MATLAB Tensor Toolbox Implementation with HOSVD Algorithm

The Tensor Toolbox in MATLAB provides robust support for handling high-dimensional data, with HOSVD (Higher-Order Singular Value Decomposition) serving as its core functionality for effectively decomposing multidimensional arrays. The toolkit simplifies tensor operations through several key implementations: 1) Storing N-order tensors as multidimensional array structures using MATLAB's native ndarray format; 2) Implementing tensor products and unfolding operations leveraging built-in matrix computation functions like 'tensorprod' and 'permute'; 3) The HOSVD algorithm performs alternating mode unfolding and SVD decomposition through iterative processes, producing core tensors and factor matrices. This decomposition holds significant application value in fields such as recommendation systems and neuroscience research. Extension possibilities include: 1) Integrating Tucker decomposition frameworks to enhance toolkit capabilities; 2) Adding GPU acceleration functionality using MATLAB's Parallel Computing Toolbox for large-scale tensor computations; 3) Developing visualization modules with MATLAB's graphics functions to intuitively display decomposition results. Implementation note: Ensure the MATLAB Optimization Toolbox is installed before use to achieve optimal SVD computation performance, particularly for handling large-scale tensor operations efficiently.