Towards One Model for Classical Dimensionality Reduction: A Probabilistic Perspective on UMAP and t-SNE
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910936131960832 |
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| author | Ravuri, Aditya Lawrence, Neil D. |
| author_facet | Ravuri, Aditya Lawrence, Neil D. |
| contents | This paper shows that dimensionality reduction methods such as UMAP and t-SNE, can be approximately recast as MAP inference methods corresponding to a model introduced in Ravuri et al. (2023), that describes the graph Laplacian (an estimate of the data precision matrix) using a Wishart distribution, with a mean given by a non-linear covariance function evaluated on the latents. This interpretation offers deeper theoretical and semantic insights into such algorithms, and forging a connection to Gaussian process latent variable models by showing that well-known kernels can be used to describe covariances implied by graph Laplacians. We also introduce tools with which similar dimensionality reduction methods can be studied. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_17412 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Towards One Model for Classical Dimensionality Reduction: A Probabilistic Perspective on UMAP and t-SNE Ravuri, Aditya Lawrence, Neil D. Machine Learning Artificial Intelligence This paper shows that dimensionality reduction methods such as UMAP and t-SNE, can be approximately recast as MAP inference methods corresponding to a model introduced in Ravuri et al. (2023), that describes the graph Laplacian (an estimate of the data precision matrix) using a Wishart distribution, with a mean given by a non-linear covariance function evaluated on the latents. This interpretation offers deeper theoretical and semantic insights into such algorithms, and forging a connection to Gaussian process latent variable models by showing that well-known kernels can be used to describe covariances implied by graph Laplacians. We also introduce tools with which similar dimensionality reduction methods can be studied. |
| title | Towards One Model for Classical Dimensionality Reduction: A Probabilistic Perspective on UMAP and t-SNE |
| topic | Machine Learning Artificial Intelligence |
| url | https://arxiv.org/abs/2405.17412 |