Related papers: Efficient Tensor Robust PCA under Hybrid Model of …

Currently, the size of scientific data is growing at an unprecedented rate. Data in the form of tensors exhibit high-order, high-dimensional, and highly sparse features. Although tensor-based analysis methods are very effective, the large…

Advanced tensor decomposition, such as Tensor train (TT) and Tensor ring (TR), has been widely studied for deep neural network (DNN) model compression, especially for recurrent neural networks (RNNs). However, compressing convolutional…

There are several factorizations of multi-dimensional tensors into lower-dimensional components, known as `tensor networks'. We consider the popular `tensor-train' (TT) format and ask: How efficiently can we compute a low-rank approximation…

Currently, low-rank tensor completion has gained cumulative attention in recovering incomplete visual data whose partial elements are missing. By taking a color image or video as a three-dimensional (3D) tensor, previous studies have…

We present efficient and scalable parallel algorithms for performing mathematical operations for low-rank tensors represented in the tensor train (TT) format. We consider algorithms for addition, elementwise multiplication, computing norms…

In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…

Recurrent Neural Networks (RNNs) and their variants, such as Long-Short Term Memory (LSTM) networks, and Gated Recurrent Unit (GRU) networks, have achieved promising performance in sequential data modeling. The hidden layers in RNNs can be…

Hyperspectral images (HSIs) are often degraded by complex mixed noise during acquisition and transmission, making effective denoising essential for subsequent analysis. Recent hybrid approaches that bridge model-driven and data-driven…

We study tensor completion (TC) through the lens of low-rank tensor decomposition (TD). Many TD algorithms use fast alternating minimization methods to solve highly structured linear regression problems at each step (e.g., for CP, Tucker,…

Traditional Recurrent Neural Networks assume vectorized data as inputs. However many data from modern science and technology come in certain structures such as tensorial time series data. To apply the recurrent neural networks for this type…

Tensor Networks (TNs) have recently been used to speed up kernel machines by constraining the model weights, yielding exponential computational and storage savings. In this paper we prove that the outputs of Canonical Polyadic Decomposition…

Robust principal component analysis (RPCA) is a critical tool in modern machine learning, which detects outliers in the task of low-rank matrix reconstruction. In this paper, we propose a scalable and learnable non-convex approach for…

Many real-world datasets are represented as tensors, i.e., multi-dimensional arrays of numerical values. Storing them without compression often requires substantial space, which grows exponentially with the order. While many tensor…

The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…

In recent years, low-rank tensor completion (LRTC) has received considerable attention due to its applications in image/video inpainting, hyperspectral data recovery, etc. With different notions of tensor rank (e.g., CP, Tucker, tensor…

We propose a Bayesian tensor-on-tensor regression approach to predict a multidimensional array (tensor) of arbitrary dimensions from another tensor of arbitrary dimensions, building upon the Tucker decomposition of the regression…

We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally…

Principal component analysis (PCA) is a widely employed statistical tool used primarily for dimensionality reduction. However, it is known to be adversely affected by the presence of outlying observations in the sample, which is quite…

Low-rank tensor completion recovers missing entries based on different tensor decompositions. Due to its outstanding performance in exploiting some higher-order data structure, low rank tensor ring has been applied in tensor completion. To…

This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…