Topological Data Analysis of High-dimensional Correlation Structures

S. Prada Alonso

This work englobes a comprehensive study of the correlation of high-dimensional datasets from a topological perspective. Derived from a lack of efficient algorithms of big data analysis and motivated by the importance of finding a structure of correlations in genomics, we have developed two analytical tools inspired by the topological data analysis approach. We applied graph-theoretic and algebraic topology principles to quantify structural patterns on local correlation networks and, based on them, we proposed a network model to measure the evolution of the correlation with the aging process. Furthermore, we developed a powerful computational algorithm to analyze the correlation structure globally that could serve as a diagnostic tool. Overall, this work establishes a novel perspective of analysis and modulation of hidden correlation structures contributing to the understanding of the epigenetic processes, and that is designed to be useful for non-biological fields too.

Keywords: Topological data analysis, correlation, high-dimensional data, epigenetics

Scheduled

RSME-SEIO Invited Session: Topological Data Analysis
June 10, 2022  10:10 AM
A16

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N. Atienza Martínez

Some new perspectives on the estimation of the volume function

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