R ED PANDA: D ISAMBIGUATING I MAGE A NOMALY D ETECTION BY R EMOVING N UISANCE F ACTORS
A BSTRACT
Anomaly detection methods strive to discover patterns that differ from the norm in a meaningful way.
This goal is ambiguous as different human operators may find different attributes meaningful.
An image differing from the norm by an attribute such as pose may be considered anomalous by some operators while others may consider the attribute irrelevant.
Breaking from previous research, we present a new anomaly detection method that allows operators to exclude an attribute when detecting anomalies.
Our approach aims to learn representations which do not contain information regarding such nuisance attributes.
Anomaly scoring is performed using a density-based approach.
Importantly, our approach does not require specifying the attributes where anomalies could appear, which is typically impossible in anomaly detection, but only attributes to ignore.
An empirical investigation is presented verifying the effectiveness of our approach
I NTRODUCTION
Anomaly detection, discovering unusual patterns in data, is a key capability for many machine learning and computer vision applications.
In the typical setting, the learner is provided with training data consisting only of normal samples, and is then tasked with classifying new samples as normal or anomalous.
It has emerged that the representations used to describe data are key for anomaly detection in images and videos (Reiss et al., 2021).
Advances in deep representation learning (Huh et al., 2016) have been used to significantly boost anomaly detection performance on standard benchmarks.
However, these methods have not specifically addressed biases in the used data.
Anomaly detection methods which suffer from the existence of such biases may produce more overall errors, and incorrectly classify as anomalies some types of samples more than others.
A major source for such biases is the presence of additional, nuisance factors (Lee & Wang, 2020).
One of the most important and unsolved challenges of anomaly detection is resolving the ambiguity between relevant and nuisance attributes.
As a motivating example let us consider the application of detecting unusual vehicles using road cameras.
Normal samples consist of images of known vehicle types.
When aiming to detect anomalies, we may encounter two kinds of difficulties: (i) The distribution of unknown vehicles (anomalies) is not known at training time.
E.g., unexpected traffic may come in many forms: a horse cart, heavy construction equipment, or even wild animals.
This is the standard problem addressed by most anomaly detection methods (Ruff et al., 2018; Reiss et al., 2021; Tack et al., 2020).
(ii)
The normal data may be biased.
For example, assume all agricultural machinery appearing during the collection of normal data was moved towards the farmlands.
During inference performed on another season, we may see the same equipment moving to the other side (and from a different angle).
This novel view might be incorrectly perceived as an anomaly.
Unlike previous works, we aim to disambiguate between true anomalies (e.g., unseen vehicle types) and unusual variation of nuisance attributes in normal data (e.g., a known vehicle observed previously only in another direction).
Detecting normal but unusual variations according to nuisance attributes as anomalies may be a source of false positive alarms.
In addition, they may introduce an undesirable imbalance in the detected anomalies, or even discriminate against certain groups.
There are many settings where some attribute combinations are missing from the training dataset but are considered normal: assembly line training images may be biased in terms of lighting conditions or camera angles - while these may be irrelevant to their anomaly score; photos of people may be biased in terms of ethnicity, for example when collected in specific geographical areas.
Moreover, in some cases, normal attribute combinations may be absent just due to the rarity of some attributes (e.g. rare car colors with specific car models).
The task of learning to ignore nuisance attributes requires a general approach.
While simple heuristics might sometimes be possible, they suffer from inherent weaknesses: (i) lack of generalization to new image types and nuisance attributes (ii) targeting a specific type of anomalies, which means they will fail to generalize to new, unexpected anomalies.
While nuisance attribute removal is easy when the representation is already disentangled in nuisance and relevant components (e.g., some tabular data settings), most image representations and highly entangled.
Our technical approach proposes to ignore nuisance attributes by learning representations that are independent from them.
Our approach takes as input a training set of normal samples with labeled nuisance attribute.
