Related papers: CUR Decompositions, Approximations, and Perturbati…

We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…

We propose a clustering-based generalized low rank approximation method, which takes advantage of appealing features from both the generalized low rank approximation of matrices (GLRAM) and cluster analysis. It exploits a more general form…

Computing optimal control policies for complex dynamical systems requires approximation methods to remain computationally tractable. Several approximation methods have been developed to tackle this problem. However, these methods do not…

Numerical methods of approximate solution of the Cauchy problem for coupled systems of evolution equations are considered. Separating simpler subproblems for individual components of the solution achieves simplification of the problem at a…

Tensor train decomposition is widely used in machine learning and quantum physics due to its concise representation of high-dimensional tensors, overcoming the curse of dimensionality. Cross approximation-originally developed for…

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…

While uniform sampling has been widely studied in the matrix completion literature, CUR sampling approximates a low-rank matrix via row and column samples. Unfortunately, both sampling models lack flexibility for various circumstances in…

Machine learning and data mining algorithms are becoming increasingly important in analyzing large volume, multi-relational and multi--modal datasets, which are often conveniently represented as multiway arrays or tensors. It is therefore…

We introduce a "learning-based" algorithm for the low-rank decomposition problem: given an $n \times d$ matrix $A$, and a parameter $k$, compute a rank-$k$ matrix $A'$ that minimizes the approximation loss $\|A-A'\|_F$. The algorithm uses a…

Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…

Motivation: Detailed mechanistic models of biological processes can pose significant challenges for analysis and parameter estimations due to the large number of equations used to track the dynamics of all distinct configurations in which…

This paper investigates connections between discrete and continuous approaches for decomposable submodular function minimization. We provide improved running time estimates for the state-of-the-art continuous algorithms for the problem…

Ashenhurst-Curtis decomposition (ACD) is a decomposition technique used, in particular, to map combinational logic into lookup tables (LUTs) structures when synthesizing hardware designs. However, available implementations of ACD suffer…

Low-rank modeling plays a pivotal role in signal processing and machine learning, with applications ranging from collaborative filtering, video surveillance, medical imaging, to dimensionality reduction and adaptive filtering. Many modern…

Modern neural networks have revolutionized the fields of computer vision (CV) and Natural Language Processing (NLP). They are widely used for solving complex CV tasks and NLP tasks such as image classification, image generation, and machine…

Low-rank matrix approximation (LRMA) is a powerful technique for signal processing and pattern analysis. However, its potential for data compression has not yet been fully investigated in the literature. In this paper, we propose sparse…

Tensor ring (TR) decomposition is a simple but effective tensor network for analyzing and interpreting latent patterns of tensors. In this work, we propose a doubly randomized optimization framework for computing TR decomposition. It can be…

We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…

Nonlinear dimensionality reduction or, equivalently, the approximation of high-dimensional data using a low-dimensional nonlinear manifold is an active area of research. In this paper, we will present a thematically different approach to…

We often use perturbations to regularize neural models. For neural encoder-decoders, previous studies applied the scheduled sampling (Bengio et al., 2015) and adversarial perturbations (Sato et al., 2019) as perturbations but these methods…