Directional quality assessment for nonlinear dimensionality reduction in data visualisation

Details

Supervisors

Lee, John Aldo

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] en science des données, orientation technologies de l'information, à finalité spécialisée

Abstract

Dimensionality reduction (DR) is crucial for simplifying complex data, but it often introduces distortions. Existing quality metrics, primarily neighborhood-based, fail to account for directionality in the data and can be sensitive to local distortions. This thesis introduces a novel, path-based approach to DR quality assessment, leveraging shortest paths in low-dimensional space to evaluate structural preservation. Two metrics are proposed: a path-based adaptation of RNX and an edit-distance-based comparison of path sequences. Experiments on MNIST and COIL-20 datasets demonstrate that the new metrics effectively capture the local vs. global trade-offs inherent in different DR techniques. While computationally intensive, the method is shown to converge efficiently via random path sampling. This path-based approach offers a more nuanced, robust, and interpretable evaluation of DR quality, bridging intuitive understanding with rigorous analysis.