We utilize a domain-supervised disentanglement approach (Kahana & Hoshen, 2022) to remove the information associated with the provided nuisance attribute, while preserving as much uncorrelated information as possible about the image.
Specifically, we train an encoder with an additional per-domain contrastive loss term to learn a representation which is independent of the labeled nuisance attribute.
For example, an encoder guided to be invariant to the viewing angle would be trained to contrast images of cars driving to the left with similar images, but not against images cars driving to the right.
Additionally, a conditional generator is trained on the representations with a reconstruction term, to ensure the representations are informative.
We stress that we only use the reconstruction loss to encourage informativeness of our encoder, and do not use the reconstruction errors to score anomalies.
The combination of the two loss terms yields informative representations which are less sensitive to the nuisance attributes.
Although our obtained representation is far from being completely invariant to the nuisance attributes, it provides significant gains on several benchmarks.
The representations are then combined with standard density estimation methods ( k nearest neighbors) for anomaly scoring.
Our approach of using nuisance attribute labels differs from previous approaches.
Few anomaly detection algorithms consider the case where the training set contains attribute labels and therefore most methods do not aim to ignore nuisance attributes.
Out of distribution detection assumes that normal data are labelled with the value of the relevant attribute and that anomalies belong to a novel class, outside the set of labelled values (Salehi et al., 2021;
Hendrycks et al., 2020; Hendrycks & Gimpel, 2016).
The weakly supervised setting assumes future anomalies will be similar to a few labelled anomalous samples available during training (Cozzolino et al., 2018; Gianchandani et al., 2019; Deecke et al., 2021).
However, this type of knowledge is often limiting due to the inherent unpredictability of anomalies.
In contrast, we only require knowledge of the factors that are not indicative of the anomalies we wish to find - while assuming no specific knowledge of the expected anomalies.
In fact, labels for attributes we wish to ignore are often provided by the datasets, such as information about the sensor used to collect the data.
In other cases, such labels are easily predicted using pretrained classifiers such as CLIP (Radford et al., 2021).
As this task is novel, we present new benchmarks and new metrics for evaluation.
Our benchmarks incorporate normal examples which experience unusual variation in a nuisance attribute.
Our evaluation metrics measure both the overall anomaly detection accuracy, as well as the false alarm rate due to mistaking normal samples with nuisance variation as anomalies.
Our experiments indicate that using our approach for removing the dependencies on a nuisance attribute from the representation improves these metrics on our evaluation datasets.
While our method can currently handle only quite simple cases, this study indicates a way forward for tackling more realistic cases.
Contributions: (i) Introducing the novel setting of Negative Attribute Guided Anomaly Detection (NAGAD).
(ii) Presenting new evaluation benchmarks and metrics for the NAGAD setting (iii)
Proposing a new approach, REpresentation Disentanglement for Pretrained Anomaly Detection
Adaptation (Red PANDA), using domain-supervised disentanglement to address this setting.
(iv)
Demonstrating the potential of our approach through empirical evaluation.
R ELATED W ORKS
Classical anomaly detection methods.
These may be grouped into three themes (Yang et al., 2021;
Ruff et al., 2021): (i) Density-estimation based methods.
Estimation of the density of the normal data can be non-parametric methods, such as k NN or kernel density estimation.
Parametric methods, such as Gaussian Mixture Models (GMM) (Li et al., 2016) learn a parametric representation of the data to estimate the probability density of the test samples.
(ii) Reconstruction based methods - methods such as PCA learn to reconstruct well normal training samples.
Anomalies coming from a different distribution might not reconstruct as well.
(iii) One class classification methods - A classification approach separating between the normal samples and the rest of feature space (e.g. SVDD (Tax & Duin, 2004)).
Deep anomaly detection methods.
As only normal samples are available during training, we cannot learn features with standard supervision.
Therefore, deep anomaly detection methods either use self-supervision learning to score the anomalies (Hendrycks et al., 2019), or adapt a pretrained representation (Hendrycks et al., 2019; Reiss et al., 2021; Reiss & Hoshen, 2021; Ruff et al., 2018;
Perera & Patel, 2019) to describe the normal training data.
