Diving into the World of Tensors and Exploring the Truths of Topological Data Structures
Abhinav Rathour, R. Jayadurga, Mohan Garg, Malatesh S. Akkur, Swati Bula Patil, P. K. Miniappan · 2024
The rapid expansion of data analysis depends on breakthroughs in tensor and topological data structure investigation. This study presents a new approach that leverages persistent homology, geometric deep learning, and tensor decomposi-tion to extract usable information from topologically complex, high-dimensional datasets. We describe the proposed idea and thoroughly test it against six alterna-tive possibilities. Several key features reveal that the proposed strategy outperforms current methods. These include processing efficiency, accuracy, scalability, robustness, interpretability, and application performance. Machine learning, topo-logical data analysis, and tensor decomposition can reveal hidden data patterns. We demonstrate how the technique simplifies many datasets, making it an excel-lent alternative for data exploration in numerous fields. Our investigation reveals that the recommended technique can handle topological data structures and high-dimensional data, which previous methods have missed. This comprehensive strategy simplifies high-dimensional data search. Academics and data scientists have more powerful, versatile, and easy-to-understand tools to explore topologi-cal data structure complexity.