Inductive Global and Local Manifold Approximation and Projection
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.
Submission Length: Long submission (more than 12 pages of main content)
Changes Since Last Submission: We have revised our manuscript to incorporate feedback from all three reviewers.
Changes are color-coded for clarity: olive for Reviewer X2sp, blue for Reviewer JCaC, and teal for Reviewer yBN5.
- To address Reviewer X2sp’s comments, we included a computational comparison and added two new measures, Silhouette and Trustworthiness scores.
- In response to Reviewer JCaC’s feedback on clarifying our contributions, we significantly revised the introduction and Section 4.1. We also added an FMNIST result.
- All questions and comments from Reviewer yBN5 have also been addressed.
We are deeply grateful to all reviewers for their valuable time and thoughtful feedback on our manuscript.
Assigned Action Editor: ~Yaoliang_Yu1
Submission Number: 3261
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