ISilDR: Isometric Seriation-Based Dimensionality Reduction for Visual Cluster Analysis

Area of Science:

• Data Science
• Computer Vision
• Statistics

Background:

• Visual cluster analysis is crucial for exploring multidimensional (MD) data.
• Dimensionality Reduction (DR) techniques visualize MD data similarities but suffer from false and missing neighbor distortions.
• Orthogonal Linear Projections (OLP) reduce distortions but only generate false neighbors.

Purpose of the Study:

• To introduce Isometric Seriation-based Dimensionality Reductions (ISilDR) that provably generate at most missing neighbors.
• To explore the combined use of ISilDR and OLP for discovering true MD clusters.
• To develop a systematic analysis for trustworthy visual cluster analysis.

Main Methods:

• ISilDR creates a seriation (ordering) of MD data points, spacing consecutive points by their MD distance.
• Multiple 1D ISilDRs can be combined to form an mD ISilDR.
• Analysis is performed using E-neighborhood graphs to study ISilDR and OLP characteristics.

Main Results:

• ISilDR provably generates at most missing neighbors, unlike other DR techniques.
• A systematic analysis based on E-neighborhood graphs is proposed.
• Rules are derived for discovering cluster patterns using linked ISilDR and OLP layouts.

Conclusions:

• ISilDR offers a complementary approach to OLP for addressing DR distortions.
• Combining ISilDR and OLP facilitates trustworthy visual cluster analysis.
• Case studies demonstrate the utility of ISilDR in various scenarios.