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Random Forest Autoencoders for Guided Representation Learning
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Proposes Random Forest Autoencoders (RF-AE), an autoencoder that reconstructs RF-GAP proximities and is regularized toward RF-PHATE embeddings, to enable out-of-sample supervised visualization.
Problem
Supervised manifold visualization methods such as RF-PHATE lack an explicit mapping, so they cannot embed unseen data efficiently or scale to large datasets and label-scarce settings.
Approach
Replace the input of a regularized autoencoder with row-normalized, symmetrized RF-GAP proximity vectors, reconstruct them with a Jensen-Shannon divergence loss, and regularize the 2D bottleneck toward precomputed RF-PHATE embeddings; class-wise k-medoids prototype selection reduces input dimensionality.
Key results
- RF-AE (lambda=0.01, N*=0.1N) achieves the highest mean k-NN accuracy (0.831 ± 0.011) across 20 datasets, versus 0.809 for SSNP and 0.794 for RF-PHATE.
- RF-AE ranks top two on local SIA (QNX 0.800, Trust 0.818) and top on global SIA (Spear 0.776, Pearson 0.776) among 14 methods.
- On a Sign MNIST example, RF-AE reaches local SIA 0.89 versus 0.62 for parametric t-SNE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add geometric regularization (lambda<1, toward RF-PHATE embedding) to RF-AE (ablation) | RF-AE · 20 datasets (10 reps) | Global SIA Spear: 0.701 at lambda=1 to 0.776 at lambda=0.01 | Helped |
| add geometric regularization (lambda<1) to RF-AE (ablation) | RF-AE · 20 datasets (10 reps) | k-NN accuracy: 0.837 at lambda=1 vs 0.831 at lambda=0.01 | Hurt |
| RF-AE with lambda=0.01 vs. default RF-PHATE linear kernel extension | RF-AE · 20 datasets (10 reps) | k-NN accuracy: 0.831 vs 0.794 | Helped |
| RF-AE (lambda=0.01) vs. standard supervised baselines on SIA metrics | RF-AE · 20 datasets (10 reps) | Local SIA QNX: 0.800 vs CE 0.795 and NCA 0.808 (NCA ranks first) | Mixed |
| lambda=0.001 vs lambda=0.01 in RF-AE (ablation) | RF-AE · 20 datasets (10 reps) | k-NN accuracy: 0.827 vs 0.831 | No clear effect |
Surprising findings
- Reconstructing RF-GAP proximities with JSD outperforms reconstructing raw features, and the feature-based MLP is more sensitive to noise than the kernel-based encoder in the artificial tree experiment.
- Parametric supervised UMAP and SSNP reach high k-NN accuracy yet show notable drops in structural importance alignment, indicating class separation at the expense of structure.
Limitations
- Scalability is still limited by the computational cost of computing RF-GAP proximities.
- Structural importance alignment relies on pseudo-ground-truth importances from a baseline classifier ensemble, since true feature importances are rarely available.
- Code is promised but no release link is given in the text.
Experimental setup
Datasets: Sign MNIST (A-K) MNIST Fashion MNIST GTZAN (3-sec) USPS Blood MNIST OrganC MNIST Isolet Landsat Satellite Optical Digits HAR Cardiotocography
Benchmarks: 20 datasets from UCI, Kaggle, Zenodo
Metrics: k-NN accuracy structural importance alignment (Kendall tau) with QNX, Trus
Baselines: RF-PHATE kernel extension vanilla AE PCA supervised PCA parametric t-SNE parametric UMAP parametric supervised UMAP PaCMAP Centroid Encoders CEBRA SSNP NCA
Builds on: RF-PHATE RF-GAP GRAE PHATE parametric t-SNE
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