Related papers: On Koopman Mode Decomposition and Tensor Component…
While time-frequency analysis provides rich representations of multicomponent signals, current decomposition methods often overlook the morphological structure where components manifest as distinct regions. This study introduces…
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…
This paper explores a new version of the Levenberg-Marquardt algorithm used for Tensor Canonical Polyadic (CP) decomposition with an emphasis on image compression and reconstruction. Tensor computation, especially CP decomposition, holds…
In this work we introduce the concept of a sub-space decomposition, subject to a partition of the coordinates. Considering metrics determined by partial orders in the set of coordinates, the so called poset metrics, we show the existence of…
There are two approaches to time series approximate factor models: the static factor model, where the factors are loaded contemporaneously by the common component, and the Generalised Dynamic Factor Model, where the factors are loaded with…
One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…
CANDECOMP/PARAFAC (CP) decomposition is the mostly used model to formulate the received tensor signal in a massive MIMO system, as the receiver generally sums the components from different paths or users. To achieve accurate and low-latency…
Spectral methods have been the mainstay in several domains such as machine learning and scientific computing. They involve finding a certain kind of spectral decomposition to obtain basis functions that can capture important structures for…
Tucker decomposition is a popular technique for many data analysis and machine learning applications. Finding a Tucker decomposition is a nonconvex optimization problem. As the scale of the problems increases, local search algorithms such…
This paper introduces a novel collaborative neurodynamic model for computing nonnegative Canonical Polyadic Decomposition (CPD). The model relies on a system of recurrent neural networks to solve the underlying nonconvex optimization…
Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by…
We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…
Efficient modelling of feature interactions underpins supervised learning for non-sequential tasks, characterized by a lack of inherent ordering of features (variables). The brute force approach of learning a parameter for each interaction…
Positive time varying frequency representation for transient signals has been a hearty desire of signal analysts due to its theoretical and practical importance. During approximately the last two decades there has formulated a signal…
Decomposition techniques for linear programming are difficult to extend to conic optimization problems with general non-polyhedral convex cones because the conic inequalities introduce an additional nonlinear coupling between the variables.…
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…
Human interpretation of the world encompasses the use of symbols to categorize sensory inputs and compose them in a hierarchical manner. One of the long-term objectives of Computer Vision and Artificial Intelligence is to endow machines…
This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our…
Markov chains have been widely employed as a fundamental model in the studies of probabilistic and stochastic communicating and concurrent systems. It is well-understood that decomposition techniques play a key role in reachability analysis…
Higher-order tensors are becoming prevalent in many scientific areas such as computer vision, social network analysis, data mining and neuroscience. Traditional tensor decomposition approaches face three major challenges: model selecting,…