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Topologically Regularized Data Embeddings
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add a circular topological prior to PCA | PCA embedding · Synthetic Cycle | r^2: $0.56\pm0.47$ -> $\bf{0.85\pm0.14}$ | Helped |
| add a circular topological prior to PCA | PCA embedding · Cell Cycle | accuracy: $0.79\pm0.07$ -> $\bf{0.81\pm0.07}$ | Helped |
| add connectedness and flare priors to UMAP | UMAP embedding · Cell Bifurcating | accuracy: $0.79\pm0.08$ -> $\bf{0.82\pm0.08}$ | Helped |
| add a two-cluster prior to DeepWalk | DeepWalk embedding · Karate | accuracy: $\bf{0.97\pm0.08}$ -> $\bf{0.97\pm0.08}$ | No clear effect |
| remove the embedding loss (ablation) | Topologically regularized PCA · Synthetic Cycle | r^2: $\bf{0.85\pm0.14}$ -> $0.77\pm0.24$ | Hurt |
| remove the embedding loss (ablation) | Topologically regularized PCA · Cell Cycle | accuracy: $\bf{0.81\pm0.07}$ -> $0.79\pm0.07$ | No clear effect |
| remove the embedding loss (ablation) | Topologically regularized UMAP · Cell Bifurcating | accuracy: $\bf{0.82\pm0.08}$ -> $0.81\pm0.07$ | No clear effect |
| remove the embedding loss (ablation) | Topologically regularized DeepWalk · Karate | accuracy: $\bf{0.97\pm0.08}$ -> $0.91\pm0.14$ | Hurt |
Closest papers by meaning
- Topological Blindspots: Understanding and Extending Topological Deep Learning Through the Lens of Expressivity (ICLR 2025 · similarity 0.88)
- Cover learning for large-scale topology representation (ICML 2025 · similarity 0.88)
- TopER: Topological Embeddings in Graph Representation Learning (NeurIPS 2025 · similarity 0.88)
- Towards Scalable Topological Regularizers (ICLR 2025 · similarity 0.87)
- Weighted Embeddings for Low-Dimensional Graph Representation (AAAI 2025 · similarity 0.87)
- Partition First, Embed Later: Laplacian-Based Feature Partitioning for Refined Embedding and Visualization of High-Dimensional Data (ICML 2025 · similarity 0.86)
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