Related papers: Concurrent Alternating Least Squares for multiple …

There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank,…

Recurrent neural networks (RNNs) are powerful in the tasks oriented to sequential data, such as natural language processing and video recognition. However, since the modern RNNs, including long-short term memory (LSTM) and gated recurrent…

Nonnegative CANDECOMP/PARAFAC (NCP) decomposition is an important tool to process nonnegative tensor. Sometimes, additional sparse regularization is needed to extract meaningful nonnegative and sparse components. Thus, an optimization…

In big-data analytics, using tensor decomposition to extract patterns from large, sparse multivariate data is a popular technique. Many challenges exist for designing parallel, high performance tensor decomposition algorithms due to…

In this paper, we discuss the acceleration of the regularized alternating least square (RALS) algorithm for tensor approximation. We propose a fast iterative method using a Aitken-Stefensen like updates for the regularized algorithm.…

We have developed a novel method for co-adding multiple under-sampled images that combines the iteratively reweighted least squares and divide-and-conquer algorithms. Our approach not only allows for the anti-aliasing of the images but also…

Often, large, high dimensional datasets collected across multiple modalities can be organized as a higher order tensor. Low-rank tensor decomposition then arises as a powerful and widely used tool to discover simple low dimensional…

Dimension reduction techniques are often used when the high-dimensional tensor has relatively low intrinsic rank compared to the ambient dimension of the tensor. The CANDECOMP/PARAFAC (CP) tensor completion is a widely used approach to find…

Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition…

In recent years, low-rank based tensor completion, which is a higher-order extension of matrix completion, has received considerable attention. However, the low-rank assumption is not sufficient for the recovery of visual data, such as…

We consider the approximate solution of parametric PDEs using the low-rank Tensor Train (TT) decomposition. Such parametric PDEs arise for example in uncertainty quantification problems in engineering applications. We propose an algorithm…

Sparse compiler is a promising solution for sparse tensor algebra optimization. In compiler implementation, reduction in sparse-dense hybrid algebra plays a key role in performance. Though GPU provides various reduction semantics that can…

The CP tensor decomposition is a low-rank approximation of a tensor. We present a distributed-memory parallel algorithm and implementation of an alternating optimization method for computing a CP decomposition of dense tensor data that can…

The PARAFAC2 model provides a flexible alternative to the popular CANDECOMP/PARAFAC (CP) model for tensor decompositions. Unlike CP, PARAFAC2 allows factor matrices in one mode (i.e., evolving mode) to change across tensor slices, which has…

Tensors have broad applications in neuroimaging, data mining, digital marketing, etc. CANDECOMP/PARAFAC (CP) tensor decomposition can effectively reduce the number of parameters to gain dimensionality-reduction and thus plays a key role in…

Reduction operations are extensively employed in many computational problems. A reduction consists of, given a finite set of numeric elements, combining into a single value all elements in that set, using for this a combiner function. A…

Sparse tensors are the most used representation of sparse multidimensional data. Operations that decompose them, selecting their most important features while reducing their dimension, have become prevalent procedures in machine learning.…

In real-life applications, most optimization problems are variants of well-known combinatorial optimization problems, including additional constraints to fit with a particular use case. Usually, efficient algorithms to handle a restricted…

In this paper we accomplish the development of the fast rank-adaptive solver for tensor-structured symmetric positive definite linear systems in higher dimensions. In [arXiv:1301.6068] this problem is approached by alternating minimization…

Multiple patterning lithography (MPL) is regarded as one of the most promising ways of overcoming the resolution limitations of conventional optical lithography due to the delay of next-generation lithography technology. As the feature size…