# Adversarial Subspace Generation for Outlier Detection in High-Dimensional Data

arXiv: https://arxiv.org/abs/2504.07522 · HTML: https://mlsanity.com/paper/2504.07522/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 62 references that are in the map.
- First posted on arXiv 10 Apr 2025.

## Builds on (most cited first, 19 of 19)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Generative Moment Matching Networks](https://mlsanity.com/paper/1502.02761/) (2015)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [ADBench: Anomaly Detection Benchmark](https://mlsanity.com/paper/2206.09426/) (2022)
- [ECOD: Unsupervised Outlier Detection Using Empirical Cumulative Distribution Functions](https://mlsanity.com/paper/2201.00382/) (2022)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Maximum Mean Discrepancy Gradient Flow](https://mlsanity.com/paper/1906.04370/) (2019)
- [Chaos is a Ladder: A New Theoretical Understanding of Contrastive Learning via Augmentation Overlap](https://mlsanity.com/paper/2203.13457/) (2022)
- [Deep Isolation Forest for Anomaly Detection](https://mlsanity.com/paper/2206.06602/) (2022)
- [Concrete Autoencoders for Differentiable Feature Selection and Reconstruction](https://mlsanity.com/paper/1901.09346/) (2019)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [Revisiting Contrastive Methods for Unsupervised Learning of Visual Representations](https://mlsanity.com/paper/2106.05967/) (2021)
- [One-Class Classification: A Survey](https://mlsanity.com/paper/2101.03064/) (2021)
- [On the Convergence of Gradient Descent in GANs: MMD GAN As a Gradient Flow](https://mlsanity.com/paper/2011.02402/) (2020)
- [Adversarial Examples Might be Avoidable: The Role of Data Concentration in Adversarial Robustness](https://mlsanity.com/paper/2309.16096/) (2023)
- [Subspace Clustering using Ensembles of K-Subspaces](https://mlsanity.com/paper/1709.04744/) (2017)
- [Generative Subspace Adversarial Active Learning for Outlier Detection in Multiple Views of High-dimensional Data](https://mlsanity.com/paper/2404.14451/) (2024)

## Built on by (most cited first, 2 of 2)

- [Minimax Lower Bounds of Kernel Discrepancy Estimation: MMD, HSIC, KSD](https://mlsanity.com/paper/2607.24235/) (2026)
- [Kernel-based External Validity of Experimental Studies](https://mlsanity.com/paper/2610.13625/) (2026)

## Abstract (arXiv)

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.