Overview Anomaly Detection

Anomaly Detection

Anomaly Detection论文及模型总结

Posted by JY on May 5, 2020

Anomaly Detection

Model

Paper

Model

异常检测思想：

在仅有负样本（正常数据）或者少量正样本的情况下：

训练阶段：网络仅仅通过负样本（正常样本）的数据分布，得到能够生成或重建正常数据的模型

测试阶段：使用测试样本输入训练好的模型，如果经过模型生成或重建后输出和输入一样或者接近，表明测试的是正常数据，否则是异常数据

异常检测模型：

Autoencoder-based

VAE-based

Adversarial Model-based (GAN, AAE)

Anogan

Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery (2017)

AnoGAN运用DCGAN学习normal data的latent space，并假设这个latent space无法重构出anomaly，重构误差高的地方被检测为anomaly

img

异常分数：

$A(\mathbf{x})=(1-\lambda) \cdot R(\mathbf{x})+\lambda \cdot D(\mathbf{x})$

f-Anogan

f-AnoGAN: Fast unsupervised anomaly detection with generative adversarial networks (2019)

Anogan的完善（会议->期刊）

img 三种训练方式：

  • ziz：$\left.L_{z i z}(z)=\frac{1}{d} | z-\hat{z}\right) |^{2}$

  • izi：$L_{i z i}(x)=\frac{1}{n}|x-G(\hat{z})|^{2}$

  • izif：$L_{i z i f}(x)=\frac{1}{n}|x-G(\hat{z})|^{2}+\lambda \frac{1}{n_{d}}|f(x)-f(G(\hat{z}))|^{2}$

对比的baseline：

img

EGBAD

Efficient GAN-Based Anomaly Detection (2018-02)

基于Bigan模型

训练时生成器将潜在表示z映射到$\hat x$，编码器E将输入样本x映射到潜在表示$\hat z$，判别器不仅考虑实际和生成图像的差异，还考虑了潜在表示的差异

img

异常分数：$A(x)=\alpha L_{G}(x)+(1-\alpha) L_{D}(x)$

  • 生成器：$L_{G}(x)=|x-G(E(x))|_{1}$

  • 判别器：$L_D(x)=\sigma(D(x, E(x)), 1)$ or $L_D(x)=\left|f_{D}(x, E(x))-f_{D}(G(E(x)), E(x))\right|_{1}$

测试时不需要将 x编码成 z这一步耗时的部分

ALOCC

Adversarially Learned One-Class Classifier for Novelty Detection (2018-05)

模型由R和D两个网络组成，其中R部分包括了一个自动编码和自动译码器，而D部分则是一个CNN网络，用于对经过R重新生成的数据进行一分类，从而实现异常检测

img

损失函数：

\[\mathcal{L}=\mathcal{L}_{\mathcal{R}+\mathcal{D}}+\lambda \mathcal{L}_{\mathcal{R}}\]
  • 生成对抗损失
\[L _{R+D}=\min _{ R } \max _{ D }\left( E _{X \sim p_{t}}[\log ( D (X))]++ E _{\tilde{X} \sim p_{t}+ N _{\sigma}}[\log (1- D ( R (\tilde{X})))]\right)\]
  • 增强原始数据，抑制异常数据
\[L _{ R }=\left\|X-X^{\prime}\right\|^{2}\]

测试阶段：

\[\operatorname{OCC}(X)=\left\{\begin{array}{ll} \text { Target Class } & \text { if } D ( R (X))>\tau \\ \text { Novelty (Outlier) } & \text { otherwise } \end{array}\right.\]

AAE

Unsupervised Detection of Lesions in Brain MRI using constrained adversarial auto-encoders (2018-06)

