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This work develops a provably accurate fully-decentralized alternating projected gradient descent (GD) algorithm for recovering a low rank (LR) matrix from mutually independent projections of each of its columns, in a fast and…
In intelligent transportation systems, traffic data imputation, estimating the missing value from partially observed data is an inevitable and challenging task. Previous studies have not fully considered traffic data's multidimensionality…
We revisit existing linear computation coding (LCC) algorithms, and introduce a new framework that measures the computational cost of computing multidimensional linear functions, not only in terms of the number of additions, but also with…
We propose an adaptive and provably accurate tensor completion approach based on combining matrix completion techniques (see, e.g., arXiv:0805.4471, arXiv:1407.3619, arXiv:1306.2979) for a small number of slices with a modified noise robust…
Semi-supervised learning on graph structured data has received significant attention with the recent introduction of Graph Convolution Networks (GCN). While traditional methods have focused on optimizing a loss augmented with Laplacian…
We consider alternating gradient descent (AGD) with fixed step size applied to the asymmetric matrix factorization objective. We show that, for a rank-$r$ matrix $\mathbf{A} \in \mathbb{R}^{m \times n}$, $T = C…
In recent years, there have been an increasing number of applications of tensor completion based on the tensor train (TT) format because of its efficiency and effectiveness in dealing with higher-order tensor data. However, existing tensor…
For the antisymmetric tensors the paper examines a low-rank approximation which is represented via only three vectors. We describe a suitable low-rank format and propose an alternating least squares structure-preserving algorithm for…
Low-rank matrix approximation (LRMA) has been arisen in many applications, such as dynamic MRI, recommendation system and so on. The alternating direction method of multipliers (ADMM) has been designed for the nuclear norm regularized least…
By adding entropic regularization, multi-marginal optimal transport problems can be transformed into tensor scaling problems, which can be solved numerically using the multi-marginal Sinkhorn algorithm. The main computational bottleneck of…
In tensor completion, the latent nuclear norm is commonly used to induce low-rank structure, while substantially failing to capture the global information due to the utilization of unbalanced unfolding scheme. To overcome this drawback, a…
In this paper, we propose a new approach to solve low-rank tensor completion and robust tensor PCA. Our approach is based on some novel notion of (even-order) tensor ranks, to be called the M-rank, the symmetric M-rank, and the strongly…
In this paper, we investigate the problem of decentralized consensus optimization over directed graphs with limited communication bandwidth. We introduce a novel decentralized optimization algorithm that combines the Reduced Consensus…
Low-rank representation (LRR) is an effective method for subspace clustering and has found wide applications in computer vision and machine learning. The existing LRR solver is based on the alternating direction method (ADM). It suffers…
Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing. This work develops a generalized canonical polyadic (GCP) low-rank tensor…
We present a factor $14D^2$ approximation algorithm for the minimum linear arrangement problem on series-parallel graphs, where $D$ is the maximum degree in the graph. Given a suitable decomposition of the graph, our algorithm runs in time…
To alleviate the bias generated by the l1-norm in the low-rank tensor completion problem, nonconvex surrogates/regularizers have been suggested to replace the tensor nuclear norm, although both can achieve sparsity. However, the…
As a tool for estimating networks in high dimensions, graphical models are commonly applied to calcium imaging data to estimate functional neuronal connectivity, i.e. relationships between the activities of neurons. However, in many calcium…
Optimal transportation provides a means of lifting distances between points on a geometric domain to distances between signals over the domain, expressed as probability distributions. On a graph, transportation problems can be used to…
We investigate a novel approach to approximate tensor-network contraction via the exact, matrix-free decomposition of full tensor-networks. We study this method as a means to eliminate the propagation of error in the approximation of…