Related papers: Convex Tensor Decomposition via Structured Schatte…
Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have…
In this paper, we bring forward a completely perturbed nonconvex Schatten $p$-minimization to address a model of completely perturbed low-rank matrix recovery. The paper that based on the restricted isometry property generalizes the…
Tensor decompositions have rich applications in statistics and machine learning, and developing efficient, accurate algorithms for the problem has received much attention recently. Here, we present a new method built on Kruskal's uniqueness…
Tensor-valued data arise naturally in neuroimaging, genomics, climate science, and spatiotemporal networks, where multilinear dependencies across modes carry information that is destroyed under vectorization. Existing approaches either…
Sparse estimation methods are aimed at using or obtaining parsimonious representations of data or models. While naturally cast as a combinatorial optimization problem, variable or feature selection admits a convex relaxation through the…
Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…
Tensor-based methods are receiving a growing interest in scientific computing for the numerical solution of problems defined in high dimensional tensor product spaces. A family of methods called Proper Generalized Decompositions methods…
We analyze a class of norms defined via an optimal interpolation problem involving the composition of norms and a linear operator. This construction, known as infimal postcomposition in convex analysis, is shown to encompass various of…
The (efficient and parsimonious) decomposition of higher-order tensors is a fundamental problem with numerous applications in a variety of fields. Several methods have been proposed in the literature to that end, with the Tucker and PARAFAC…
Tensors in the form of multilinear arrays are ubiquitous in data science applications. Captured real-world data, including video, hyperspectral images, and discretized physical systems, naturally occur as tensors and often come with…
In this paper, we study the problem of decomposing a superposition of a low-rank matrix and a sparse matrix when a relatively few linear measurements are available. This problem arises in many data processing tasks such as aligning multiple…
Anomaly detection in spatiotemporal data is a challenging problem encountered in a variety of applications including hyperspectral imaging, video surveillance, and urban traffic monitoring. Existing anomaly detection methods are most suited…
This paper studies the Schatten-$q$ error of low-rank matrix estimation by singular value decomposition under perturbation. We specifically establish a perturbation bound on the low-rank matrix estimation via a perturbation projection error…
A new decomposition optimization algorithm, called \textit{path-following gradient-based decomposition}, is proposed to solve separable convex optimization problems. Unlike path-following Newton methods considered in the literature, this…
We present a new method for online prediction and learning of tensors ($N$-way arrays, $N >2$) from sequential measurements. We focus on the specific case of 3-D tensors and exploit a recently developed framework of structured tensor…
Convolutional neural networks show outstanding results in a variety of computer vision tasks. However, a neural network architecture design usually faces a trade-off between model performance and computational/memory complexity. For some…
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
This paper studies the computational and statistical aspects of quantile and pseudo-Huber tensor decomposition. The integrated investigation of computational and statistical issues of robust tensor decomposition poses challenges due to the…
This paper presents a patch-wise low-rank based image denoising method with constrained variational model involving local and nonlocal regularization. On one hand, recent patch-wise methods can be represented as a low-rank matrix…