Machine- Learning Aided Singular Value Decomposition

This paper is part of an ongoing research regarding the creation of an efficient machine-learning model in the scope of performing Singular Value Decomposition (SVD) able to be utilized in micro computers with proper evaluation and results. This research focuses on the application of SVD in image classification applications. Image processing utilizes matrices of large dimensions in order to represent the data, while for the case of color images, three matrices are necessary in order to encode color information. The application of SVD in this case aims to increase the efficiency of the necessary processing, which is computationally intensive. SVD image analysis has the ability to reduce the dimension of the problem. Addressing the challenges of numerical instability in eigenvalue calculations, we leverage Taylor expansions to enhance training efficiency and accuracy, particularly in image processing tasks. The proposed approach demonstrates superior performance over traditional Power Iteration methods, reducing error rates and training times significantly. This advancement has broad applications in computer vision and resource-constrained environments. All these applications benefit from the ability of SVD to reduce data dimensionality while preserving significant image features. Unlike Power Iteration methods prone to numerical instability, the Taylor expansion approach introduced here addresses gradient issues in deep-learning models with closely spaced eigenvalues. This paper evaluates the effectiveness of the model on microcomputers by assessing both performance metrics and output quality. An approach of this kind would make viable the implementation of advanced SVD techniques on a wider range of hardware. This will allow a wider range of applications in image processing and other fields requiring efficient matrix factorization on constrained devices.