Topology and Its Applications in Data Analysis: A Novel Framework for Big Data

Abstract

In the rapidly evolving landscape of big data, traditional data analysis methods often struggle with the complexity and scale of modern datasets. Topological Data Analysis (TDA) offers a promising alternative by applying algebraic topology to uncover the intrinsic structure and patterns within data. This paper introduces a novel framework that integrates topological methods with big data analytics, aiming to enhance data interpretation and feature extraction. The proposed framework encompasses several key components: data preprocessing, complex construction, persistent homology computation, feature extraction, and integration with traditional methods. By applying TDA to diverse datasets, including social networks, genomic data, and sensor data, the framework demonstrates its ability to reveal hidden structures and improve insights. Case studies illustrate how topological features can complement traditional analysis techniques, providing new perspectives and enhancing predictive performance. This work highlights the potential of topological approaches to address the challenges of big data analytics and suggests directions for future research. The framework offers a robust tool for managing and interpreting high-dimensional datasets, paving the way for more nuanced and effective data analysis strategies.