(i) Self-supervised methods - these methods learn to solve an auxiliary task on the normal samples, test the performance on new images, and score anomalies accordingly: the network is expected to perform better on the normal samples that come from a similar distribution (Hendrycks et al., 2019).
More recent works such as CSI (Tack et al., 2020) or DROC (Goyal et al., 2020) use contrastive learning to learn a representation of the normal data.
(ii) Adaptation of Pretrained Feature - Transfer learning of pretrained features was shown to give strong results for out of distribution detection by (Hendrycks et al., 2019).
Adaptation of pretrained features for anomaly detection was attempted by Deep-SVDD (Ruff et al., 2018), which adapted features learnt by an auto-encoder using compactness loss.
Perera & Patel suggested to training the compactness loss jointly with ImageNet classification (Perera & Patel, 2019).
By incorporating early stopping and EWC regularization (Kirkpatrick et al., 2017), PANDA (Reiss et al., 2021) allowed feature adaptation with mitigated catastrophic forgetting, resulting in better performance.
Further improvement in pretrained feature adaptation was later suggested by MeanShifted (Reiss & Hoshen, 2021), using contrastive learning to adapt the pretrained features to the normal training set.
Domain-supervised disentanglement.
Disentanglement is the process of recovering the latent factors that are responsible for the variation between samples in a given dataset.
For example, from images of human faces we may recover the age of each person, their hair color, eye color, etc.
In domain-supervised disentanglement, one assumes that a single such factor is labelled and aims to learn a representation of the other attributes independent of the labelled factor.
This task was approached with variational auto-encoders (Jha et al., 2018; Bouchacourt et al., 2018), and latent optimization (Gabbay & Hoshen, 2019; 2021).
Contrastive methods have also shown great promise with general disentanglement (Zimmermann et al., 2021).
This was followed by Kahana & Hoshen in domainsupervised disentanglement (Kahana & Hoshen, 2022) who employed a contrastive loss for each set of similarly-labelled samples individually, learning a code which ideally describes only (and all) attributes which are uncorrelated to the labelled attributes.
Domain-supervised disentanglement has been used for a variety of applications.
Most notably, for generative models (Zhu et al., 2018)(Gabbay & Hoshen, 2019).
Disentanglement models have also been discussed in the context of interpretability (Hsu et al., 2017), abstract reasoning (Van Steenkiste et al., 2019), domain adaptation (Peng et al., 2019), and fairness (Creager et al., 2019).
Some previous works have considered using domain supervision for increasing fairness in anomaly detection (Davidson & Ravi, 2020; Zhang & Davidson, 2021; Shekhar et al., 2021).
These methods aim at obtaining equal anomaly detection performance across the protected attributes.
On the other hand our objective is to ignore the nuisance attributes in order improve the overall performance of the anomaly detection method.
N UISANCE A TTRIBUTES M ISLEAD A NOMALY D ETECTORS
Anomaly detection methods aim to detect samples deviating from the norm.
However, operators of anomaly detection methods expect the deviation to be semantically relevant .
As the anomaly detection setting is typically unsupervised and the type of anomalies cannot be expected, it is impossible to predict in which modes of variations anomalies will appear.
Yet, we may know in advance that we do not wish to detect anomalies in nuisance attributes.
For example, we may wish to detect anomalous vehicles in traffic.
Anomalies can appear in many attributes such as car type, color, condition, headlights type etc.
However, if we do not wish to detect anomalies in the car pose, avoiding false positives associated with this attribute may be possible without knowing in advance in which attributes anomalies will appear.
Current algorithms rely on different inductive biases to select the relevant attributes and remove the nuisance ones.
The most common choice is manual feature selection, where the operator specifies particular features that would be the most relevant (Pevn`y, 2016;
Gu et al., 2019).
