Related papers: On Koopman Mode Decomposition and Tensor Component…

Additive models can be used for interpretable machine learning for their clarity and simplicity. However, In the classical models for high-order data, the vectorization operation disrupts the data structure, which may lead to degenerated…

Fourier PCA is Principal Component Analysis of a matrix obtained from higher order derivatives of the logarithm of the Fourier transform of a distribution.We make this method algorithmic by developing a tensor decomposition method for a…

Low-rank tensor decompositions (TDs) provide an effective framework for multiway data analysis. Traditional TD methods rely on predefined structural assumptions, such as CP or Tucker decompositions. From a probabilistic perspective, these…

Modern intelligent transportation systems rely on accurate spatiotemporal traffic analysis to optimize urban mobility and infrastructure resilience. However, pervasive missing data caused by sensor failures and heterogeneous sensing gaps…

Tensor decomposition serves as a powerful primitive in statistics and machine learning, and has numerous applications in problems such as learning latent variable models or mixture of Gaussians. In this paper, we focus on using power…

Coupled decompositions are a widely used tool for data fusion. As the volume of data increases, so does the dimensionality of matrices and tensors, highlighting the need for more efficient coupled decomposition algorithms. This paper…

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…

Tensor CANDECOMP/PARAFAC (CP) decomposition is an important tool that solves a wide class of machine learning problems. Existing popular approaches recover components one by one, not necessarily in the order of larger components first.…

The Koopman operator is beneficial for analyzing nonlinear and stochastic dynamics; it is linear but infinite-dimensional, and it governs the evolution of observables. The extended dynamic mode decomposition (EDMD) is one of the famous…

The paper surveys the topic of tensor decompositions in modern machine learning applications. It focuses on three active research topics of significant relevance for the community. After a brief review of consolidated works on multi-way…

This work proposes a new framework of model reduction for parametric complex systems. The framework employs a popular model reduction technique dynamic mode decomposition (DMD), which is capable of combining data-driven learning and physics…

Tensor decompositions such as the canonical format and the tensor train format have been widely utilized to reduce storage costs and operational complexities for high-dimensional data, achieving linear scaling with the input dimension…

Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor factorization of the probability mass function for…

Multivariate functions emerge naturally in a wide variety of data-driven models. Popular choices are expressions in the form of basis expansions or neural networks. While highly effective, the resulting functions tend to be hard to…

We discuss how recently discovered techniques and tools from compressed sensing can be used in tensor decompositions, with a view towards modeling signals from multiple arrays of multiple sensors. We show that with appropriate bounds on a…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

A theoretic framework for dynamics is obtained by transferring dynamics from state space to its dual space. As a result, the linear structure where dynamics are analytically decomposed to subcomponents and invariant subspaces decomposition…

Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…

A novel algorithm is proposed for CANDECOMP/PARAFAC tensor decomposition to exploit best rank-1 tensor approximation. Different from the existing algorithms, our algorithm updates rank-1 tensors simultaneously in parallel. In order to…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…