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An Introduction to Topological Data Analysis Ball Mapper in R
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The Topological Data Analysis Ball Mapper (TDABM) algorithm of Dlotko (2019) provides a model free means to visualize multi-dimensional data. The visualizations are abstract two-dimensional representations of covers of the dataset. To construct a TDABM plot, each variable in the dataset should be ordinal and suitable for representing as an axis of a scatter plot. The graphs produced by TDABM provide a map of the dataset on which outcomes may be charted, models assessed and new models formed. The benefits of TDABM are powering a growing literature. This document provides a step-by-step introduction to the algorithm with code in R.
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A Three Axis Evaluation Framework for Mapper Algorithms
The paper reviews a three-axis evaluation framework (stability, cluster quality, topological shape preservation) for Mapper algorithms, analyzes variants on synthetic and UCI Digits data, and finds the axes often conf...
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