Research map / Learning theory and algorithms / Clustering
The Flag Median and FlagIRLS
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the flag median instead of the flag mean | Grassmannian prototypes · Synthetic data with 20 outliers | chordal distance to center: 0.0128 -> 0.0017 | Helped |
| Use the flag median instead of the ℓ2-median | Grassmannian prototypes · Synthetic data with 20 outliers | chordal distance to center: 0.0022 -> 0.0017 | Helped |
| Use FlagIRLS instead of the Weiszfeld-type algorithm | Grassmannian median computation · Synthetic 200 points on Gr(6,100) | mean iterations: $795.50 \pm 227.40$ -> $4.55 \pm 0.50$ | Helped |
| Use the flag median instead of the flag mean or ℓ2-median | Grassmannian LBG clustering · Mind's Eye, codebook size 20 | cluster purity: at least a 10% improvement | Helped |
| Use the flag median instead of the flag mean | Grassmannian LBG clustering · UCF YouTube action dataset, codebook sizes 4, 8, 12, 16, and 20 | cluster purity | Helped |
| Use the flag median instead of the ℓ2-median or flag mean | MNIST prototypes · 20 examples of digit 1 with added digit 9 examples | correct prototype classification: 9; 10; 11 | Helped |
| Use the flag median instead of the flag mean or ℓ2-median | Grassmannian prototypes · MNIST examples of 7 with added examples of 6 | prototype movement under outliers: 0,2,4,6,8 | Helped |
| Use FlagIRLS instead of Grassmannian gradient descent | Flag median optimization · Synthetic dataset, 100 random initializations | iterations to convergence | Helped |
| Use FlagIRLS to compute the flag median | Flag median optimization · Synthetic dataset, 100 random initializations | converged trials: 100 % | Helped |
Closest papers by meaning
- Fun with Flags: Robust Principal Directions via Flag Manifolds (CVPR 2024 · similarity 0.88)
- A Flag Decomposition for Hierarchical Datasets (CVPR 2025 · similarity 0.87)
- Random features for Grassmannian kernel approximation with bounded rank-one projections (NeurIPS 2026 · similarity 0.85)
- A Subspace-Constrained Tyler's Estimator and its Applications to Structure from Motion (CVPR 2024 · similarity 0.83)
- Robust Consensus Anchor Learning for Efficient Multi-view Subspace Clustering (ICML 2025 · similarity 0.83)
- Flag Aggregator: Scalable Distributed Training under Failures and Augmented Losses using Convex Optimization (ICLR 2024 · similarity 0.83)
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