Mapper Based Classifier

Jacek Cyranka, Alexander Georges, David Meyer
10/17/2019
cs.LGcs.CVstat.ML

Official code: asgeorges/mapper-classifier (8 stars, last commit 2023-03-25).

Abstract

Topological data analysis aims to extract topological quantities from data, which tend to focus on the broader global structure of the data rather than local information. The Mapper method, specifically, generalizes clustering methods to identify significant global mathematical structures, which are out of reach of many other approaches. We propose a classifier based on applying the Mapper algorithm to data projected onto a latent space. We obtain the latent space by using PCA or autoencoders. Notably, a classifier based on the Mapper method is immune to any gradient based attack, and improves robustness over traditional CNNs (convolutional neural networks). We report theoretical justification and some numerical experiments that confirm our claims.

View on arXivView PDF

Code Implementations(1)

asgeorges/mapper-classifierOfficial100%

This repository contains the initial PoC software to build a mapper based classifier, which utilizes tools from topological data analysis. The package here does not scale well & is optimally inefficient (you're welcome) - however, work is currently being done to refactor this code into a polished package.

80R, HTMLOct 9, 20193 years ago

Similar Papers

On Interpretable Approaches to Cluster, Classify and Represent Multi-Subspace Data via Minimum Lossy Coding Length based on Rate-Distortion Theory

82% match2023

Topological Deep Learning: A Review of an Emerging Paradigm

82% match2023

Research on fusing topological data analysis with convolutional neural network

82% match2024

Point-Level Topological Representation Learning on Point Clouds

80% match1 repo272024

Enhancing cluster analysis via topological manifold learning

80% match1 repo32022

Challenges in 3D Data Synthesis for Training Neural Networks on Topological Features

80% match2025

Cite this paper

@article{cyranka2019mapper,
  title  = {Mapper Based Classifier},
  author = {Jacek Cyranka and Alexander Georges and David Meyer},
  year   = {2019},
  eprint = {1910.08103},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1910.08103}
}

Add a badge to your README

Shows whether official code is linked for this paper.

Code of Paper badge
[![Code of Paper](https://codeofpaper.com/badge/1910.08103.svg)](https://codeofpaper.com/paper/1910.08103)

Discussion