Cluster-based multidimensional scaling embedding tool for data visualization

TL;DR

This paper introduces cluster MDS (cl-MDS), a visualization technique that combines multidimensional scaling with clustering to effectively preserve local and global data structures in 2D representations.

Contribution

The paper presents a novel clustering-based MDS method that enables hierarchical embedding, sparsification, and estimation of 2D coordinates, improving data visualization quality.

Findings

Enhanced visualization of complex non-linear data

Improved preservation of local and global structures

Effective hierarchical embedding and sparsification

Abstract

We present a new technique for visualizing high-dimensional data called cluster MDS (cl-MDS), which addresses a common difficulty of dimensionality reduction methods: preserving both local and global structures of the original sample in a single 2-dimensional visualization. Its algorithm combines the well-known multidimensional scaling (MDS) tool with the $k$-medoids data clustering technique, and enables hierarchical embedding, sparsification and estimation of 2-dimensional coordinates for additional points. While cl-MDS is a generally applicable tool, we also include specific recipes for atomic structure applications. We apply this method to non-linear data of increasing complexity where different layers of locality are relevant, showing a clear improvement in their retrieval and visualization quality.