Research map / Learning theory and algorithms / Matrix and tensor methods
Low-Rank Riemannian Optimization on Positive Semidefinite Stochastic Matrices with Applications to Graph Clustering
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Low-rank factorization X=YY^T with CG on the embedded manifold instead of CG on the symmetric multinomial manifold | similarity clustering via convex programming · Dog breed similarity clustering (n=473, p=3) | Running time (s): 6.12 s to 4.78 s | Helped |
| Low-rank factorization with CG on the quotient manifold instead of CG on the symmetric multinomial manifold | similarity clustering via convex programming · Dog breed similarity clustering (n=473, p=3) | Running time (s): 6.12 s to 3.81 s | Helped |
| Low-rank Riemannian optimization instead of CVX | similarity clustering via convex programming · Dog breed similarity clustering (n=473, p=3) | Running time (s): 3183 s to 3.8 s (about 3 orders of magnitude) | Helped |
| Low-rank quotient manifold CG vs ALM at comparable runtime | similarity clustering via convex programming · Dog breed similarity clustering (n=473, p=3) | Variation of information: 0.8688 (ALM) to 0.5501 (quotient) | Helped |
| Quotient manifold instead of embedded manifold | low-rank CG optimization · Dog breed similarity clustering (n=473, p=3) | Error rate / variation of information: VI 0.5403 embedded vs 0.5501 quotient; error 6.3% vs 6.5% | Mixed |
| Quotient manifold instead of embedded manifold | low-rank CG optimization · Large-scale synthetic community detection (8000<=n<=10000, p=n/1000) | Running time: quotient and embedded curves shown in Figure 2 | Mixed |
| Low-rank embedded/quotient CG instead of CG on the symmetric multinomial manifold | synthetic SBM clustering with p=4n/1000 · Varying dimension n (Figure 1) | Running time: Same performance with drastically lower running time (figure only) | Helped |
| Increasing number of clusters p (rank of factorization) for fixed n=2000 (ablation) | low-rank CG on quotient and embedded manifolds · Synthetic, n=2000, p from 2 to 12 | Running time: running time rises with p (approx. 60 to 110 range in figure) | Hurt |
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