A new visual quality metric for Evaluating the performance of multidimensional projections

TL;DR

This work introduces a learned visual quality metric for evaluating multidimensional projections, particularly improving LAMP by integrating three perceptual cues: silhouette coefficient, neighborhood preservation, and silhouette ratio. The metric $M_{new} = w_1 m_1 + w_2 m_2 + w_3 m_3$ is learned via regression on labeled projection grades, with weights obtained from normal equations and LU decomposition. A hyperparameter tuning algorithm searches over scale intervals to identify the best projection scale per dataset, and cross-validated results show low MAE values ($MAE_{train} = 0.5414$, $MAE_{test} = 0.5630$) and strong alignment between metric scores and visual quality. The approach provides a practical path to automatically select scales and assess MP quality, with future work aiming to refine neighbor definitions and radius-based control for MLS-based projections.

Abstract

Multidimensional projections (MP) are among the most essential approaches in the visual analysis of multidimensional data. It transforms multidimensional data into two-dimensional representations that may be shown as scatter plots while preserving their similarity with the original data. Human visual perception is frequently used to evaluate the quality of MP. In this work, we propose to study and improve on a well-known map called Local Affine Multidimensional Projection (LAMP), which takes a multidimensional instance and embeds it in Cartesian space via moving least squares deformation. We propose a new visual quality metric based on human perception. The new metric combines three previously used metrics: silhouette coefficient, neighborhood preservation, and silhouette ratio. We show that the proposed metric produces more precise results in analyzing the quality of MP than other previously used metrics. Finally, we describe an algorithm that attempts to overcome a limitation of the LAMP method which requires a similar scale for control points and their counterparts in the Cartesian space.

Figures (10)

• Figure 1: Figures showing projections on wine dataset with different scales.
• Figure 2: Figures showing projections on iris dataset with different scales.
• Figure 3: Figures showing projections on vehicle dataset with different scales.
• Figure 4: Figures showing projections used to train the new metric.
• Figure 5: Figures showing projections with the result of the learnt metric.