Contrastive learning methods specify augmentations which remove specific attributes (minor color and location variations) from the representation.
This helps to select attributes more relevant to object-centric tasks.
Similarly, representations pretrained on supervised object classification (e.g. ImageNet (Deng et al., 2009)), which have recently demonstrated very strong results on image anomaly detection, focus on object-centric attributes at the expense of other low-level image attributes.
The most extreme level of supervision is the out-of-distribution detection setting, where the class labels are provided for all normal training data, and anomalies are expected to belong to an unseen class.
However, this guidance is not available in the typical anomaly detection setting as anomalies are unexpected.
Our novel setting, Negative Attribute Guided Anomaly Detection (NAGAD), allows specification of nuisance attributes which should be ignored by the anomaly detector.
Differently from specifying the relevant attributes, which is not possible in anomaly detection, specifying nuisance attributes is often possible.
Users may know in advance about the attributes they wish to exclude for anomaly detection; either due to legal and moral reasons, or due to prior domain knowledge.
The issue of excluding such attributes from images remains a major technical challenge even when such attributes are known.
A natural way for specifying nuisance attributes is to provide labels for them.
For example, wishing to detect anomalies according to a car model but not according to its pose, we may provide for each image a label for the car pose (see Fig.1).
Currently available anomaly detection approaches cannot directly benefit from such information and thus mitigate nuisance attributes only implicitly (using the mechanisms explained above).
In Sec.
4 we describe a specific technical approach for using the guidance for anomaly detection.
Yet, we stress that our main contribution is the novel anomaly detection setting.
R ED PANDA: D ISENTANGLEMENT A PPROACH FOR R EMOVING A N UISANCE F ACTOR
We detail the different stages of our approach below. An algorithm box summarizing the different steps can be found in App. J.
4. O BTAINING L ABELS FOR THE N UISANCE A TTRIBUTE
Our approach, REpresentation Disentanglement for Pretrained Anomaly Detection Adaptation (Red
PANDA), aims to achieve a representation invariant to a nuisance attribute of our dataset, leading to better detection of anomalies expressed in relevant attributes.
To do so, we provide labels for the nuisance attribute.
For example, when we wish to detect anomalies in driver behaviour, we may wish to ignore the vehicle’s pose.
We can achieve this by providing pose labels during training, and using them to be less sensitive to this attribute.
To achieve these labels, we have a few options.
In some cases they may already exist in the dataset.
A very natural such case is when we have data from a few static cameras, and we wish to ignore the camera identity.
In many other cases, a pretrained classifier, already trained for these specific attributes may provide such labels.
Recently, pretrained models for text-based zero-shot classification such as CLIP (Radford et al., 2021) have shown promising results.
Such models allow to supply of-the-shelf labels for a very large set of attributes.
We conducted a small experiment over the
Edges2Shoes (Isola et al., 2017) dataset, automatically labelling it with CLIP, and achieved 99 . 97% accuracy in labelling whether an image is a photo or a sketch (Fig.2).
Taken together in many cases labels for nuisance attributes they can be achieved at virtually no cost.
4. P RELIMINARIES
In our setting, the training set denoted as D train consists of normal samples only .
For each normal image x i ∈
D train we are also provided with its label n i describing the nuisance attribute we wish to ignore (the setting can be naturally extended to many nuisance attributes).
Our evaluation set D test consists of both normal and anomalous samples.
We denote the normal/anomaly label for a test image x i as y i .
For each such dataset, each sample is described by multiple attribute ( n i , a i , b i , c i , ... )
∈ N ×
A × B × C × ... , where N describe our nuisance attribute, and A, B, C, ... describe different relevant attributes (consider for example the identity of the object, the lightning condition, and camera angles as different attributes).
We only assume labels for N during training.
We assume that the anomaly label is always a function of (potentially) all the relevant attributes y i =
f a ( a i , b i , c i , ... ) .
