Interpretable Maximum Margin Deep Anomaly Detection

Zhiji Yang; Mei Huang; Xinyu Li; Xianli Pan; Qi Wang; Jianhua Zhao

cs.LGMar 7, 2026

Interpretable Maximum Margin Deep Anomaly Detection

Authors: Zhiji Yang, Mei Huang, Xinyu Li, Xianli Pan, Qi Wang, Jianhua Zhao

Organizations: the School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221, China · the Academy for Multidisciplinary Studies, Capital Normal University, Beijing 100048, China

Abstract

Anomaly detection is a crucial machine-learning task with wide-ranging applications. Deep Support Vector Data Description (Deep SVDD) is a prominent deep one-class method, but it is vulnerable to hypersphere collapse, often relies on heuristic choices for hypersphere parameters, and provides limited interpretability. To address these issues, we propose Interpretable Maximum Margin Deep Anomaly Detection (IMD-AD), which leverages a small set of labeled anomalies and a maximum margin objective to stabilize training and improve discrimination. It is inherently resilient to hypersphere collapse. Furthermore, we prove an equivalence between hypersphere parameters and the network's final-layer weights, which allows the center and radius to be learned end-to-end as part of the model and yields intrinsic interpretability and visualizable outputs. We further develop an efficient training algorithm that jointly optimizes representation, margin, and final-layer parameters. Extensive experiments and ablation studies on image and tabular benchmarks demonstrate that IMD-AD empirically improves detection performance over several state-of-the-art baselines while providing interpretable decision diagnostics.

Figures & tables

Panel of Figure 1 — Fig. 1: Training framework of Deep SVDD and IMD-AD, respectively. Green points represent normal samples, and red points represent abnormal samples. $R$ and $\mathbf{c}$ represent the radius and center of the hypersphere, respectively. $\rho$ represents the margin between abnormal samples and the surface of the hypersphere.

Datasets	#Classes	Sample size	Dimensions	Hidden layers
MNINST	10	60000 (train) + 10000 (test)	28*28	CNN $\times$ 2+FC $\times$ 3
Fashion MNIST	10	60000 (train) + 10000 (test)	28*28	CNN $\times$ 2+FC $\times$ 3
CIFAR-10	10	50000 (train) + 10000 (test)	32*32	CNN $\times$ 3+FC $\times$ 3
ON	4	1060	21	FC $\times$ 3
Card	10	2126	21	FC $\times$ 3
BC	2	569	30	FC $\times$ 3

TABLE I: Overview of Datasets and Corresponding Network Architecture.

	Methods
MNIST	IF	KDE	OCSVM	SVDD	SSLM	AE	Deep SVDD	DROCC	IMD-AD
0	90.33	96.28	99.01	90.39	93.88	97.47	98.00	100.00	99.86
1	97.46	92.54	99.56	98.34	98.61	96.93	99.70	99.96	99.93
2	78.96	85.56	95.78	53.33	85.49	80.06	91.70	100.00	99.66
3	82.12	87.17	93.96	72.44	83.67	86.94	91.90	100.00	99.66
4	80.35	82.34	95.79	84.50	89.04	83.73	94.90	100.00	99.90

TABLE II: AUC (%) OF NINE METHOD ON THREE IMAGE DATASETS.

Datasets	Class	IF	KDE	OCSVM	SVDD	SSLM	AE	Deep SVDD	DROCC	IMD-AD
	NB-No Block	79.89 $\pm$ 3.21	79.09 $\pm$ 3.36	71.82 $\pm$ 2.36	57.39 $\pm$ 3.00	81.81 $\pm$ 2.24	79.40 $\pm$ 1.94	51.26 $\pm$ 7.49	74.83 $\pm$ 0.75	88.86 $\pm$ 5.35
	Block	88.90 $\pm$ 4.55	95.79 $\pm$ 0.89	93.49 $\pm$ 1.46	92.11 $\pm$ 1.23	99.43 $\pm$ 0.33	80.46 $\pm$ 1.71	76.12 $\pm$ 14.06	86.76 $\pm$ 0.69	99.45 $\pm$ 0.53
ON	No Block	92.90 $\pm$ 4.42	97.86 $\pm$ 0.59	96.73 $\pm$ 3.59	95.65 $\pm$ 1.83	99.96 $\pm$ 0.05	86.74 $\pm$ 4.46	84.14 $\pm$ 7.96	97.97 $\pm$ 1.64	99.92 $\pm$ 0.15
	NB-Wait	80.62 $\pm$ 3.48	84.90 $\pm$ 3.64	83.23 $\pm$ 3.99	55.40 $\pm$ 3.59	76.77 $\pm$ 5.73	83.75 $\pm$ 2.13	56.56 $\pm$ 10.99	82.36 $\pm$ 0.47	89.00 $\pm$ 2.93
	avg.	85.58 $\pm$ 6.37	89.41 $\pm$ 8.92	86.32 $\pm$ 11.25	75.14 $\pm$ 21.71	89.49 $\pm$ 11.96	82.59 $\pm$ 3.33	67.02 $\pm$ 15.64	85.48 $\pm$ 0.89	94.31 $\pm$ 6.21
	Rank	5	3	4	8	2	7	9	6	1

