Summary of Entropic Optimal Transport Eigenmaps For Nonlinear Alignment and Joint Embedding Of High-dimensional Datasets, by Boris Landa et al.
Entropic Optimal Transport Eigenmaps for Nonlinear Alignment and Joint Embedding of High-Dimensional Datasets
by Boris Landa, Yuval Kluger, Rong Ma
First submitted to arxiv on: 1 Jul 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Statistics Theory (math.ST)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper proposes a novel method called Entropic Optimal Transport (EOT) eigenmaps for aligning and jointly embedding multiple datasets from different studies or experimental conditions. The approach leverages the leading singular vectors of the EOT plan matrix between two datasets to extract their shared underlying structure and align them accordingly in a common embedding space. The authors show that their method enjoys favorable properties analogous to classical Laplacian eigenmaps and diffusion maps embeddings. The paper also analyzes a data-generative model where two observed high-dimensional datasets share latent variables on a common low-dimensional manifold, but each dataset is subject to data-specific translation, scaling, nuisance structures, and noise. The authors demonstrate the performance of their approach for data integration and embedding through simulations and analyses of real-world biological data. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about finding ways to combine different datasets from different studies or experiments. When these datasets are very high-dimensional (meaning they have many features), it’s hard to find a way to align them correctly. The authors propose a new method called Entropic Optimal Transport (EOT) eigenmaps that can help with this problem. They show that their method works well in simulations and real-world biological data. This could be useful for scientists who want to combine data from different studies to get a better understanding of the underlying patterns. |
Keywords
» Artificial intelligence » Diffusion » Embedding » Embedding space » Generative model » Translation
