Related papers: t-Product and t-STP of Cubic Matrices With Applica…
The semi-tensor product (STP) of matrices is extended to the STP of hypermatrices. Some basic properties of the STP of matrices are extended to the STP of hypermatrices. The hyperdeterminant of hypersquares is introduced. Some algebraic and…
Semi-tensor product(STP) or matrix (M-) product of matrices turns the set of matrices with arbitrary dimensions into a monoid $({\cal M},\ltimes)$. A matrix (M-) addition is defined over subsets of a partition of ${\cal M}$, and a matrix…
A new matrix product, called the semi-tensor product (STP), is briefly reviewed. The STP extends the classical matrix product to two arbitrary matrices. Under STP the set of matrices becomes a monoid (semi-group with identity). Some related…
An equivalence of matrices via semi-tensor product (STP) is proposed. Using this equivalence, the quotient space is obtained. Parallel and sequential arrangements of the natural projection on different shapes of matrices leads to the…
Data-driven control is a powerful tool that enables the design and implementation of control strategies directly from data without explicitly identifying the underlying system dynamics. While various data-driven control techniques, such as…
In compressed sensing (CS), sparse signals can be reconstructed from significantly fewer samples than required by the Nyquist-Shannon sampling theorem. While non-sparse signals can be sparsely represented in appropriate transformation…
The tensor-tensor product (t-product) [M. E. Kilmer and C. D. Martin, 2011] is a natural generalization of matrix multiplication. Based on t-product, many operations on matrix can be extended to tensor cases, including tensor SVD, tensor…
A novel model reduction framework for large-scale complex systems is proposed by introducing function-type dynamic control systems via the dimension-keeping semi-tensor product (DK-STP) of matrices. Utilizing bridge matrices, the DK-STP…
The existing tensor networks adopt conventional matrix product for connection. The classical matrix product requires strict dimensionality consistency between factors, which can result in redundancy in data representation. In this paper,…
There is a significant expansion in both volume and range of applications along with the concomitant increase in the variety of data sources. These ever-expanding trends have highlighted the necessity for more versatile analysis tools that…
We propose a tensor neural network ($t$-NN) framework that offers an exciting new paradigm for designing neural networks with multidimensional (tensor) data. Our network architecture is based on the $t$-product (Kilmer and Martin, 2011), an…
A wide variety of data can be represented using third-order tensors, spanning applications in chemometrics, psychometrics, and image processing. However, traditional data-driven frameworks are not naturally equipped to process tensors…
Tensor decompositions have become essential tools for feature extraction and compression of multiway data. Recent advances in tensor operators have enabled desirable properties of standard matrix algebra to be retained for multilinear…
Tensor decompositions are powerful tools for analyzing multi-dimensional data in their original format. Besides tensor decompositions like Tucker and CP, Tensor SVD (t-SVD) which is based on the t-product of tensors is another extension of…
The control properties of discrete-time switched linear systems (SLS) with switching signals generated by logical dynamic systems are studied using the semi-tensor product (STP) approach. With the algebraic state space representation…
This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear…
A new matrix product, called dimension-keeping semi-tensor product (DK-STP), is proposed. Under DK-STP, the set of $m\times n$ matrices becomes a semi-group $G({m\times n},\mathbb{F})$, and a ring, denoted by $R(m\times n,\mathbb{F})$.…
Deep learning models for Time Series Classification (TSC) have achieved strong predictive performance but their high computational and memory requirements often limit deployment on resource-constrained devices. While structured pruning can…
Dynamic mode decomposition (DMD) has become a powerful data-driven method for analyzing the spatiotemporal dynamics of complex, high-dimensional systems. However, conventional DMD methods are limited to matrix-based formulations, which…
An equivalent definition of hypermatrices is introduced. The matrix expression of hypermatrices is proposed. Using permutation matrices, the conversion of different matrix expressions is revealed. The various contracted products of…