A Probabilistic Graph Coupling View of Dimension Reduction

• URL: http://arxiv.org/abs/2201.13053v3
• Date: Thu, 5 Oct 2023 11:16:04 GMT
• Title: A Probabilistic Graph Coupling View of Dimension Reduction
• Authors: Hugues Van Assel, Thibault Espinasse, Julien Chiquet, Franck Picard
• Abstract summary: We introduce a unifying statistical framework based on the coupling of hidden graphs using cross entropy. We show that existing pairwise similarity DR methods can be retrieved from our framework with particular choices of priors for the graphs. Our model is leveraged and extended to address the issue while new links are drawn with Laplacian eigenmaps and PCA.
• Score: 5.35952718937799
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Most popular dimension reduction (DR) methods like t-SNE and UMAP are based on minimizing a cost between input and latent pairwise similarities. Though widely used, these approaches lack clear probabilistic foundations to enable a full understanding of their properties and limitations. To that extent, we introduce a unifying statistical framework based on the coupling of hidden graphs using cross entropy. These graphs induce a Markov random field dependency structure among the observations in both input and latent spaces. We show that existing pairwise similarity DR methods can be retrieved from our framework with particular choices of priors for the graphs. Moreover this reveals that these methods suffer from a statistical deficiency that explains poor performances in conserving coarse-grain dependencies. Our model is leveraged and extended to address this issue while new links are drawn with Laplacian eigenmaps and PCA.

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