# A Vectorization Method Induced By Maximal Margin Classification For Persistent Diagrams

arXiv: https://arxiv.org/abs/2407.21298 · HTML: https://mlsanity.com/paper/2407.21298/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 32 references that are in the map.
- First posted on arXiv 31 Jul 2024.

## Builds on (most cited first, 9 of 9)

- [node2vec: Scalable Feature Learning for Networks](https://mlsanity.com/paper/1607.00653/) (2016)
- [An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists](https://mlsanity.com/paper/1710.04019/) (2017)
- [Ripser: efficient computation of Vietoris-Rips persistence barcodes](https://mlsanity.com/paper/1908.02518/) (2019)
- [Topological Deep Learning: A Review of an Emerging Paradigm](https://mlsanity.com/paper/2302.03836/) (2023)
- [Persistence Curves: A canonical framework for summarizing persistence diagrams](https://mlsanity.com/paper/1904.07768/) (2019)
- [Persistence paths and signature features in topological data analysis](https://mlsanity.com/paper/1806.00381/) (2018)
- [Topological Time Series Analysis](https://mlsanity.com/paper/1812.05143/) (2018)
- [Persistence Codebooks for Topological Data Analysis](https://mlsanity.com/paper/1802.04852/) (2018)
- [Persistence B-Spline Grids: Stable Vector Representation of Persistence Diagrams Based on Data Fitting](https://mlsanity.com/paper/1909.08417/) (2019)

## Abstract (arXiv)

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.