Tensor Unfolding: A Fundamental Technique with Verified Implementation
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Resource Overview
Tensor mode unfolding is a fundamental technique where existing implementations often yield varying results. This code is developed based on formulas from the authoritative reference "Tensor Decompositions and Applications" and has been validated through multiple test cases, demonstrating full compliance with theoretical descriptions. The package includes two MATLAB files: one performs mode-n unfolding while the other implements the inverse transformation (mode-n folding). The implementation maintains mathematical rigor while providing clear operational functions for tensor manipulations.
Detailed Documentation
In tensor analysis, mode unfolding represents a fundamental and crucial technique. Although various unfolding codes have been developed, their outputs often differ significantly. This implementation is programmed according to formulas from the seminal work "Tensor Decompositions and Applications" and has undergone extensive empirical validation, confirming perfect alignment with theoretical expectations. The package contains two MATLAB files: the first executes mode-n unfolding by reorganizing tensor elements into matrix format along specified dimensions, while the second performs the inverse operation of mode-n folding to reconstruct the original tensor structure. When utilizing this code, users can confidently apply these functions to enhance their understanding of tensor unfolding operations and support advanced research applications. The implementation features dimension-aware indexing and permutation mechanisms that ensure mathematical accuracy while maintaining computational efficiency.
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