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TDABM

TDABM (Topological Data Analysis Ball Mapper)

CRISP-T implements the Topological Data Analysis Ball Mapper (TDABM) algorithm based on Rudkin and Dlotko (2024). TDABM provides a model-free method to visualize multidimensional data and uncover hidden, global patterns in complex, noisy, or high-dimensional datasets.

How TDABM Works

  1. Point Cloud Creation: Data is transformed into a point cloud where each axis represents one of the selected variables (X variables).
  2. Ball Covering: The algorithm randomly selects landmark points and creates balls of a specified radius around them, covering all data points.
  3. Connection Mapping: Landmark points with non-empty intersections are connected, revealing the topological structure of the data.
  4. Visualization: The result is visualized as a 2D graph where:
  5. Circle size represents the number of points in each ball
  6. Circle color represents the mean value of the outcome variable (Y), ranging from red (low) to purple (high)
  7. Lines connect overlapping balls, showing the data's topological structure

Using TDABM

# Perform TDABM analysis
crispt --inp corpus_dir --tdabm satisfaction:age,income,education:0.3 --out corpus_dir

# Visualize TDABM results
crispviz --inp corpus_dir --tdabm --out visualizations

When to Use TDABM

  • Discovering hidden patterns in multidimensional data
  • Visualizing relationships between multiple variables
  • Identifying clusters and connections in complex datasets
  • Performing model-free exploratory data analysis
  • Understanding global structure in high-dimensional data

Reference

Rudkin, S., & Dlotko, P. (2024). Topological Data Analysis Ball Mapper for multidimensional data visualization. Paper reference to be added - algorithm implementation based on the TDABM methodology described by the authors.