic. Some multi-view learning methods assume that the multi-view data is complete, which means that all instances are present, but this too…

In Automatic Speech Recognition (ASR) systems, a recurring obstacle is the generation of narrowly focused output distributions. This phenomenon emerges as a side effect of Connectionist Temporal Classification (CTC), a robust sequence…

We consider the low-rank tensor train completion problem when additional side information is available in the form of subspaces that contain the mode-$k$ fiber spans. We propose an algorithm based on Riemannian optimization to solve the…

Originally developed for imputing missing entries in low rank, or approximately low rank matrices, matrix completion has proven widely effective in many problems where there is no reason to assume low-dimensional linear structure in the…

We develop a new collaborative filtering (CF) method that combines both previously known users' preferences, i.e. standard CF, as well as product/user attributes, i.e. classical function approximation, to predict a given user's interest in…

Multitask learning (MTL) can utilize the relatedness between multiple tasks for performance improvement. The advent of multimodal data allows tasks to be referenced by multiple indices. High-order tensors are capable of providing efficient…

In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm or t-TNN for short. The twist tensor denotes a 3-way tensor representation to laterally store 2D data slices in order.…

A novel low-rank completion algorithm based on the quaternion tensor is proposed in this paper. This approach uses the TQt-rank of quaternion tensor to maintain the structure of RGB channels throughout the entire process. In more detail,…

Low-rank tensor recovery has attracted much attention among various tensor recovery approaches. A tensor rank has several definitions, unlike the matrix rank--e.g. the CP rank and the Tucker rank. Many low-rank tensor recovery methods are…

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

Attempts of studying implicit regularization associated to gradient descent (GD) have identified matrix completion as a suitable test-bed. Late findings suggest that this phenomenon cannot be phrased as a minimization-norm problem, implying…

This paper develops an adaptive proximal alternating direction method of multipliers (ADMM) for solving linearly constrained, composite optimization problems under the assumption that the smooth component of the objective is weakly convex,…

Spatiotemporal traffic time series (e.g., traffic volume/speed) collected from sensing systems are often incomplete with considerable corruption and large amounts of missing values, preventing users from harnessing the full power of the…