Research map / Learning theory and algorithms / Clustering
Understanding the Generalization Performance of Spectral Clustering Algorithms
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use integral-operator extensions to compare empirical and population continuous solutions | Relaxed RatioCut · Population-level continuous solution | excess-risk convergence rate: \mathcal{O}\left(\frac{1}{\sqrt{n}} \right) | Helped |
| Use the auxiliary RKHS and integral-operator analysis for the normalized Laplacian | Relaxed NCut · Population-level continuous solution | excess-risk convergence rate: \mathcal{O}\left(\frac{1}{\sqrt{n}}\right) | Helped |
| Add orthonormal-transform discretization to minimize distance from the continuous solution | Spectral clustering discrete solution · Population-level discrete solution | excess-risk upper bound: 4C\epsilon | Helped |
| Extend eigenfunctions to new samples and discretize with the orthonormal-transform procedure | GPOD for relaxed RatioCut and relaxed NCut · Out-of-sample clustering | ability to cluster unseen samples without re-eigendecomposition | Helped |
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