Tensor ring decompositions provide a powerful framework for analyzing multidimensional data. These decompositions represent tensors as a sum of rank-1 or low-rank matrices, leading to significant computational advantages over traditional tensor representations. By exploiting the inherent structure of multiway data, tensor ring decompositions enable

Tensor rings offer a novel approach to representing multidimensional data. By decomposing complex tensors into a sum of rank-1 matrices, tensor ring representations capture crucial patterns and structures within the data. This factorization enables dimensionality reduction, allowing for compact storage and processing of high-dimensional information

Tensor ring decomposition presents a powerful framework for analyzing high-order data. This technique decomposes complex tensors into a sum of simpler matrices, often referred to as core matrices and factor matrices. Thus, tensor ring decomposition facilitates efficient storage and computation with large datasets by exploiting the underlying patter

Tensor ring decomposition presents a powerful framework for analyzing high-order data. This technique decomposes complex tensors into a sum of simpler matrices, often referred to as core matrices and factor matrices. Therefore, tensor ring decomposition facilitates efficient storage and computation with large datasets by exploiting the underlying p

Tensors articulate multi-dimensional data, extending the concept of vectors and matrices to encompass higher dimensions. These structures find widespread application in fields such as machine learning, physics, and computer graphics. Rings, with their well-defined operations of addition and multiplication, provide a powerful framework for manipulat