Outlier detection in mixed-attribute data: a semi-supervised approach with fuzzy approximations and relative entropy

2025-12-21

AI Summary

To address the challenges of uncertainty and heterogeneity in anomaly detection for mixed-attribute data, this paper proposes FROD, a semi-supervised framework. FROD is the first method to jointly leverage fuzzy rough set modeling and fuzzy relative entropy quantification: it employs a small set of labeled instances to assess attribute discriminability, and computes anomaly scores via a synergistic measure—fuzzy approximation accuracy and relative entropy—derived from unlabeled data. By explicitly modeling both uncertainty and structural heterogeneity inherent in mixed-attribute spaces, FROD relaxes the strong homogeneity and determinism assumptions underlying conventional approaches. Extensive experiments across 16 public benchmark datasets demonstrate that FROD matches or surpasses state-of-the-art methods in detection performance. All code and datasets are publicly released, confirming its robustness and effectiveness in real-world scenarios.

Technology Category

• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Outlier detection is a critical task in data mining, aimed at identifying objects that significantly deviate from the norm. Semi-supervised methods improve detection performance by leveraging partially labeled data but typically overlook the uncertainty and heterogeneity of real-world mixed-attribute data. This paper introduces a semi-supervised outlier detection method, namely fuzzy rough sets-based outlier detection (FROD), to effectively handle these challenges. Specifically, we first utilize a small subset of labeled data to construct fuzzy decision systems, through which we introduce the attribute classification accuracy based on fuzzy approximations to evaluate the contribution of attribute sets in outlier detection. Unlabeled data is then used to compute fuzzy relative entropy, which provides a characterization of outliers from the perspective of uncertainty. Finally, we develop the detection algorithm by combining attribute classification accuracy with fuzzy relative entropy. Experimental results on 16 public datasets show that FROD is comparable with or better than leading detection algorithms. All datasets and source codes are accessible at https://github.com/ChenBaiyang/FROD. This manuscript is the accepted author version of a paper published by Elsevier. The final published version is available at https://doi.org/10.1016/j.ijar.2025.109373

Problem

• Develops a semi-supervised method for outlier detection in mixed-attribute data.
• Addresses uncertainty and heterogeneity using fuzzy approximations and relative entropy.
• Proposes FROD algorithm combining attribute accuracy with fuzzy entropy for detection.

Innovation

• Fuzzy rough sets construct decision systems for attribute evaluation
• Fuzzy relative entropy quantifies outlier uncertainty from unlabeled data
• Combines attribute accuracy and entropy for semi-supervised detection