Research map / Learning theory and algorithms / Optimal transport
Hierarchical Optimal Transport for Multimodal Distribution Alignment
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use hierarchical alignment with clustered structure instead of global Wasserstein alignment without cluster structure (ablation) | Unsupervised alignment · Synthetic low-rank Gaussian mixtures | alignment and correspondence error | Helped |
| Estimate clusters with sparse subspace clustering rather than use known clusters (ablation) | HiWA · Synthetic low-rank Gaussian mixtures | alignment and correspondence error | Hurt |
| Remove cluster structure (ablation) | HiWA · Synthetic low-rank Gaussian mixtures | alignment and correspondence error | Hurt |
| Use HiWA rather than Wasserstein alignment without hierarchical structure (ablation) | Neural population decoding · Macaque neural decoding | cluster correspondence | Helped |
| Use HiWA rather than distribution alignment decoding (ablation) | Neural population decoding · Macaque neural decoding, decreasing source sample count | cluster correspondence accuracy | Helped |
| Reduce the number of source samples per cluster to 8 | HiWA · Macaque neural decoding | cluster correspondence accuracy: > 70% | No clear effect |
| Use equally spaced rather than randomly selected subspaces | HiWA · Synthetic low-rank Gaussian mixtures | alignment and correspondence error | Hurt |
| Use subspace alignment methods in higher dimensions instead of HiWA (ablation) | Synthetic low-rank Gaussian mixtures · Higher-dimensional synthetic setting | alignment performance | Hurt |
| Use iterative closest point instead of HiWA (ablation) | Synthetic low-rank Gaussian mixtures · Synthetic alignment | alignment performance | Hurt |
| Align two reach directions without sufficient cluster asymmetry | HiWA · Neural decoding, two reach directions | correct alignment | Hurt |
| Align three reach directions in symmetrical cases without adequate local asymmetries or labels | HiWA · Neural decoding, three reach directions | correct alignment | Hurt |
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