Outlyingness Scores with Cluster Catch Digraphs (2501.05530v1)

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.

• The paper introduces two novel Outlyingness Scores (OOS and IOS) based on Cluster Catch Digraphs to improve interpretable outlier detection.
• Empirical evaluation shows the Inbound Outlyingness Score (IOS) is more robust than OOS and state-of-the-art methods, particularly in high-dimensional data and against the masking problem.
• These new scores, especially IOS, offer enhanced interpretability for high-dimensional data irregularities and have potential applications in fields like fraud detection and network security.

Outlyingness Scores with Cluster Catch Digraphs: A Critical Review

The paper under review presents two innovative methods for determining outlyingness scores (OSs) based on Cluster Catch Digraphs (CCDs): the Outbound Outlyingness Score (OOS) and the Inbound Outlyingness Score (IOS). This novel approach aims to improve interpretability in outlier detection across various scenarios involving high-dimensional datasets with different cluster configurations. The methods offer robust mechanisms for identifying outliers, addressing crucial areas such as global and local outlier detection while maintaining invariance to data collinearity and improvements over existing CCD-based techniques.

Methodological Insights

The work explores constructing OSs using combined graph-, density-, and distribution-based approaches. OOS measures the outlyingness by evaluating a point's vicinity density relative to its outbound neighbors, whereas IOS considers the cumulative influence received from inbound neighbors within a cluster. The paper articulates the strengths and weaknesses of both: OOS is less effective for collective outliers due to potential masking effects, while IOS is more robust against such challenges, accurately identifying outliers in most data settings evaluated.

Empirical Evaluation

The effectiveness of the proposed methods is corroborated through extensive Monte Carlo simulations and real-life data integration. The paper extensively elaborates on empirical setups covering diverse dimensionalities and datasets, highlighting competitive TPRs and TNRs for both OOSs and IOSs under varied conditions. Notably, the IOS particularly shines in high-dimensional settings and scenarios prone to the masking problem, outperforming both OOS and other state-of-the-art outlier detection methods.

Comparative Analysis

Both methods are compared against conventional CCD-based approaches and robust detection mechanisms such as LOF, DBSCAN, and iForest. The simulations reflect that while OOS methods suffer in the presence of dense collective outliers, IOS maintains high performance, tying or surpassing traditional methods regarding $F_2$-scores in many contexts. These outcomes suggest that IOS provides a substantial enhancement in realizing reliable and efficient outlier detection, especially as dimensionality escalates and data complexity increases.

Implications and Future Directions

The development of OOS and IOS has pivotal implications for the domain of outlier detection, particularly for high-dimensional data analysis. These scores afford a more nuanced interpretation of data irregularities that can be seamlessly integrated into existing data analysis frameworks. Additionally, the robustness of IOS against the masking effect suggests extensive applicability across fields where detecting subtle anomalies is paramount, such as fraud detection and network security.

Future research can explore the extension of these methods to dynamic datasets and further refine their scalability. Moreover, integrating these methodologies into machine learning pipelines where preprocessing and interpretability of anomalous data are crucial can open new vistas of interdisciplinary applications. Fine-tuning these models through additional parameter adaptations and accelerating their operational efficiency are promising avenues for subsequent exploration.

In conclusion, this paper significantly contributes to the outlier detection domain, presenting methods that not only enhance interpretability but also address prevalent limitations in existing approaches. The detailed exploration and comprehensive evaluations underscore their potential utility across diverse application areas, marking a noteworthy step forward in high-dimensional data analytics.