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