A tractable latent variable model for nonlinear dimensionality reduction.

Area of Science:

• Machine Learning
• Data Science
• Dimensionality Reduction

Background:

• High-dimensional data presents challenges for analysis and visualization.
• Existing methods like t-SNE, LargeVis, and UMAP have limitations in preserving neighborhood structures and learning higher-dimensional embeddings.
• Latent variable models offer potential for discovering meaningful low-dimensional representations.

Purpose of the Study:

• To propose a novel latent variable model for learning faithful low-dimensional representations of high-dimensional data.
• To extend current leading approaches by incorporating latent variables for enhanced structure learning.
• To enable both visualization (2D/3D) and other applications requiring higher-dimensional embeddings.

Main Methods:

• The model computes low-dimensional embeddings by preserving neighborhood relationships encoded by a sparse graph.
• It balances pulling nearby examples closer and pushing distant examples apart.
• An Expectation-Maximization procedure with closed-form updates is derived, utilizing a discrete graph Laplacian for iterative adaptation.

Main Results:

• The proposed model leverages latent variables to provide additional structure for learning.
• It demonstrates effectiveness on image and text datasets.
• An approximate coarse-graining procedure is developed for scalability in large problems, avoiding negative sampling.

Conclusions:

• The latent variable model offers a powerful and flexible approach to dimensionality reduction.
• It successfully preserves neighborhood relationships while offering advantages over existing techniques.
• The method is effective for various data types and scalable for large datasets.