Research map / Learning theory and algorithms / Matrix and tensor methods
Extending Kernel PCA through Dualization: Sparsity, Robustness and Fast Algorithms
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use dual LBFGS optimization instead of RSVD | Standard KPCA · Synth 1, Protein, RCV1, CIFAR-10 | training time: 1.97 -> 0.53; 6.70 -> 1.07; 12.50 -> 2.12; 123.89 -> 13.51 | Helped |
| Use dual LBFGS optimization instead of RSVD | Standard KPCA · Synth 1, Protein, RCV1, CIFAR-10 | training time: 1.97 -> 0.56; 6.95 -> 1.07; 12.75 -> 3.78; 122.58 -> 29.26 | Helped |
| Replace square loss with Huber Hκ² | KPCA · Contaminated Iris, τ=10, 25, 50, 75 | MSE: 7.591059 -> 6.833484; 7.910846 -> 7.182663; 8.691805 -> 8.045477; 9.782740 -> 9.259353 | Helped |
| Use Huber Hκ¹ rather than square loss | KPCA · Contaminated Iris, τ=100 | MSE: 11.183650 -> 10.791766 | Helped |
| Increase ε in the ε-insensitive loss (ablation) | KPCA dual solution H · Synthetic Gaussian-kernel data | sparsity | Helped |
| Increase ε in the ε-insensitive loss (ablation) | KPCA learned representation · Synthetic Gaussian-kernel data | reconstruction error | Hurt |
| Use ℓε² or ℓε∞ instead of SKPCA at matched sparsity | Sparse KPCA · Sparse KPCA comparison, 10%–50% sparsity | reconstruction error ratio: At 10%: 1.19053 vs 1.04675; at 50%: 2.75248 vs 1.10164 | Helped |
| Increase the number of components s at fixed ε (ablation) | ℓε² KPCA · Synthetic Gaussian-kernel data | sparsity | Hurt |
| Increase the number of components s at a fixed sparsity level (ablation) | ℓε² KPCA · Synthetic Gaussian-kernel data | reconstruction error ratio | Hurt |
| Use Huber loss with Laplacian rather than Gaussian kernel (ablation) | Robust KPCA · Contaminated Iris | MSE | Mixed |
Closest papers by meaning
- Rethinking PCA Through Duality (NeurIPS 2025 · similarity 0.91)
- Stochastic Optimization for Kernel PCA (AAAI 2016 · similarity 0.88)
- Upper bounds for Model-Free Row-Sparse Principal Component Analysis (ICML 2020 · similarity 0.87)
- A Kernel Random Matrix-Based Approach for Sparse PCA (ICLR 2019 · similarity 0.87)
- Efficient Sparse PCA via Block-Diagonalization (ICLR 2025 · similarity 0.86)
- Kernel PCA for Out-of-Distribution Detection (NeurIPS 2024 · similarity 0.85)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.