Outlyingness Scores with Cluster Catch Digraphs

TL;DR

This paper proposes two new outlyingness scores based on Cluster Catch Digraphs that improve outlier detection interpretability and performance, especially in high-dimensional data, by addressing issues like collinearity and masking.

Contribution

Introduction of Outbound and Inbound Outlyingness Scores using graph-based techniques for better outlier detection in high-dimensional data.

Findings

Both OSs outperform traditional CCD-based methods in simulations.

IOS achieves the best overall performance, especially in high-dimensional data.

The methods are robust to collinearity and masking effects.

Abstract

This paper introduces two novel, outlyingness scores (OSs) based on Cluster Catch Digraphs (CCDs): Outbound Outlyingness Score (OOS) and Inbound Outlyingness Score (IOS). These scores enhance the interpretability of outlier detection results. Both OSs employ graph-, density-, and distribution-based techniques, tailored to high-dimensional data with varying cluster shapes and intensities. OOS evaluates the outlyingness of a point relative to its nearest neighbors, while IOS assesses the total ``influence" a point receives from others within its cluster. Both OSs effectively identify global and local outliers, invariant to data collinearity. Moreover, IOS is robust to the masking problems. With extensive Monte Carlo simulations, we compare the performance of both OSs with CCD-based, traditional, and state-of-the-art outlier detection methods. Both OSs exhibit substantial overall improvements over the CCD-based methods in both artificial and real-world data sets, particularly with IOS, which delivers the best overall performance among all the methods, especially in high-dimensional settings. Keywords: Outlier detection, Outlyingness score, Graph-based clustering, Cluster catch digraphs, High-dimensional data.