A Vectorization Method Induced By Maximal Margin Classification For Persistent Diagrams

TL;DR

This work tackles the challenge of turning persistent diagrams into usable vectors for function-oriented learning in proteins. It introduces a maximal margin classifier on Banach spaces, instantiated via Kuratowski embedding of the persistent diagram space, yielding a distance-based encoder that reduces to a quadratic program. Compared against thirteen vectorization methods on a dataset of Cas-associated proteins and transposases, the proposed BS method demonstrates superior robustness and precision, offering a practical framework for predicting protein functions from topological features. The approach provides interpretable topological encodings and suggests pathways for integrating with neural models and broader geometric vectorizations to advance protein function prediction.

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.

Figures (4)

• Figure 1: Framework of protein functional prediction by TDA
• Figure 2: An Intuitive Explanation of Persistent Homology
• Figure 3: Visualizations of topological features
• Figure 4: Evolution tree of 72 proteins

Theorems & Definitions (5)

• Lemma 1.1
• Theorem 1.1
• Remark 2.1
• Lemma 2.1
• Lemma 2.2