Tensor Decomposition Methods Based on Eigenfunctions

This article presents implementation approaches for tensor decomposition methods based on eigenfunctions, incorporating multiple optimization algorithms such as Levenberg-Marquardt (LM) and Alternating Least Squares (ALS). These algorithmic implementations primarily address underdetermined MIMO system identification challenges through iterative optimization techniques. The code architecture allows for performance improvement via parameter optimization in convergence criteria and regularization terms, along with additional data preprocessing modules. Furthermore, the framework demonstrates potential for extension to other domains such as image processing (through tensor-based feature extraction) and natural language processing (via high-dimensional semantic representation). The implementation employs checkpointing for iterative computations and includes validation metrics for decomposition accuracy. Continuous refinement of these algorithmic approaches enables better understanding and resolution of complex real-world problems involving high-dimensional data analysis.