TABLE III: Average AUC (%) with StdDevs (5 Seeds) per Method on Three Tabular Datasets.

Dataset Type	IF	KDE	OCSVM	SVDD	SSLM	AE	Deep SVDD	DROCC
Image Datasets	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0010
Tabular Datasets	0.0001	0.0001	0.0001	0.0001	0.0237	0.0001	0.0001	0.0003
All Datasets	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000

TABLE IV:

p

-values of the Friedman test with post-hoc Wilcoxon signed-rank test for comparisons versus IMD-AD across different dataset types.

Panel of Figure 6 — Fig. 2: Critical Difference diagrams from Friedman test with Nemenyi posthoc test ( $\alpha=0.05$ ).

Fig. 3: The visualization of IMD-AD on Spiral and Moon Datasets. (a) (c) (e) (g) display the scatter plots on original data. (b) (d) (f) (h) show the extracted samples and the corresponding detection boundaries of IMD-AD.

Fig. 4: Performance curves of IMD-AD with epochs on Spiral and Moon datasets.

Fig. 5: Model classification results on MNIST with normal class 0 over training epochs.

Fig. 6: MNIST heatmap visualization comparing normal and abnormal samples for class 0.

Fig. 7: Ratio of outliers with the change of the hyperparameters on the MNIST dataset. The horizontal axis represents the theoretical upper bound determined by the model hyperparameters— $(\nu+1)\nu_{1}$ for normal data and $\nu\nu_{2}$ for abnormal data, while the vertical axis reports the empirical outlier ratio under the same settings. In each subfigure, the solid red line depicts the continuous theoretical limit. Red “ $\times$ ” markers denote discrete values of that limit. Blue “ $\cdot$ ” represent experimental observations.

Fig. 8: The density of squared distance between training samples and the hypersphere center $\mathbf{c}$ in representation space of MNINST dataset. Subfigure (a) shows the distributions at 1st epoch, while subfigure (b) corresponds to the converged distributions at 100th epoch.

Fig. 9: AUC of ablation experiments on the CIFAR-10 dataset.

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Deep Convolutional Large-Margin $\ell_p$ -SVDD for Visual Anomaly Detection

Alireza Dastmalchi Saei, Shervin Rahimzadeh Arashloo

Department of Computer Engineering, Bilkent University, 06800 Ankara, Türkiye

Kernel Methods One-Class Classification

Open paper AskPDF arXiv

Visual anomaly detection requires adaptive representations and reliable decision boundaries, particularly when anomalous training samples are scarce and class distributions are highly imbalanced. Classical kernel-based methods yield principled geometric decision regions but typically operate on fixed features, while deep detectors learn task-specific representations but often fail to provide an explicit margin-aware kernel boundary. In this study, we propose DLM-SVDD, a deep large-margin novelty-detection framework that jointly learns convolutional features and an explicit kernel-based decision boundary. By drawing on the large-margin

\ell_p

-Support Vector Data Description (

\ell_p

-SVDD) approach, the proposed method performs explicit margin maximization and nonlinear slack penalization while adapting the representation to the target task. To train the proposed model, we present an optimization scheme that alternates between a Frank--Wolfe--based update of the convex dual boundary and a CNN update step operating on a smooth margin-violation loss induced by the recovered boundary. To improve scalability, we analyze the efficiency--accuracy trade-offs for different kernel approximation strategies, deriving practical propositions for large-scale anomaly detection. Extensive experiments on multiple standard benchmarks show consistent performance improvements over the baseline and strong overall performance compared with state-of-the-art methods while illustrating that the proposed joint representation--boundary learning scheme remains effective under severe imbalanced class distributions.

Abstract

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