Outlier Detection for Robust Multi-Dimensional Scaling.

Area of Science:

• Data Science
• Machine Learning
• Computational Geometry

Background:

• Multi-dimensional scaling (MDS) is crucial for data exploration, dimensionality reduction, and visualization.
• Current MDS algorithms lack robustness to outliers, causing significant embedding errors.

Purpose of the Study:

• To develop a novel technique for detecting and filtering outliers in MDS.
• To enhance the robustness and accuracy of MDS embeddings.

Main Methods:

• A geometric reasoning approach is employed to identify outliers.
• Triangle inequality is used to validate geometric configurations of point triplets.
• Outliers are detected by identifying triangles with violated triangle inequalities.

Main Results:

• The proposed method effectively detects and filters outliers based on geometric principles.
• Performance was evaluated on diverse datasets with varying outlier distributions.
• Significant improvements in embedding quality were observed with up to 20% outliers.

Conclusions:

• The geometric outlier detection method enhances MDS robustness.
• This technique leads to higher quality embeddings in the presence of outliers.
• The approach is effective for practical data exploration and visualization tasks.