用AAE来学习建模正常数据分布

img

  • 对于在正常分布的的两个数据之间的距离，有时比一个正常和一个异常之间的距离还大，所以提出在隐空间也加一个约束

  • 通过潜在约束，以确保正常样本在潜在空间的一致性，能够更准确地检测异常区域

实验：

img

VAE

Anomaly Detection for Skin Disease Images Using Variational Autoencoder (2018-07)

img

异常分数：

\[\begin{equation} \text { Anomaly score }=s_{i w a e}^{k l}(x)+s_{i w a e}^{r e c o n s t}(x) \end{equation}\]
  • 包括隐空间分布损失和重构损失：
\[\begin{aligned} &s_{i w a e}^{k l}(x)=-\log \left(\frac{1}{L} \sum_{i=1}^{L} \frac{p\left(z_{i}\right)}{q\left(z_{i} | x\right)}\right)\\ &s_{i w a e}^{r e c o n s t}(x)=-\log \left(\frac{1}{L} \sum_{i=1}^{L} p\left(x | z_{i}\right)\right) \end{aligned}\]

ganomaly

Ganomaly: Semi-supervised anomaly detection via adversarial training (2018-11)

img

损失函数：

\[\mathcal{L}=w_{adv}\mathcal{L}_{adv}+w_{con}\mathcal{L}_{con}+w_{enc} \mathcal{L}_{enc}\]

异常分数：$\mathcal{A}(\hat{x})=\left|G_{E}(\hat{x})-E(G(\hat{x}))\right|_{1}$

ALAD

Adversarially Learned Anomaly Detection (2018-12)

Efficient GAN的升级版

img

训练过程：

img

异常分数：$A(x)=\left|f_{x x}(x, x)-f_{x x}(x, G(E(x)))\right|_{1}$

Skip-GANomaly

Skip-ganomaly: Skip connected and adversarially trained encoder-decoder anomaly detection (2019-01)

img img

损失函数：

\[\mathcal{L}=\lambda_{a d v} \mathcal{L}_{a d v}+\lambda_{c o n} \mathcal{L}_{c o n}+\lambda_{l a t} \mathcal{L}_{l a t}\]

异常分数：

\[\mathcal{A}(\dot{x})=\lambda R(\dot{x})+(1-\lambda) L(\dot{x})\]

ADAE

Anomaly Detection with Adversarial Dual Autoencoders (2019-02)

img

训练过程：

  • 重建实际输入，但不重建生成输入
\[{L}_{D}=\|X-D(X)\|_{1}-\|G(X)-D(G(X))\|_{1}\]
  • 生成器除了重建实际输入之外，还重建生成的数据
\[{L}_{G}=\|X-G(X)\|_{1}+\|G(X)-D(G(X))\|_{1}\]

测试过程：

  • 异常分数：${A}(\hat{x})=|\hat{x}-{D}({G}(\hat{x}))|_{2}$

img

RSRAE

$\begin{equation} x \stackrel{\mathscr{E}}{\longrightarrow} Z \stackrel{ A }{\longrightarrow} \tilde{ Z } \stackrel{\mathscr{D}}{\longrightarrow} \tilde{ X } \end{equation}$，引入RSR layer，将隐编码嵌入到\(R ^{D}\)空间

损失函数：

\[\begin{equation} L_{ AE }^{p}(\mathscr{E}, A , \mathscr{D})=\sum_{t=1}^{N}\left\| x ^{(t)}-\tilde{ x }^{(t)}\right\|_{2}^{p} \end{equation}\] \[L_{ RSR }^{q}( A )=L_{ RSR _{1}}( A )+L_{ RSR _{2}}( A )=\lambda_{1} \sum_{t=1}^{N}\| z ^{(t)}- A ^{ T } \underbrace{ A z ^{(t)}}_{ Z ^{(t)}}\|_{2}^{q}+\lambda_{2}\left\| A A ^{ T }- I _{d}\right\|_{ F }\]

$P$为恢复子空间上的正交投影（$\begin{equation} x^{(t)} \stackrel{\mathscr{E}}{\longrightarrow} \tilde{ x }^{(t)} \end{equation}$）

$q$为$\begin{equation} L( P )=\sum_{t=1}^{N}\left|( I - P ) y ^{(t)}\right|_{2}^{ q } \end{equation}$的幂次

\[\begin{equation} L_{\text {RSRAE }}( E , A , \mathscr{D})=L_{\text {AK }}^{1}( E , A , \mathscr{D})+L_{\text {TSR }}^{1}( A ) \end{equation}\]

p = 1, q = 1

adVAE

adVAE: A self-adversarial variational autoencoder with Gaussian anomaly prior knowledge for anomaly detection (2019-11)

深度生成模型存在过度拟合训练样本的风险，因此adVAE提出了一种具有高斯异常先验（Gaussian anomaly prior）的自对抗变分自编码器

Training Process

img

模型包括三个模块: 编码器网络E，生成网络G 和 Gaussian transformer网络T

  • Training Step1:

