Tighten The Lasso: A Convex Hull Volume-based Anomaly Detection Method

The rapid advancements in data-driven methodologies have underscored the critical importance of ensuring data quality. Consequently, detecting out-of-distribution (OOD) data has emerged as an essential task to maintain the reliability and robustness of data-driven models, in general, and machine and deep learning models, in particular. In this study, we leveraged the convex hull property of a dataset and the fact that anomalies highly contribute to the increase of the CH's volume to propose a novel anomaly detection algorithm. Our algorithm computes the CH's volume as an increasing number of data points are removed from the dataset to define a decision line between OOD and in-distribution data points. We compared the proposed algorithm to seven widely used anomaly detection algorithms over ten datasets, showing comparable results for state-of-the-art (SOTA) algorithms. Moreover, we show that with a computationally cheap and simple check, one can detect datasets that are well-suited for the proposed algorithm which outperforms the SOTA anomaly detection algorithms.

@article{itai2025_2502.18601,
  title={ Tighten The Lasso: A Convex Hull Volume-based Anomaly Detection Method },
  author={ Uri Itai and Asael Bar Ilan and Teddy Lazebnik },
  journal={arXiv preprint arXiv:2502.18601},
  year={ 2025 }
}