mahalanobis distance scoring

Existing anomaly detection methods in separable Banach spaces lack basis-independent, data-driven distance metrics. Method: We propose the Variance Norm—a generalization of the Mahalanobis distance—that relies solely on the inner product structure of a Hilbert space, without assuming a predefined coordinate system or invertibility of the covariance operator. Theoretically, we extend Cameron–Martin theory to non-Gaussian probability measures and rigorously establish the well-definedness of this norm in reproducing kernel Hilbert spaces (RKHS). Methodologically, we develop a kernelized nearest-neighbor Mahalanobis distance for semi-supervised time-series novelty detection. Results: Experiments on 12 real-world datasets demonstrate significant improvements over state-of-the-art baselines. We further prove statistical consistency of the Variance Norm in finite-dimensional Gaussian settings, confirming its theoretical soundness and practical efficacy.

This work addresses the challenge of out-of-distribution (OOD) detection under heterogeneous inter-class covariance structures and extreme per-class sample scarcity. We propose a novel Bayesian nonparametric modeling paradigm tailored to this setting. First, we theoretically reveal the Bayesian nonparametric nature of the relative Mahalanobis distance (RMDS). Building upon this insight, we develop a hierarchical Dirichlet process-based nonparametric mixture model that adaptively captures inter-class covariance heterogeneity and enables principled generalization of RMDS. Evaluated on the OpenOOD benchmark, our method significantly outperforms existing OOD detectors—particularly under strong covariance heterogeneity and ultra-sparse regimes (e.g., <10 samples per class). These results demonstrate superior robustness and generalization in small-sample, structurally complex OOD scenarios.

To address the challenge of reliable collision and mechanical fault detection in autonomous robots under visual/LiDAR failure scenarios, this paper proposes an unsupervised multimodal anomaly detection method leveraging audio and IMU signals. The method introduces two key innovations: (1) the first integration of Mahalanobis distance into the Support Vector Data Description (SVDD) framework to adaptively model feature covariance structure; and (2) a reconstruction-auxiliary branch that mitigates representation collapse and enhances discriminative capability for anomaly boundaries—particularly under limited training samples. Evaluated on a custom robot dataset and four public benchmarks, the approach achieves a 7.2% average improvement in detection accuracy over state-of-the-art unsupervised methods. It further demonstrates strong robustness against noise, occlusion, and dynamic operational conditions.

This work addresses the challenge of industrial anomaly detection under contaminated training data—where normal samples are inadvertently mixed with anomalies—a scenario that undermines the performance of existing methods relying on either purely clean or entirely unlabeled data. To tackle this, we propose a robust anomaly detection framework that leverages a small number of annotated anomalous samples under contamination. Our approach introduces adaptive bias learning and a tripartite anomaly scoring mechanism that integrates statistical deviation, entropy-based uncertainty, and segmentation-space anomaly cues to enable accurate detection and interpretable localization. Coupled with gradient-guided localization and adaptive instance weighting, the method achieves state-of-the-art performance on the MVTec and VisA benchmarks, demonstrating consistently high detection accuracy, precise localization, and strong robustness across varying contamination levels.

Existing one-class anomaly detection methods suffer from poor generalization due to geometric bias in benchmark datasets, while prevailing pseudo-anomaly generation techniques fail to faithfully model the intrinsic structure of normal data and over-rely on image-domain operations. Method: This paper proposes a novel paradigm that synthesizes pseudo-anomalies exclusively within a frozen pre-trained feature space—bypassing image-level augmentation entirely. Contribution/Results: Key innovations include (1) an adaptive linear feature perturbation mechanism that dynamically tailors noise distribution per sample, and (2) a contrastive learning objective explicitly decoupling geometric bias from semantic anomaly modeling. Evaluated on both standard and geometric-bias-mitigated benchmarks, our method consistently outperforms state-of-the-art approaches, demonstrating superior generalization and robustness. The implementation is publicly available.

Under label shift, existing methods for multiclass classification and anomaly detection suffer from high resampling overhead, unstable coverage for minority classes, and overly conservative prediction sets. To address these issues, we propose MMDCP—a distribution-agnostic framework jointly performing classification and anomaly detection. Its core contributions are threefold: (1) a class-specific Mahalanobis-distance-based scoring function that eliminates the need for data splitting or resampling; (2) the first theoretical characterization of the deviation between empirical and ideal conformal p-values, leading to a cross-class global error metric—SCW-FDR; and (3) rigorous finite-sample guarantees on coverage validity and CW-FDR control under heterogeneous distributions, along with convergence rate analysis of prediction sets. Experiments on synthetic and real-world datasets demonstrate that MMDCP significantly reduces conservativeness, stably controls both coverage probability and SCW-FDR, and improves detection power and computational efficiency.

This work addresses the lack of dedicated Python tools for Invariant Coordinate Selection (ICS) in the current machine learning ecosystem, which has hindered its adoption in tasks such as clustering and anomaly detection. We propose a dimensionality reduction method based on the joint diagonalization of two scatter matrices, effectively extracting features by optimizing directions corresponding to extremal generalized kurtosis. To enhance accessibility and reproducibility, we introduce ICSpyLab—the first open-source implementation of ICS under the MIT license—featuring support for multiple scatter matrix types, joint diagonalization algorithms, and component selection criteria. The library strictly adheres to the scikit-learn estimator interface and is accompanied by comprehensive documentation and reproducible examples, significantly improving the usability and extensibility of ICS methods.

This work addresses the severe distortion of conventional mean and covariance estimates caused by outliers in interval-valued data. To this end, it introduces the first extension of the Minimum Covariance Determinant (MCD) estimator to the interval-valued setting, integrating robust location and scale estimates based on the Mallows distance to construct a robust interval Mahalanobis distance. An adaptive thresholding mechanism is further incorporated to enable effective outlier detection. The proposed method demonstrates superior performance over classical approaches across varying contamination levels, achieving notably higher accuracy in both covariance estimation and outlier identification. Its efficacy is validated through experiments on real-world datasets, confirming its practical applicability and robustness.

Existing anomaly detection methods typically assume that normal data occupy a non-zero volume in the ambient space, overlooking their intrinsic geometric structure as lying on a low-dimensional manifold, which limits performance. This work proposes a novel manifold projection paradigm: learning a projection operator that maps inputs onto the manifold of normal samples and using the projection residual as the anomaly criterion. By avoiding explicit modeling of the degenerate data distribution, the approach prevents misclassifying rare yet normal instances and provides a unified explanation for both the effectiveness and failure modes of reconstruction-based methods. Extensive experiments demonstrate that the proposed framework significantly outperforms conventional boundary-learning approaches and achieves state-of-the-art results across multiple benchmarks compared to existing reconstruction-based models.

This study addresses the challenges of detecting distribution drift in high-dimensional data streams, which are often hindered by excessive computational costs, loss of geometric structure, and unstable cluster identities. The authors propose a framework that tracks local statistics based on a fixed Voronoi tessellation and introduces a rotation- and reflection-invariant drift metric to enable robust detection under coordinate transformations while preserving the intrinsic geometry of high-dimensional manifolds. By modeling drift propagation through graph-theoretic constructs, incorporating an O(N) efficient update mechanism, and leveraging product quantization for scalability to ultra-high-dimensional settings, the method significantly reduces computational overhead and false positives. Experimental results demonstrate its effectiveness in lowering computational burden, minimizing spurious alerts, and providing spatial localization of drift occurrences.