    通过T和G之间的对抗训练，将有效的正则化引入生成器，合成了潜变量，并使生成器将异常与正常的潜编码区分开（普通VAE的生成器很难区分正常和异常隐编码因为它们在潜空间中有重叠）

    • 冻结E网络中的权重并更新G和T
    • Gaussian transformer T接收从正常训练样本编码的正常高斯潜变量z作为输入，并将z转换为具有不同均值$\mu_T$和标准差$\sigma_{T}$的异常高斯潜变量$z_T$
    • T的作用是减少${z;\mu,\sigma}$和${z_T;\mu_T,\sigma_T}$的KL距离
    • G从两个相似的潜编码$z$和$z_T$尽可能生成不同的样本
    • T希望$z_T$接近$z$，而G希望$z_T$远离$z$，最终达到平衡（T将生成接近正常潜变量的异常潜变量，并且生成器将通过不同的重构误差来区分）

  • Training Step2：

    冻结T和G，训练编码器E作为判别器

    • 编码器将数据样本映射到高斯潜变量z进行正常和异常的判别

上述两个训练步骤交替进行，adVAE的训练过程如下：

img

Testing Process

img

测试阶段应用训练好的E和G，首先通过训练数据集得到异常分数的阈值（通过重构误差的核密度估计KDE）；对于测试图片，若重构误差超过阈值则判别为异常，否则为正常。

HADGAN

Discriminative Reconstruction Constrained Generative Adversarial Network for Hyperspectral Anomaly Detection (2020-01)

HADGAN的应用对象为高光谱图像

利用原图和生成图像得到Residual image进行异常检测

训练模型在f-Anogan的基础上加入了类似于AAE中的隐空间分布约束

img

img

测试时利用Residual image计算得到$D_{spatial}$和$D_{spectral}$，最终得到$D_{SS}=\lambda_1D_{spatial}+(1-\lambda_1)D_{spectral}$

CAVGA

Attention Guided Anomaly Localization in Images (v1: 2019-11 v2:2020-05)

img

无监督$CAVGA_u$：

  • 使用卷积潜变量来保留输入数据的空间信息（VAE架构），并加入鉴别器提升VAE模型重构性能

  • 对于由编码器得到的的feature map，计算得到attention map，使得潜变量的特征表示可以编码所有的正常区域

  • Attention Expansion Loss损失使从卷积潜变量中生成的attention map覆盖正常图像的全图

损失函数：

\[L_{\text {final}}=w_{r} L+w_{a d v} L_{a d v}+w_{a e} L_{a e}\]
  • 重构损失：
\[\begin{equation} L=L_{R}(x, \hat{x})+K L\left(q_{\phi}(z | x)|| p_{\theta}(z | x)\right) \end{equation}\]

​

  • 对抗损失：
\[L_{a d v}=-\frac{1}{N} \sum_{i=1}^{N} \log \left(D\left(x_{i}\right)\right)+\log \left(1-D\left(\hat{x}_{i}\right)\right)\]

​

  • 注意力分布损失:
\[\begin{equation} L_{a e, 1}=\frac{1}{|A|} \sum_{i, j}\left(1-A_{i, j}\right) \end{equation}\]

使用Grad-CAM计算A并使用Sigmoid进行归一化，$A_{i,j}\in[0,1]$

对于正常图像，注意力应遍布全图

img

弱监督$CAVGA_w$：在训练集中加入少量的异常图片来提高模型的检测和定位效果

以无监督$CAVGA_u$为基础，在输出$z$后加入一个二分类器$C$，用二元交叉熵损失$L_{bce}$来训练

由于生成的attention map依赖于分类器的性能，通过complementary guided attention loss（互补引导注意损失）来提升$C$的性能

  • $L_{cga}$使异常attention map注意的区域最小化，同时正常attention map尽可能覆盖全图
  • 仅在$p=y=c_n$即正常图像分类正确的时候计算互补引导注意损失项