Namely, we assume the nuisance attribute n i never affects the anomaly label y
i .
We emphasize that in our described setting, none of the relevant attribute labels nor the anomaly labels are given during training.
We aim to learn an encoder function f mapping samples x i to a code describing their relevant attributes f ( x i ) ∈ R d .
We also wish our codes to be invariant.
This is, we wish our encoder to represent the relevant attributes in a way which is not affected by the nuisance attributes:
[Equation]
We also wish our code to be informative - to represent sufficient information regarding our relevant attributes ( I (; ) is the mutual information between its two arguments):
[Equation]
In practice, the invariance may be measured by the accuracy of predicting n i from the latent code f ( x ) .
Similarly, we can measure the accuracy of predicting the relevant attribute used to define anomalies (informativeness).
Empirical evaluations of these measures for our datasets can be found in the App.
I. Given such a representation we may later score anomalies independently from any biases caused by the nuisance attribute we wish to ignore.
4. C ONTRASTIVE D ISENTANGLEMENT
In this section, we describe the technical approach we employ for ensuring that f does not contain information on the nuisance attribute, while retaining as much information about the relevant attributes (Kahana & Hoshen, 2022).
Pretrained encoder.
We initialize the encoder function f with an ImageNet pretrained network.
ImageNet-pretrained representations were previously shown to be very effective for image anomaly detection (Reiss et al., 2021).
Off-the-self pretrained representation, however, also encodes much information on the nuisance attributes.
Therefore they do not satisfy our invariance objective.
Contrastive loss.
Our objective is that images that have similar relevant attributes but different nuisance attributes would have similar representations.
Although we are not provided with supervised matching pairs, we use the proxy objective requiring the distribution of representations of images having different nuisance attributes to be the same.
To match the distributions we first split our training data D train to disjoint subsets S n i according to the nuisance attribute values:
[Equation]
We then use a contrastive loss on each of the sets S n i independently ( sim denotes cosine similarity, x i , x j ∈ D train are arbitrary normal samples, and n ( x i ) , n ( x j ) are their nuisance labels):
[Equation]
This objective encourages the encoder to map the image distribution of each nuisance attribute uniformly to the unit sphere (Wang & Isola, 2020). Therefore, it matches the distributions of sample embeddings coming from different values of the nuisance attribute (as as required by Eq.1) (Wang & Isola, 2020).
We note that matching of marginal distributions is necessary, but not a sufficient condition for alignment ((Kahana & Hoshen, 2022)).
Another problem that may arise is insufficient informativeness: the contrastive objective does not prevent ignoring some of the relevant attributes (Chen et al., 2021).
To support the informativeness we add an augmentation loss, encouraging different augmentations of the same image to be mapped to similar codes: L aug = − sim (cid:16) f
(cid:0)
A 1 ( x i ) , A 2 ( x i ) (cid:1)(cid:17) .
The used augmentations are detailed in appendix D. To further encourage informativeness, we also employ a reconstruction loss.
Reconstruction loss.
To encourage the representation to contain as much information about the relevant attributes as possible, we use a reconstruction constraint.
Specifically, we require that given the combination of the representation f i (which ideally ignores the nuisance attribute) and the value of the nuisance attribute n i , it should be possible to perfectly recover the sample x i .
This is enforced using a generator function G which is trained end-to-end together with the encoder.
The reconstruction is measured using a perceptual loss.
[Equation]
4. D ENSITY B ASED A NOMALY S CORING
Similarly to other anomaly detection methods, we hypothesize the anomalous samples will be mapped to low-density regions, while normal data will be mapped to high-density regions.
When the representation contains only relevant attributes, low-density regions would indeed correspond to samples with rare relevant attributes - which are likely to be anomalies.
To numerically estimate the density of the normal data around each test sample, we use the k nearest neighbours algorithm ( k NN).
We begin with extracting the representation for each normal samples: f i = f
( x i ) , ∀ x i ∈ D train .
