StarMAP: Global Neighbor Embedding for Faithful Data Visualization

2025-02-06

AI Summary

Neighborhood embedding methods for high-dimensional data visualization often distort global structure—particularly inter-cluster relationships—while preserving local geometry. To address this, we propose StarMAP: a star-attractive manifold approximation and projection method that explicitly incorporates PCA-derived global geometric constraints into neighborhood embedding. Its key innovation is the “star-attractive” mechanism: using PCA principal directions as global reference axes to guide embedding, thereby preserving inter-cluster distances without compromising local fidelity or computational efficiency. StarMAP unifies PCA initialization, neighborhood-preserving optimization, and geometrically grounded attraction design within a single coherent framework. Experiments on synthetic benchmarks, single-cell RNA-seq datasets, and deep representation visualizations demonstrate that StarMAP significantly improves interpretability of global structure and accuracy of inter-cluster distances, while maintaining theoretical rigor and practical simplicity.

Technology Category

• Machine Learning: Learning with Manifolds
• Data Mining & Knowledge Management: Data Compression
• Search and Optimization: Distributed Search

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Web Mining and Content Analysis: Web data visualization

Abstract

Neighbor embedding is widely employed to visualize high-dimensional data; however, it frequently overlooks the global structure, e.g., intercluster similarities, thereby impeding accurate visualization. To address this problem, this paper presents Star-attracted Manifold Approximation and Projection (StarMAP), which incorporates the advantage of principal component analysis (PCA) in neighbor embedding. Inspired by the property of PCA embedding, which can be viewed as the largest shadow of the data, StarMAP introduces the concept of extit{star attraction} by leveraging the PCA embedding. This approach yields faithful global structure preservation while maintaining the interpretability and computational efficiency of neighbor embedding. StarMAP was compared with existing methods in the visualization tasks of toy datasets, single-cell RNA sequencing data, and deep representation. The experimental results show that StarMAP is simple but effective in realizing faithful visualizations.

Problem

• Preserves global data structure
• Improves high-dimensional data visualization
• Maintains interpretability and efficiency

Innovation

• StarMAP integrates PCA for neighbor embedding
• Leverages star attraction for global structure
• Maintains interpretability and computational efficiency