Fixed Point Theory in Generalized Metric Vector Spaces and their applications in Machine Learning and Optimization Algorithms - Vinsensia, Desi; Utami, Yulia (Institute of Computer Science (IOCS), 2024)
This study introduces a novel formulation of fixed-point theory within Generalized metric spaces, with an emphasis on applications in machine learning optimization and high-dimensional data analysis. Recall on the concept of complete G-metric spaces, we define a generalized contraction condition tailored for operators representing iterative updates in machine learning algorithms. The proposed framework is exemplified through gradient descent with regularization, demonstrating convergence within a non-Euclidean, high-dimensional setting. Results reveal that our approach not only strengthens convergence properties in iterative algorithms but also complements modern regularization techniques, supporting sparsity and robustness in high-dimensional spaces. These findings underscore the relevance of G-metric spaces and auxiliary functions within fixed-point theory, highlighting their potential to advance adaptive optimization methods. Future work will explore further applications across machine learning paradigms, addressing challenges such as sparse data representation and scalability in complex data environments.