PaCMAP

Overview

PaCMAP (Pairwise Controlled Manifold Approximation) is a dimensionality reduction method that preserves local and global structure through careful control of pair selection during optimization.

Key Innovation

Three types of point pairs:

• Near pairs: Preserve local structure
• Mid-near pairs: Maintain global structure
• Further pairs: Prevent collapse

Advantages

Better Structure Preservation:

• Superior global structure vs. t-SNE
• Better local structure vs. UMAP
• Balanced representation

Stability:

• More robust to hyperparameters
• Consistent results
• Less tuning required

Speed:

• Competitive with UMAP
• Faster than t-SNE
• Scales well

Use Cases

• Embedding space visualization
• Quality assessment for vector models
• Cluster analysis
• Anomaly detection
• Interactive exploration

Comparison

• vs. t-SNE: Better global structure, faster
• vs. UMAP: Better balance, more stable
• vs. PCA: Non-linear, preserves structure

Availability

Python package: pacmap on PyPI

GitHub: YingfanWang/PaCMAP