PaCMAP Operator

This operator performs PaCMAP (Pairwise Controlled Manifold Approximation) dimensionality reduction on image data in Tercen.

Overview

PaCMAP is a dimensionality reduction algorithm that preserves both local and global structure of the data. It is particularly useful for visualization and exploration of high-dimensional data. This operator takes image data in a long format and applies PaCMAP to reduce it to a lower-dimensional representation.

Input Data

The operator expects data in the following format:

Main Projection

• .y: The pixel value
• .ci: Column index linking to the Column Projection
• .ri: Row index linking to the Row Projection

Column Projection

• eventId: Unique identifier for each image/event
• .ci: Column index linking to the Main Projection

Row Projection

• pixel_id: Unique identifier for each pixel position
• .ri: Row index linking to the Main Projection

Example of input data:

Main Projection

.ci .ri .y  
0   0  1.3  
1   0  0.1 
0   1  0.5 
1   1  0.8 

Row Projection

.ri pixel_id
0  1
1  2

Column Projection

.ci eventId
0  1
1  2

Output Data

The operator outputs a data frame with the following columns:

• PaCMAP_1, PaCMAP_2, ...: The coordinates in the reduced dimensionality space
• eventId: The original event identifier
• .ci: Column index
• .ri: Row index (set to 0)

Parameters

• n_components (default: 2): Number of dimensions in the embedding
• n_neighbors (default: 10): Number of neighbors for the kNN graph
• MN_ratio (default: 0.5): Ratio of mid-near pairs to be sampled
• FP_ratio (default: 2.0): Ratio of further pairs to be sampled

References

• PaCMAP GitHub Repository
• Wang, Y., Huang, H., Rudin, C., & Shaposhnik, Y. (2021). Understanding How Dimension Reduction Tools Work: An Empirical Approach to Deciphering t-SNE, UMAP, TriMAP, and PaCMAP for Data Visualization. Journal of Machine Learning Research, 22(1), 3794-3841.