Related papers: Nonnegative Tensor Decomposition Via Collaborative…

This paper proposes a channel estimation method for Multiple-Input Multiple-Output (MIMO) systems based on Canonical Polyadic (CP) decomposition applied to a mode-factorized tensor representation of the channel. The proposed approach…

This paper presents a canonical polyadic (CP) tensor decomposition that addresses unaligned observations. The mode with unaligned observations is represented using functions in a reproducing kernel Hilbert space (RKHS). We introduce a…

In recent work (Soltani, Kilmer, Hansen, BIT 2016), an algorithm for non-negative tensor patch dictionary learning in the context of X-ray CT imaging and based on a tensor-tensor product called the $t$-product (Kilmer and Martin, 2011) was…

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…

This paper proposes a domain decomposition subspace neural network method for efficiently solving linear and nonlinear partial differential equations. By combining the principles of domain decomposition and subspace neural networks, the…

Convolutional neural networks (CNNs) are one of the most effective deep learning methods to solve image classification problems, but the best architecture of a CNN to solve a specific problem can be extremely complicated and hard to design.…

In this paper, we consider the model reduction problem of large-scale systems, such as systems obtained through the discretization of partial differential equations. We propose a computationally optimal randomized proper orthogonal…

Conventional gradient descent methods compute the gradients for multiple variables through the partial derivative. Treating the coupled variables independently while ignoring the interaction, however, leads to an insufficient optimization…

Tensor CANDECOMP/PARAFAC decomposition (CPD) is a fundamental model for tensor reconstruction. Although the Bayesian framework allows for principled uncertainty quantification and automatic hyperparameter learning, existing methods do not…

We consider the problem of factorizing a structured 3-way tensor into its constituent Canonical Polyadic (CP) factors. This decomposition, which can be viewed as a generalization of singular value decomposition (SVD) for tensors, reveals…

Continuous optimization is an important problem in many areas of AI, including vision, robotics, probabilistic inference, and machine learning. Unfortunately, most real-world optimization problems are nonconvex, causing standard convex…

Koopman mode decomposition and tensor component analysis (also known as CANDECOMP/PARAFAC or canonical polyadic decomposition) are two popular approaches of decomposing high dimensional data sets into low dimensional modes that capture the…

We propose a neural network model with transient chaos, or a transiently chaotic neural network (TCNN) as an approximation method for combinatorial optimization problem, by introducing transiently chaotic dynamics into neural networks.…

Uncertainties such as manufacturing tolerances cause performance variations in complex engineering systems, making robust design optimization (RDO) essential. However, simulation-based RDO faces high computational cost for statistical…

Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…

In general, algorithms for order-3 CANDECOMP/-PARAFAC (CP), also coined canonical polyadic decomposition (CPD), are easily to implement and can be extended to higher order CPD. Unfortunately, the algorithms become computationally demanding,…

This paper introduces an interacting-particle optimization method tailored to possibly non-convex composite optimization problems, which arise widely in signal processing. The proposed method, \emph{ProxiCBO}, integrates consensus-based…

This paper defines a convertible nonconvex function(CN function for short) and a weak (strong) uniform (decomposable, exact) CN function, proves the optimization conditions for their global solutions and proposes algorithms for solving the…

Recent developments in diagnostic and computing technologies offer to leverage numerous forms of nonintrusive modeling approaches from data where machine learning can be used to build computationally cheap and accurate surrogate models. To…

For lossy image compression, we develop a neural-based system which learns a nonlinear estimator for decoding from quantized representations. The system links two recurrent networks that \help" each other reconstruct same target image…