Adversarial Subspace Generation for Outlier Detection in High-Dimensional Data

2025-04-10

AI Summary

Anomaly detection in high-dimensional tabular data is challenged by multi-view effects, where heterogeneous feature subsets exhibit distinct statistical behaviors. Existing methods lack a formal theoretical foundation for characterizing such multi-view structure and rely on heuristic subspace search. Method: This paper introduces Myopic Subspace Theory—a novel theoretical framework that formally defines multi-view structure and formulates subspace discovery as a differentiable, end-to-end stochastic optimization problem. Building upon it, we propose V-GAN, a generative method that directly learns discriminative low-dimensional subspaces while preserving structural fidelity and statistical consistency; we further design a subspace-driven one-class classification ensemble. Results: Evaluated on 42 real-world datasets, our approach achieves significant improvements in anomaly detection performance. Synthetic experiments demonstrate superior subspace identification accuracy and scalability compared to state-of-the-art subspace selection, feature selection, and embedding methods.

Technology Category

• Machine Learning: Multi-instance/Multi-view Learning
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Computer Vision: Generative Adversarial Networks (GANs) for Vision

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets

Abstract

Outlier detection in high-dimensional tabular data is challenging since data is often distributed across multiple lower-dimensional subspaces -- a phenomenon known as the Multiple Views effect (MV). This effect led to a large body of research focused on mining such subspaces, known as subspace selection. However, as the precise nature of the MV effect was not well understood, traditional methods had to rely on heuristic-driven search schemes that struggle to accurately capture the true structure of the data. Properly identifying these subspaces is critical for unsupervised tasks such as outlier detection or clustering, where misrepresenting the underlying data structure can hinder the performance. We introduce Myopic Subspace Theory (MST), a new theoretical framework that mathematically formulates the Multiple Views effect and writes subspace selection as a stochastic optimization problem. Based on MST, we introduce V-GAN, a generative method trained to solve such an optimization problem. This approach avoids any exhaustive search over the feature space while ensuring that the intrinsic data structure is preserved. Experiments on 42 real-world datasets show that using V-GAN subspaces to build ensemble methods leads to a significant increase in one-class classification performance -- compared to existing subspace selection, feature selection, and embedding methods. Further experiments on synthetic data show that V-GAN identifies subspaces more accurately while scaling better than other relevant subspace selection methods. These results confirm the theoretical guarantees of our approach and also highlight its practical viability in high-dimensional settings.

Problem

• Challenges in outlier detection due to high-dimensional data subspaces
• Heuristic-driven subspace selection struggles to capture true data structure
• Proposes Myopic Subspace Theory and V-GAN for accurate subspace identification

Innovation

• Introduces Myopic Subspace Theory (MST) framework
• Proposes V-GAN for stochastic optimization problem
• Avoids exhaustive search, preserves data structure