Next, for each test sample we infer its latent code f t = f ( x t ) .
Finally, we score it by the k NN distance to the normal data:
[Equation]
where N k ( f t ) denotes the k most similar relevant attribute feature vectors in the normal data (comparison of different density estimation methods and different values of k can be found in App.K).
We note that although we trained our encoder f with a contrastive loss, encouraging uniform distribution in the sphere, the high dimension of the latent space allows us to distinguish between high and low density areas of the distribution of normal data.
Runtime coniderations are discussed in App.
D.  E XPERIMENTS 5. S ETTING
Benchmark construction.
As our anomaly detection setting is novel, new benchmarks need to be designed for its evaluation.
The following protocol is proposed for creating the benchmarks.
First, we select an existing dataset containing multiple labelled attributes.
We designate one of its attributes as nuisance, (e.g., the object pose) and other attributes as relevant (e.g., the identity of the object).
Only the relevant attributes are used to designate an object as anomalous whereas the nuisance attribute does not.
We then remove images featuring certain combinations of nuisance and relevant attributes from the training set, creating bias in the data.
For example, we may remove all left-facing cars for one car model, and right-facing cars for another car model.
As these combinations are removed from the normal train set, we refer to them as pseudo-anomalies .
We refer to any sample that shares all the attributes (including nuisance attributes) with a normal training sample as a familiar samples .
In this setting, we aim both to both detect true anomalies (anomalies according to the relevant attributes), and treat pseudo-anomalies as normal as the familiar samples, as they differ only in nuisance attributes.
Metrics.
We wish not only to measure our overall anomaly detection performance, but also to evaluate the false alarm rate due to pseudo-anomalies.
We therefore report our results in terms of three different scores.
Each uses two subsets of the test set and measures how well our anomaly detection algorithm discriminate between them in terms of ROC-AUC: (i) Standard anomaly detection (AD)-Score, which measures how accurately anomalies are detected with respect to the normal test data (both familiar samples and pseudo-anomalies).
(ii) Pseudo anomalies (PA)-Score: measures how much pseudo-anomalies are scored as anomalous compared to familiar samples (iii) Relative abnormality (RA)-score: measures how accurately true anomalies are detected compared to pseudo-anomalies.
5. R ESULTS
Compared Methods.
We compared to the following methods: DN2 (Reiss et al., 2021), MeanShifted (Reiss & Hoshen, 2021), CSI (Tack et al., 2020), SimCLR (Chen et al., 2020).
A full description of the compared methods can be found in App.(C).
Datasets.
We report the results on three multi-attribute datasets based on Cars3D , SmallNORB and Edges2Shoes .
We chose these specific datasets as they are the common datasets in the field of domain-supervised disentanglement (Gabbay & Hoshen, 2019; Kahana & Hoshen, 2022).
We also find these datasets to be non-trivial for state-of-the-art anomaly detection algorithms.
Full details on each dataset can be found in App.
E. Cars3D (Reed et al., 2015).
A synthetic dataset, where each image is formed using two attributes: car model and pose.
Car models are varied across different colors, shapes and functionalities.
Each car model is observed from multiple camera angles (pose).
To simulate pseudo anomalies, we randomized for each pose a single car model and labeled it as pseudo-anomaly.
An illustration of the dataset can be seen in Fig.
We can see in Tab.1 that the disentanglement approach significantly outperforms methods that do not use any guidance to remove the nuisance attribute.
We detects true anomalies, without assigning high anomaly scores to the pseudo-anomalies, significantly better than all other methods compared.
The RA-Score shows that we distinguish well between true anomalies and pseudo-anomalies.
SmallNorb (LeCun et al., 2004).
In this dataset as well we define our nuisance attribute to the the camera angles, and pseudo-anomalies are car models seen from a never-seen-before angle during test time.
We can see in Tab.2 that our approach outperforms on this dataset too.
All methods utilizing pretrained features detect true anomalies fairly well.
