🍩 Database of Original & Non-Theoretical Uses of Topology

1. A Topological Data Analysis Based Classification Method for Multiple Measurements (2019)

   Henri Riihimäki, Wojciech Chachólski, Jakob Theorell, Jan Hillert, Ryan Ramanujam

   Abstract

   \textlessh3\textgreaterAbstract\textless/h3\textgreater \textlessh3\textgreaterBackground\textless/h3\textgreater \textlessp\textgreaterMachine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology. When applying this to two case studies, accuracy exceeds alternative models with additional benefits such as reporting data subsets with high purity along with feature values.\textless/p\textgreater\textlessh3\textgreaterResults\textless/h3\textgreater \textlessp\textgreaterFor 300 examples of 3 tree species, the accuracy reached 80% after 30 datapoints, which was improved to 90% after increased sampling to 400 datapoints. Using data from 100 examples of each of 6 point processes, the classifier achieved 96.8% accuracy. In both datasets, the TDA classifier outperformed an alternative model.\textless/p\textgreater\textlessh3\textgreaterConclusions\textless/h3\textgreater \textlessp\textgreaterThis algorithm and software can be beneficial for repeated measurement data common in biological sciences, as both an accurate classifier and a feature selection tool.\textless/p\textgreater

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   • Biology
   • Point process
   • Tree species
   • Machine learning
   • Mapper
   • Point process