Quality assessment of dimensionality reduction: which criterion for which purpose?

Details

Supervisors

Lee, John Aldo

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en science des données, à finalité spécialisée: analyse de données

Abstract

enDimensionality reduction (DR) is essential for visualising and interpreting high‑dimensional data, yet every embedding introduces distortions. This study provides a systematic evaluation of six DR methods (PCA, MDS, Isomap, UMAP, FMsSNE, and FMsTSNE) across six datasets with diverse structures (COIL‑20, MNIST, Phoneme, Isolet, CoverType, and PBMC3K). The analysis combines visual diagnostics (ZADUVis), quantitative metrics (silhouette, label correlation, rank-based criteria and AUC), and the 17‑measure ZADU framework to characterise local, cluster‑level and global fidelity. A concordance study quantifies how neighbourhood preservation at different scales relates to specific distortion types. Results show that no DR method is universally optimal: each exhibits strengths and weaknesses depending on data topology and preservation goals. The study highlights the risk of visually convincing but structurally misleading embeddings and demonstrates that reliable DR assessment requires integrating visual inspection with scale‑aware rank‑based and cluster‑level metrics. Together, these findings provide a clearer understanding of how DR methods behave across manifold types and offer practical guidance for selecting an embedding strategy aligned with the structural properties of the data.