Methods
INTRODUCTION
This documentation series guides you through the mathematical foundations and practical implementations of Normalized Cuts. You will learn about exact methods for small graphs, linear-time approximations for million-scale datasets, and specialized techniques for feature alignment and visualization.
What you'll learn
- Spectral Clustering: The math behind Normalized Cuts.
- Scalability: How to handle large datasets efficiently with Nyström approximation.
- Analyze Quality: How balanced sampling improve segmentation quality.
- Advanced Partitioning: Multi-way cuts and discrete optimization.
- Visualization: Tools for interpreting high-dimensional embeddings.
Core Modules
1. Basic NCut
Master the foundational implementation of Normalized Cuts and spectral clustering. Understand the graph Laplacian, eigenvector computations, and the core mathematics behind the algorithm.
Start learning →2. Nyström NCut: Complexity
Learn how to scale spectral clustering to million-node graphs using Nyström approximation. This module covers sub-sampling strategies and kNN propagation to achieve linear time complexity O(N).
Explore complexity →3. Nyström NCut: Quality
Discover how Farthest Point Sampling (FPS) and balanced sampling strategies enhance segmentation quality, especially for handling class imbalance and boundary preservation.
Analyze quality →Advanced Topics
4. K-way Discrete NCut
Extend binary partitioning to multi-way clustering. Learn algorithms for partitioning graphs into k clusters simultaneously without recursive bisection.
Go to K-way NCut →5. Mspace Coloring
Techniques for visualizing high-dimensional spectral embeddings in interpretable color spaces.
View coloring methods →6. Feature Alignment
Methods for aligning features from different models or embedding spaces, useful for model comparison and ensemble techniques.
Learn alignment →