损失函数：

\[L_{\text {final}}=w_{r} L+w_{\text {adv}} L_{a d v}+w_{c} L_{b c e}+w_{\text {cga}} L_{\text {cga}}\]
\[\begin{equation} L=L_{R}(x, \hat{x})+K L\left(q_{\phi}(z | x) \| p_{\theta}(z | x)\right) \end{equation}\] \[L_{bce}=-\left[y_{i} \log x_{i}+\left(1-y_{i}\right) \log \left(1-x_{i}\right)\right]\] \[L_{a d v}=-\frac{1}{N} \sum_{i=1}^{N} \log \left(D\left(x_{i}\right)\right)+\log \left(1-D\left(\hat{x}_{i}\right)\right)\] \[L_{c g a, 1}=\frac{1\left(p=y=c_{n}\right)}{\left|A_{x}^{c_{n}}\right|} \sum_{i, j}\left(1-\left(A_{x}^{c_{n}}\right)_{i, j}+\left(A_{x}^{c_{a}}\right)_{i, j}\right)\]

ALAE

img

融合了AAE和GAN的最新架构，还未应用到Anomaly Detection中

Paper

Anomaly-Classification-Target

基于一分类的异常分类方法

  • Estimating the Support of a High- Dimensional Distribution [OC-SVM] [Journal of Neural Computation’ 01] [pdf]
  • A Survey of Recent Trends in One Class Classification [AICS’ 09] [pdf]
  • Anomaly detection using autoencoders with nonlinear dimensionality reduction [MLSDA Workshop’ 14] [link]
  • A review of novelty detection [Signal Processing’ 14] [link]
  • Variational Autoencoder based Anomaly Detection using Reconstruction Probability [SNU DMC Tech’ 15] [pdf]
  • High-dimensional and large-scale anomaly detection using a linear one-class SVM with deep learning [Pattern Recognition’ 16] [link]
  • Transfer Representation-Learning for Anomaly Detection [ICML’ 16] [pdf]
  • Outlier Detection with Autoencoder Ensembles [SDM’ 17] [pdf]
  • Provable self-representation based outlier detection in a union of subspaces [CVPR’ 17] [pdf]
  • [ALOCC]Adversarially Learned One-Class Classifier for Novelty Detection [CVPR’ 18] [pdf] [code]
  • Learning Deep Features for One-Class Classification [arXiv’ 18] [pdf] [code]
  • Efficient GAN-Based Anomaly Detection [arXiv’ 18] [pdf]
  • Hierarchical Novelty Detection for Visual Object Recognition [CVPR’ 18] [pdf]
  • Deep One-Class Classification [ICML’ 18] [pdf]
  • Reliably Decoding Autoencoders’ Latent Spaces for One-Class Learning Image Inspection Scenarios [OAGM Workshop’ 18] [pdf]
  • q-Space Novelty Detection with Variational Autoencoders [arXiv’ 18] [pdf]
  • GANomaly: Semi-Supervised Anomaly Detection via Adversarial Training [ACCV’ 18] [pdf]
  • Deep Anomaly Detection Using Geometric Transformations [NIPS’ 18] [pdf]
  • Generative Probabilistic Novelty Detection with Adversarial Autoencoders [NIPS’ 18] [pdf]
  • A loss framework for calibrated anomaly detection [NIPS’ 18] [pdf]
  • A Practical Algorithm for Distributed Clustering and Outlier Detection [NIPS’ 18] [pdf]
  • Efficient Anomaly Detection via Matrix Sketching [NIPS’ 18] [pdf]
  • Adversarially Learned Anomaly Detection [IEEE ICDM’ 18] [pdf]
  • Anomaly Detection With Multiple-Hypotheses Predictions [ICML’ 19] [pdf]
  • Exploring Deep Anomaly Detection Methods Based on Capsule Net [ICMLW’ 19] [pdf]
  • Latent Space Autoregression for Novelty Detection [CVPR’ 19] [pdf]
  • OCGAN: One-Class Novelty Detection Using GANs With Constrained Latent Representations [CVPR’ 19] [pdf]
  • Unsupervised Learning of Anomaly Detection from Contaminated Image Data using Simultaneous Encoder Training [arXiv’ 19] [pdf]
  • Using Self-Supervised Learning Can Improve Model Robustness and Uncertainty [NeurIPS’ 19] [pdf] [code]
  • Classification-Based Anomaly Detection for General Data [ICLR’ 20] [pdf]
  • Robust Subspace Recovery Layer for Unsupervised Anomaly Detection [ICLR’ 20] [pdf]
  • RaPP: Novelty Detection with Reconstruction along Projection Pathway [ICLR’ 20] [pdf]
  • Novelty Detection Via Blurring [ICLR’ 20] [pdf]
  • Deep Semi-Supervised Anomaly Detection [ICLR’ 20] [pdf]
  • Robust anomaly detection and backdoor attack detection via differential privacy [ICLR’ 20] [pdf]

