Inductive Global and Local Manifold Approximation and Projection

TL;DR

This paper introduces GLoMAP and its inductive variant iGLoMAP, novel manifold learning methods that preserve global and local data structures for visualization and handle unseen data efficiently.

Contribution

The paper presents GLoMAP, a new manifold learning algorithm, and iGLoMAP, an inductive extension using neural networks for scalable, out-of-sample data embedding.

Findings

GLoMAP effectively preserves global and local structures in data visualization.

iGLoMAP enables out-of-sample embedding without retraining.

Both methods outperform state-of-the-art techniques in experiments.

Abstract

Nonlinear dimensional reduction with the manifold assumption, often called manifold learning, has proven its usefulness in a wide range of high-dimensional data analysis. The significant impact of t-SNE and UMAP has catalyzed intense research interest, seeking further innovations toward visualizing not only the local but also the global structure information of the data. Moreover, there have been consistent efforts toward generalizable dimensional reduction that handles unseen data. In this paper, we first propose GLoMAP, a novel manifold learning method for dimensional reduction and high-dimensional data visualization. GLoMAP preserves locally and globally meaningful distance estimates and displays a progression from global to local formation during the course of optimization. Furthermore, we extend GLoMAP to its inductive version, iGLoMAP, which utilizes a deep neural network to map data to its lower-dimensional representation. This allows iGLoMAP to provide lower-dimensional embeddings for unseen points without needing to re-train the algorithm. iGLoMAP is also well-suited for mini-batch learning, enabling large-scale, accelerated gradient calculations. We have successfully applied both GLoMAP and iGLoMAP to the simulated and real-data settings, with competitive experiments against the state-of-the-art methods.