{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-topological-data-analysis-based-classifier","title":"A Topological Data Analysis Based Classifier","arxiv_id":"2111.05214","date":"2021-11-09","proceeding":null,"authors":["Rolando Kindelan","José Frías","Mauricio Cerda","Nancy Hitschfeld"],"abstract":"Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML) methods. This paper proposes an algorithm that applies TDA directly to multi-class classification problems, without any further ML stage, showing advantages for imbalanced datasets. The proposed algorithm builds a filtered simplicial complex on the dataset. Persistent Homology (PH) is applied to guide the selection of a sub-complex where unlabeled points obtain the label with the majority of votes from labeled neighboring points. We select 8 datasets with different dimensions, degrees of class overlap and imbalanced samples per class. On average, the proposed TDABC method was better than KNN and weighted-KNN. It behaves competitively with Local SVM and Random Forest baseline classifiers in balanced datasets, and it outperforms all baseline methods classifying entangled and minority classes.","url_abs":"https://arxiv.org/abs/2111.05214v3","url_pdf":"https://arxiv.org/pdf/2111.05214v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-topological-data-analysis-based-classifier","repo_url":"https://github.com/rolan2kn/tdabc-4-adac","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[{"task_slug":"multi-class-classification","task_name":"Multi-class Classification"},{"task_slug":"topological-data-analysis","task_name":"Topological Data Analysis"}],"methods":[{"method_slug":"svm","method_name":"SVM"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}