Outlier Detection for Robust Multi-dimensional Scaling

TL;DR

This paper presents a geometric approach to detect and filter outliers in multi-dimensional scaling, improving embedding quality in the presence of up to 20% outliers.

Contribution

It introduces a novel outlier detection method based on triangle inequality violations, enhancing robustness of MDS algorithms.

Findings

Effective detection of outliers under 20% contamination.

Significant improvement in embedding quality with outlier filtering.

Validated on various datasets and outlier distributions.

Abstract

Multi-dimensional scaling (MDS) plays a central role in data-exploration, dimensionality reduction and visualization. State-of-the-art MDS algorithms are not robust to outliers, yielding significant errors in the embedding even when only a handful of outliers are present. In this paper, we introduce a technique to detect and filter outliers based on geometric reasoning. We test the validity of triangles formed by three points, and mark a triangle as broken if its triangle inequality does not hold. The premise of our work is that unlike inliers, outlier distances tend to break many triangles. Our method is tested and its performance is evaluated on various datasets and distributions of outliers. We demonstrate that for a reasonable amount of outliers, e.g., under $20\%$, our method is effective, and leads to a high embedding quality.