SQuadMDS: a lean Stochastic Quartet MDS improving global structure preservation in neighbor embedding like t-SNE and UMAP

TL;DR

SQuadMDS introduces a scalable stochastic force-directed multidimensional scaling method that preserves global and local data structures, outperforming existing approaches in visualization tasks.

Contribution

It presents a novel O(N) complexity stochastic MDS algorithm that can be integrated with neighbor embedding methods like t-SNE for improved data visualization.

Findings

Outperforms state-of-the-art methods in preserving data structure

Achieves linear time and space complexity for large datasets

Provides competitive qualitative and quantitative embedding quality

Abstract

Multidimensional scaling is a statistical process that aims to embed high dimensional data into a lower-dimensional space; this process is often used for the purpose of data visualisation. Common multidimensional scaling algorithms tend to have high computational complexities, making them inapplicable on large data sets. This work introduces a stochastic, force directed approach to multidimensional scaling with a time and space complexity of O(N), with N data points. The method can be combined with force directed layouts of the family of neighbour embedding such as t-SNE, to produce embeddings that preserve both the global and the local structures of the data. Experiments assess the quality of the embeddings produced by the standalone version and its hybrid extension both quantitatively and qualitatively, showing competitive results outperforming state-of-the-art approaches. Codes are available at https://github.com/PierreLambert3/SQuaD-MDS-and-FItSNE-hybrid.