A Vectorization Method Induced By Maximal Margin Classification For Persistent Diagrams

TL;DR

This paper introduces a geometrical vectorization method for persistent diagrams based on maximal margin classification, improving protein function prediction by leveraging topological data analysis.

Contribution

It presents a novel vectorization technique for persistent diagrams using maximal margin classification, enhancing the effectiveness of topological data analysis in protein function prediction.

Findings

Outperforms existing statistical vectorization methods in robustness.

Achieves higher precision in protein classification tasks.

Demonstrates the effectiveness of geometrical vectorization in topological data analysis.

Abstract

Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate Persistent homology in machine learning methods of protein function prediction have resulted in several techniques for vectorizing persistent diagrams. However, current vectorization methods are excessively artificial and cannot ensure the effective utilization of information or the rationality of the methods. To address this problem, we propose a more geometrical vectorization method of persistent diagrams based on maximal margin classification for Banach space, and additionaly propose a framework that utilizes topological data analysis to identify proteins with specific functions. We evaluated our vectorization method using a binary classification task on proteins and compared it with the statistical methods that exhibit the best performance among thirteen commonly used vectorization methods. The experimental results indicate that our approach surpasses the statistical methods in both robustness and precision.