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- W4385848304 abstract "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 SVD to tensors that recently developed and has found numerous applications in analyzing high dimensional data. This paper offers a new insight into the t-Product and shows that this product is a block convolution of two tensors with periodic boundary conditions. Based on this viewpoint, we propose a new tensor-tensor product called the $star_c{}text{-Product}$ based on Block convolution with reflective boundary conditions. Using a tensor framework, this product can be easily extended to tensors of arbitrary order. Additionally, we introduce a tensor decomposition based on our $star_c{}text{-Product}$ for arbitrary order tensors. Compared to t-SVD, our new decomposition has lower complexity, and experiments show that it yields higher-quality results in applications such as classification and compression." @default.
- W4385848304 created "2023-08-16" @default.
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- W4385848304 date "2023-08-03" @default.
- W4385848304 modified "2023-09-26" @default.
- W4385848304 title "Multidimensional Data Analysis Based on Block Convolutional Tensor Decomposition" @default.
- W4385848304 doi "https://doi.org/10.48550/arxiv.2308.01768" @default.
- W4385848304 hasPublicationYear "2023" @default.
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