{"title":"机器学习中的拓扑方法:从业人员教程","authors":"Baris Coskunuzer, Cüneyt Gürcan Akçora","doi":"arxiv-2409.02901","DOIUrl":null,"url":null,"abstract":"Topological Machine Learning (TML) is an emerging field that leverages\ntechniques from algebraic topology to analyze complex data structures in ways\nthat traditional machine learning methods may not capture. This tutorial\nprovides a comprehensive introduction to two key TML techniques, persistent\nhomology and the Mapper algorithm, with an emphasis on practical applications.\nPersistent homology captures multi-scale topological features such as clusters,\nloops, and voids, while the Mapper algorithm creates an interpretable graph\nsummarizing high-dimensional data. To enhance accessibility, we adopt a\ndata-centric approach, enabling readers to gain hands-on experience applying\nthese techniques to relevant tasks. We provide step-by-step explanations,\nimplementations, hands-on examples, and case studies to demonstrate how these\ntools can be applied to real-world problems. The goal is to equip researchers\nand practitioners with the knowledge and resources to incorporate TML into\ntheir work, revealing insights often hidden from conventional machine learning\nmethods. The tutorial code is available at\nhttps://github.com/cakcora/TopologyForML","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"24 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Topological Methods in Machine Learning: A Tutorial for Practitioners\",\"authors\":\"Baris Coskunuzer, Cüneyt Gürcan Akçora\",\"doi\":\"arxiv-2409.02901\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Topological Machine Learning (TML) is an emerging field that leverages\\ntechniques from algebraic topology to analyze complex data structures in ways\\nthat traditional machine learning methods may not capture. This tutorial\\nprovides a comprehensive introduction to two key TML techniques, persistent\\nhomology and the Mapper algorithm, with an emphasis on practical applications.\\nPersistent homology captures multi-scale topological features such as clusters,\\nloops, and voids, while the Mapper algorithm creates an interpretable graph\\nsummarizing high-dimensional data. To enhance accessibility, we adopt a\\ndata-centric approach, enabling readers to gain hands-on experience applying\\nthese techniques to relevant tasks. We provide step-by-step explanations,\\nimplementations, hands-on examples, and case studies to demonstrate how these\\ntools can be applied to real-world problems. The goal is to equip researchers\\nand practitioners with the knowledge and resources to incorporate TML into\\ntheir work, revealing insights often hidden from conventional machine learning\\nmethods. The tutorial code is available at\\nhttps://github.com/cakcora/TopologyForML\",\"PeriodicalId\":501119,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Topology\",\"volume\":\"24 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Algebraic Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.02901\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.02901","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Topological Methods in Machine Learning: A Tutorial for Practitioners
Topological Machine Learning (TML) is an emerging field that leverages
techniques from algebraic topology to analyze complex data structures in ways
that traditional machine learning methods may not capture. This tutorial
provides a comprehensive introduction to two key TML techniques, persistent
homology and the Mapper algorithm, with an emphasis on practical applications.
Persistent homology captures multi-scale topological features such as clusters,
loops, and voids, while the Mapper algorithm creates an interpretable graph
summarizing high-dimensional data. To enhance accessibility, we adopt a
data-centric approach, enabling readers to gain hands-on experience applying
these techniques to relevant tasks. We provide step-by-step explanations,
implementations, hands-on examples, and case studies to demonstrate how these
tools can be applied to real-world problems. The goal is to equip researchers
and practitioners with the knowledge and resources to incorporate TML into
their work, revealing insights often hidden from conventional machine learning
methods. The tutorial code is available at
https://github.com/cakcora/TopologyForML