Spectral clustering method groups Markov chains via P² eigenvectors and weighted k-means
michaelchchoi · x · 2026-07-22
- The thread outlines an algorithm for partitioning a Markov chain with stationary distribution \(\pi\).
- First, it computes the bottom \(k-1\) eigenvectors of \(P^2\), embeds states as \(\Phi(x)=(\phi1(x),\dots,\phi{k-1}(x))\), and then runs weighted k-means in that space.
- The method repeats the clustering \(l\) times to produce multiple candidate partitions.
- It then selects the best partition \(\mathcal{O}\) by scoring with the Frobenius norm of the distance to stationarity.
- The resulting quotient chain \(G{\mathcal{O}}P\) is claimed to mix faster than the original chain \(P\).
Related event: Markov Chain Partitioning via Spectral Features and Weighted k-Means(2 posts)→
More from Research
- Cell-therapy company acquires STEM-PD to test its biology foundation model in clinic — arjunrajlab · 2026-07-22
- Token-level constrained decoding can drive JSON parsing errors to zero in production — demirtasfurkan_ · 2026-07-22
- Frontier LLMs all lost money in a 1.6-year synthetic trading test — Scobleizer · 2026-07-22
- A 2025 Jacobian Conjecture paper revives a long-running open problem in algebra — littmath · 2026-07-22
- RAND publishes first roadmap for protecting valuable algorithmic know-how — Scobleizer · 2026-07-22
- Shengshu says world models, not LLMs alone, will power video, robots and agents — 生数科技 · 2026-07-22