The Impact of Regularization in Spectral Clustering
summary
Regularizing the graph by adding a constant to the adjacency (or to degrees) reduces eigenvector variability and uncovers large communities that unregularized spectral clustering hides. On gene‑expression embryo images (pixels as nodes, ~90th‑percentile correlation threshold) regularization recovers a known fate map; on the political blogs it lifts the main liberal/conservative split from the third to the second eigenvector. A data‑driven selection minimizes an estimated upper bound under a stochastic block model (data‑driven tau selection). Method works but is computationally heavy.
AI-written summary · about
chapters (13)
- 0:00Start
- 0:22Overview
- 1:16Image dataset from the fruit fly project
- 4:01Discovery of fate map
- 6:24Notation
- 7:38Popularity of spectral clustering
- 12:21Comparing unregularized vs. regularized SC
- 15:02Recap: Regularized spectral clustering
- 15:20Population level quantities
- 16:57Understanding pert
- 21:37Example
- 26:06Comparing unregularized vs. regularized Spectral Clustering (SC)
- 26:55Summary
related talks
38mBias-Adjusted Spectral Clustering In Multi-Layer Stochastic Block Models
47mLearning Probabilistic Models for Graph Partitioning in the Presence of Noise
01h 02mGraph Powering
36mExtracting Relevant Metrics with Spectral Clustering
43mInformation-Theoretic Bounds and Phase Transitions in Community Detection and High-Dimensional Clust
25mConstrained Rank Aggregation and Correlation Clustering
38mWhy Deep Learning Works: Implicit Self-Regularization in Deep Neural Networks
54mSzemerédi Regularity Lemma in Graph Machine Learning