OOD-Detction-Target

基于异常分布的异常检测方法

  • A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks [ICLR’ 17] [pdf]
  • [ODIN] Enhancing The Reliability of Out-of-distribution Image Detection in Neural Networks [ICLR’ 18] [pdf]
  • Training Confidence-calibrated Classifiers for Detecting Out-of-Distribution Samples [ICLR’ 18] [pdf]
  • Learning Confidence for Out-of-Distribution Detection in Neural Networks [arXiv’ 18] [pdf]
  • Out-of-Distribution Detection using Multiple Semantic Label Representations [NIPS’ 18] [pdf]
  • A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks [NIPS’ 18] [pdf]
  • Deep Anomaly Detection with Outlier Exposure [ICLR’ 19] [pdf]
  • Why ReLU networks yield high-confidence predictions far away from the training data and how to mitigate the problem [CVPR’ 19] [pdf]
  • Outlier Exposure with Confidence Control for Out-of-Distribution Detection [arXiv’ 19] [pdf] [code]
  • Likelihood Ratios for Out-of-Distribution Detection [NeurIPS’ 19] [pdf]
  • Input Complexity and Out-of-distribution Detection with Likelihood-based Generative Models [ICLR’ 20] [pdf]

Anomaly-Segmentation-Target

基于一分类的异常分割方法

  • Anomaly Detection and Localization in Crowded Scenes [TPAMI’ 14] [pdf]
  • Novelty detection in images by sparse representations [IEEE Symposium on IES’ 14] [link]
  • Detecting anomalous structures by convolutional sparse models [IJCNN’ 15] [pdf]
  • Real-Time Anomaly Detection and Localization in Crowded Scenes [CVPR Workshop’ 15] [pdf]
  • Learning Deep Representations of Appearance and Motion for Anomalous Event Detection [BMVC’ 15] [pdf]
  • Scale-invariant anomaly detection with multiscale group-sparse models [IEEE ICIP’ 16] [link]
  • [AnoGAN] Unsupervised Anomaly Detection with Generative Adversarial Networks to Guide Marker Discovery [IPMI’ 17] [pdf]
  • Deep-Anomaly: Fully Convolutional Neural Network for Fast Anomaly Detection in Crowded Scenes [Journal of Computer Vision and Image Understanding’ 17] [pdf]
  • Anomaly Detection using a Convolutional Winner-Take-All Autoencoder [BMVC’ 17] [pdf]
  • Anomaly Detection in Nanofibrous Materials by CNN-Based Self-Similarity [Sensors’ 17] [pdf]
  • Defect Detection in SEM Images of Nanofibrous Materials [IEEE Trans. on Industrial Informatics’ 17] [pdf]
  • Abnormal event detection in videos using generative adversarial nets [ICIP’ 17] [link]
  • An overview of deep learning based methods for unsupervised and semi-supervised anomaly detection in videos [arXiv’ 18] [pdf]
  • Improving Unsupervised Defect Segmentation by Applying Structural Similarity to Autoencoders [arXiv’ 18] [pdf]
  • Satellite Image Forgery Detection and Localization Using GAN and One-Class Classifier [IS&T EI’ 18] [pdf]
  • Deep Autoencoding Models for Unsupervised Anomaly Segmentation in Brain MR Images [arXiv’ 18] [pdf]
  • AVID: Adversarial Visual Irregularity Detection [arXiv’ 18] [pdf]
  • MVTec AD – A Comprehensive Real-World Dataset for Unsupervised Anomaly Detection [CVPR’ 19] [pdf]
  • Exploiting Epistemic Uncertainty of Anatomy Segmentation for Anomaly Detection in Retinal OCT [IEEE TMI’ 19] [pdf]
  • Uninformed Students: Student-Teacher Anomaly Detection with Discriminative Latent Embeddings [arXiv’ 19] [pdf]
  • Attention Guided Anomaly Detection and Localization in Images [arXiv’ 19] [pdf]
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