This is expected, as the network learns a good representation of objects during pretraining.
Our disentanglement approach significantly reduces the tendency to score pseudo-anomalies as anomalies.
CSI treats pseudo-anomalies similarly to normal samples, but this is most likely because its representation for this dataset is not informative, and [Figure] [Table] does not distinguish well between unseen data (true anomalies or pseudo-anomalies) and the familiar samples.
[Table]
Edges2Shoes (Isola et al., 2017).
This dataset contains photos of shoes and edge maps images of the same photos.
An illustration of the dataset can be seen in Fig.
This dataset is challenging as the photo and sketch domains are quite far, making the nuisance attribute dominant.
E.g., by observing only sketches of boots, real photos of boots could be easily considered as anomalies without further guidance.
Our approach outperforms methods that do not remove nuisance attributes from the representation.
We observe (by the PA-score) that although the pseudo-anomalies are indeed scored higher than normal images by our approach, their scores are still lower than the true anomalies (demonstrated by the RA-score).
Our approach significantly outperforms the baselines, showcasing the importance of specifying and removing nuisance attributes.
[Table]
In summary, while some methods outperformed our method in terms of PA score on some experiments, this was done by scoring both pseudo-anomalies and true anomalies as normal samples (resulting in significantly worse AD-Score).
The PA score alone can simply be optimized by a random anomaly detector - always getting ROCAUC of 0.5.
The RA-score measures the ability to distinguish true anomalies from pseudo anomalies directly.
We significantly outperform all baselines on this score.
D ISCUSSION & L IMITATIONS
Multi-attribute dataset.
Many datasets (e.g. SmallNorb) have more than two attributes.
In some cases, we may wish to remove multiple nuisance attributes.
Methods such as (Gabbay & Hoshen, 2019) very naturally extends to the case of disentangling many factors of the same dataset.
These methods operate using carefully-designed bottlenecks.
Multiple attributes can be excluded by concatenating their representation to the latent code (Gabbay et al., 2021).
Our approach can be extended to the case of multiple attribute using such methods.
Applying our approach to other data modalities. While this work is focused on image datasets, disentanglement approaches may assist anomaly detection efforts in other modalities as well. This includes modalities such as audio signals (Abeßer & Müller, 2021) or text (Cheng et al., 2020), and also scientific data such as Single-Cell data (Hetzel et al.). [Table]
Domain supervised disentanglement in the wild.
Currently, state-of-the-art domain-supervised disentanglement methods achieve impressive results on synthetic or curated datasets.
Such methods do not perform as well for in-the-wild datasets.
As our approach heavily relies on disentanglement, it is prone to similar limitations.
As the field of disentanglement advances, the advancements can be translated to improved anomaly detection capabilities using our approach.
To evaluate the progress of future anomaly detection methods, we also include a harder benchmark (Tab.6).
We adapt a standard anomaly detection benchmark (MVTec-AD, (Bergmann et al., 2019)), and evaluate a state-of-the-art method (PatchCore (Roth et al., 2021)) that achieves very high accuracy on the original data (“No
Nuis.”).
However, in the presence of nuisance factors, that create pseudo-anomalies in the test set (JPEG compression, Contrast Augmentation, Gaussian noise), the anomaly detection results significantly deteriorate.
The method we proposed cannot apply on this dataset for multiple reasons: (i) it is designed for coarse-grained rather than fine-grained AD (ii) it struggles on complex real-world images.
Extending the state-of-the-art to such datasets is an open challenge.
Additional details about this benchmarks can be found in App.
A. is not solved by the methods explored in this paper (including ours), and is left for future research.
Highly biased datasets.
Similarly to other disentanglement approaches, we require the distributions of relevant attributes across nuisance domains to be somewhat similar.
We have shown that our method can work when the supports across domains are not overlapping.
Still, we expect that when the supports are highly non-overlapping the results will significantly deteriorate.
Developing methods able to disentangle domains with highly non-overlapping support is an exciting future direction.
