Anomaly Detection via Autoencoder Composite Features and NCE

Yalin Liao; Austin J. Brockmeier

cs.LGFeb 4, 2025

Anomaly Detection via Autoencoder Composite Features and NCE

Authors: Yalin Liao, Austin J. Brockmeier

Organizations: Department of Electrical and Computer Engineering, University of Delaware, Newark, Delaware · Department of Electrical and Computer Engineering, Department of Computer and Information Sciences, University of Delaware, Newark, Delaware

Abstract

Unsupervised anomaly detection is a challenging task. Autoencoders (AEs) or generative models are often employed to model the data distribution of normal inputs and subsequently identify anomalous, out-of-distribution inputs by high reconstruction error or low likelihood, respectively. However, AEs may generalize and achieve small reconstruction errors on abnormal inputs. We propose a decoupled training approach for anomaly detection that both an AE and a likelihood model trained with noise contrastive estimation (NCE). After training the AE, NCE estimates a probability density function, to serve as the anomaly score, on the joint space of the AE's latent representation combined with features of the reconstruction quality. To further reduce the false negative rate in NCE we systematically varying the reconstruction features to augment the training and optimize the contrastive Gaussian noise distribution. Experimental assessments on multiple benchmark datasets demonstrate that the proposed approach matches the performance of prevalent state-of-the-art anomaly detection algorithms.

Figures & tables

Figure 1: Illustration of Proposition 1 with normal observations

Y=(Y_{1},Y_{2})^{T}

, where

Y_{i}=X+\epsilon_{i},X\sim U([0,1])

, and

\epsilon_{i}\sim\mathcal{N}(0,0.08^{2})

. Anomalies are generated by perturbing

Y

0.7v_{r}

along the residual direction

v_{r}=(-1,1)^{T}/\sqrt{2}

. The panels show the observations, latent representations, and reconstruction errors.

Data	Error	LatNCE	CNCE	CANCE
Unimodal
MNIST	$95.1$	$84.1$	$97.0$	$97.7$
F-MNIST	$90.4$	$89.6$	$92.2$	$92.5$
CIFAR-10	$54.1$	$65.1$	$65.3$	$65.4$
Multimodal
MNIST	$94.6$	$87.6$	$97.3$	$97.6$

Table 1: AUROC for CANCE ablations

Method	Mean AUROC (%)	Best Count
DAGMM	65.05	1
DSVDD	67.89	0
DROCC	60.30	0
GOAD	68.82	3
DDPM	77.92	3
DTE-NP	81.59	19

Table 2: Performance comparison across 57 datasets in terms of average AUROC and best count. The best count indicates the number of datasets on which each method achieves the highest AUROC.

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

Hyperparameter	MNIST	F-MNIST	CIFAR-10	MNIST-C
AE
Input channels	1	1	3	1
Hidden channels	8	8	32	8
Latent dimension	6	6	64	10
Activation	GELU	GELU	GELU	GELU
Learning rate	$10^{-4}$	$10^{-4}$	$10^{-4}$	$10^{-4}$

Appendix

Table 3: Training configurations for the ablation experiments.

Data	Error	LatNCE	CNCE	CANCE
MNIST
$0$	$99.4(0.1)$	$85.0(3.5)$	$99.5(0.0)$	$99.6(0.0)$
$1$	$99.9(0.0)$	$98.4(0.3)$	$99.8(0.0)$	$99.8(0.0)$
$2$	$90.3(1.5)$	$81.9(6.5)$	$96.6(0.7)$	$97.1(0.5)$
$3$	$92.6(0.6)$	$81.2(1.2)$	$95.6(0.4)$	$96.7(0.3)$
$4$	$95.5(1.3)$	$75.0(3.8)$	$95.8(0.3)$	$96.9(0.4)$

Appendix

Table 4: Ablation study on unimodal training dataset

Data	Error	LatNCE	CNCE	CANCE
MNIST
$0,1$	$99.4(0.1)$	$93.8(1.1)$	$99.5(0.1)$	$99.6(0.1)$
$0,8$	$87.8(0.7)$	$79.8(1.3)$	$95.0(0.5)$	$95.5(0.4)$
$1,8$	$96.7(0.7)$	$89.3(2.3)$	$97.4(0.3)$	$97.8(0.2)$
Avg	$94.6$	$87.6$	$97.3$	$97.6$
F-MNIST

