Cluster and then Embed: A Modular Approach for Visualization

2026-07-13 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics, Mathematics & Computational Sciences · Depth: Expert, long

Summary

The paper introduces "Cluster+Embed" (C+E), a modular visualization approach designed to overcome the global geometry distortion issues prevalent in methods like t-SNE and UMAP. C+E operates in three distinct steps: first, it clusters the high-dimensional data using a user-selected method such as Louvain or DBSCAN; second, it embeds each identified cluster individually using a chosen technique like PCA, Isomap, or LOE, aiming to minimize distortion within clusters; and finally, it aligns these separately embedded clusters using rigid transformations, incorporating a tuning parameter α to control inter-cluster separation. This framework, demonstrated on datasets including GMM, MNIST, Fashion MNIST, and single-cell RNA sequencing data, offers competitive performance against existing methods while providing enhanced transparency and flexibility in preserving both local and global data structures.

Key takeaway

For Data Scientists or Machine Learning Engineers visualizing high-dimensional data with inherent cluster structures, consider adopting the Cluster+Embed (C+E) approach. This modular method allows you to explicitly control clustering and embedding steps, mitigating the global geometry distortions common in t-SNE or UMAP. You can select optimal algorithms for each stage and fine-tune inter-cluster separation, leading to more transparent and geometrically faithful visualizations for exploratory data analysis or model interpretation.

Key insights

A modular "Cluster+Embed" approach improves high-dimensional data visualization by preserving both local and global geometry.

Principles

• Dimensionality reduction methods often trade local structure preservation for global geometry distortion.
• Separating clustering from embedding enhances transparency and control in visualization.
• Individual cluster embedding reduces distortion compared to global embedding.

Method

First, cluster the data using any suitable method. Second, embed each cluster separately. Third, align embedded clusters with rigid transformations, using a tuning parameter α for separation.

In practice

• Apply C+E for visualizing clustered high-dimensional datasets.
• Choose specific clustering (e.g., Louvain) and embedding (e.g., Isomap) algorithms.
• Adjust the α parameter to control visual separation between clusters.

Topics

• Dimensionality Reduction
• Data Visualization
• Cluster Analysis
• t-SNE
• UMAP
• Manifold Learning

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.