Appendix

Table 5: Ablation study on the multimodal datasets

Data	Error	LatNCE	CNCE	CANCE
MNIST, ResNet-18\|ResNet-50
0	$98.1\mid 96.3$	$78.4(0.9)\mid 75.2(0.4)$	$96.7(0.6)\mid 95.8(0.4)$	$98.6(0.0)\mid 97.4(0.1)$
1	$99.8\mid 98.6$	$98.6(0.1)\mid 95.9(0.6)$	$99.6(0.0)\mid 98.5(0.1)$	$99.7(0.0)\mid 98.5(0.1)$
2	$88.3\mid 76.6$	$74.4(0.7)\mid 66.1(0.8)$	$83.8(1.4)\mid 80.2(1.0)$	$91.0(0.1)\mid 83.9(0.2)$
3	$95.1\mid 95.9$	$74.1(0.5)\mid 90.7(0.1)$	$92.5(0.3)\mid 94.8(0.1)$	$94.7(0.2)\mid 95.5(0.1)$
4	$97.3\mid 95.2$	$84.4(0.5)\mid 81.7(0.8)$	$96.3(0.3)\mid 94.1(0.1)$	$97.3(0.2)\mid 95.2(0.2)$

Appendix

Table 6: Ablation study on features extracted by ResNet on MNIST, F-MNIST, and CIFAR-10

	DAGMM	DSVDD	DROCC	GOAD	DDPM	DTE-NP	DTE-IG	DTE-C	CANCE
aloi	50.84(2.97)	50.89(2.05)	50.0(0.0)	48.01(0.92)	49.91(0.35)	51.19(0.46)	50.87(1.17)	50.44(0.19)	52.33(0.97)
amazon	50.47(2.01)	51.2(4.42)	50.0(0.0)	56.07(0.9)	55.09(0.1)	60.82(0.0)	51.93(3.5)	56.71(2.15)	61.49(0.79)
annthy- roid	72.23(15.13)	55.01(3.62)	88.9(2.31)	81.01(5.16)	88.82(1.34)	92.9(0.25)	87.6(4.46)	97.52(0.15)	88.19(1.58)
backdoor	54.36(19.91)	91.14(2.62)	94.25(0.73)	52.9(14.48)	80.93(0.56)	99.31(1.7)	94.02(1.46)	91.65(1.73)	91.85(0.63)
breastw	89.53(10.2)	96.96(0.92)	47.32(31.95)	98.86(0.33)	98.7(0.43)	99.28(0.12)	78.65(11.1)	92.78(1.75)	99.52(0.09)
campaign	61.47(2.73)	62.21(12.88)	50.0(0.0)	47.89(12.32)	74.51(0.42)	78.79(0.25)	74.81(1.69)	68.84(6.50)	68.84(6.50)

Appendix

Table 7: Average AUROC and standard deviations on ADBench dataset.

Data	KDE	VAE	PC	LSA	DAGMM	CANCE
MNIST
$0$	$88.5$	$99.8$	$53.1$	$99.3$	$53.6$	$99.6(0.0)$
$1$	$99.6$	$99.9$	$99.5$	$99.9$	$51.5$	$99.8(0.0)$
$2$	$71.0$	$96.2$	$47.6$	$95.9$	$53.5$	$97.1(0.5)$
$3$	$69.3$	$94.7$	$51.7$	$96.6$	$49.7$	$96.7(0.3)$
$4$	$84.4$	$96.5$	$73.9$	$95.6$	$52.7$	$96.9(0.4)$

Appendix

Table 8: AUCROC [%] for baseline methods, Pix-CNN (PC) and DAGMM, compared to CANCE mean and std. value across

5

independent runs.

Method	Precision	Recall	$F_{1}$
DAGMM-0	$93.0$	$94.4$	$93.7$
DAGMM-1	$97.7(0.3)$	$96.9(0.6)$	$97.3(0.5)$
DAGMM-CANCE	$97.6(0.3)$	$96.9(0.6)$	$97.3(0.5)$

Appendix

Table 9: AD results on contaminated training data from KDDCUP99

Data	DAGMM	DSVDD	NN	DROCC	DPAD	CANCE	CANCE18	CANCE50
F-MNIST
0	$42.1$	$79.1$	$91.2\mid 100$	$88.1$	$93.7(0.2)$	$90.6(0.4)$	$89.7(0.3)$	$91.3(0.3)$
1	$55.1$	$94.0$	$98.6\mid 100$	$97.7$	$98.7(0.0)$	$98.4(0.1)$	$98.5(0.1)$	$98.7(0.0)$
2	$50.4$	$83.0$	$88.5\mid 100$	$87.6$	$90.3(0.0)$	$89.0(0.4)$	$91.0(0.2)$	$92.6(0.1)$
3	$57.0$	$82.9$	$93.6\mid 100$	$87.7$	$94.7(0.3)$	$91.8(0.6)$	$85.7(0.2)$	$90.1(0.5)$
4	$26.9$	$87.0$	$89.4\mid 100$	$87.2$	$92.2(0.1)$	$90.7(0.2)$	$92.3(0.2)$	$91.7(0.1)$

Appendix

Table 10: AUROC[%] CANCE vs DPAD on F-MNIST and CIFAR-10. NN (nearest neighbor, use raw | ResNet-18 feature), CANCE (AE), CANCE18 (ResNet-18), CANCE50 (ResNet-50)

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