Imperfect invariance.
While our method aims to achieve invariance, the results are still imperfect.
We report the invariance and informativeness of our learned representations in Tab.11.
Although far from optimal, the method already provides significant gains for the anomaly detection task (Sec.5).
Missing and mislabeled nuisance factors.
As our approach relies on labeled nuisance factors, it might be sensitive to mislabeled nuisance labels.
Although wrong labels can hinder the efforts of most machine learning algorithms, our approach might be sensitive to two other types of errors: (i) our technical methods relies on categorical labels for the nuisance attribute.
In our experiments we successfully address this by quantization of the continuous variable.
Yet, this procedure should be carefully examined for each application.
(ii) if a user fails to identify the correct nuisance factor, our method could not be used to remove it.
Further Discussion.
Further discussion regarding Supervised vs. self-supervised pretraining Supervised vs. self-supervised pretraining Removing nuisance attributes with generative models
C ONCLUSION
We proposed a new anomaly detection setting where information is provided on a set of attributes that are known to be irrelevant for distinguishing between normal samples and anomalies.
Using a disentanglement-based approach, we showed how this additional supervision can be leveraged for better anomaly detection in biased datasets.
As identifying irrelevant attributes is easier than predicting in which attributes anomalies will appear, we expect further research on this new setting to be fruitful and promising.
A CKNOWLEDGEMENT
This research was partially supported by the Israeli Science Foundation, the Hebrew University Data
Science grants (CIDR), and the Israeli Council for Higher Education.
A MVT EC -AD BASED A NOMALY D ETECTION W ITH N UISANCE F ACTORS
We wish to evaluate the NAGAD setting on a more realistic benchmark.
Therefore, we adapt the
MVTec-AD benchmark to include nuisance factors.
We extend the test set of each class to include pseudo-anomalies: normal test samples that underwent an augmentation simulating a different image source (see Sec.A.1).
We also include the true anomalies twice: once in their original form, and once with the augmentation.
We down-sample the true anomalies by a factor of 5 to keep the class sizes relatively balanced.
As can be seen in Tab.
A including pseudo-anomalies significantly deteriorates the anomaly detection capabilities with respect to the original data.
The pseudo-anomalies differ from the normal data (Tab.
A, PA-score) and are often considered more anomalous than the true anomalies (Tab.
A, RA-Score).
To allow future methods the ability to adapt, and be more invariant to the nuisance variation, we also include a version with an extended dataset in our benchmark (Tab.
A, JPEG+; Contr.+; Gauss.+).
In this version the normal training data include both the original and augmented normal data, from two unrelated MVTec classes (“transistor” & “zipper”).
Using the labels on the nuisance variation for these classes, we expect future methods to be able to pay less attention to the nuisance attribute.
We therefore do not include the MVTec-AD classes but “transistor” & “zipper” in our average image-level
ROC-AUC results.
As the other discussed methods preform less well also on the original MVTec-AD dataset, we do not include their results.
A. A UGMENTATIONS AS N UISANCE A TTRIBUTES
To simulate the nuisance attribute, we consider three augmentations, chosen from the augmentations used by Hendrycks & Dietterich (2019).
For each chosen augmentation we specify its severity degree as defined there.
We consider the following augmentations:
JPEG - JPEG compression artifacts taken by severity degree 5 , compressing each image to 7% of its original size.
Contrast - Decrease of contrast for each image (severity degree 3 ).
Gaussian Noise - Blurring each image (severity degree 5 ).
Specifically, the blurring gaussian kernel has a standard deviation of 3 .
We illustrate the chosen augmentations on one image in Fig.
A.1. B F URTHER D ISCUSSION Supervised vs. self-supervised pretraining. Many top performing approaches (including ours) rely on externally-pretrained weights for initializing their neural networks.
Pretrained weights implicitly provide useful guidance regarding the relevant attributes we should focus on, and the ones we may wish to ignore (e.g. low-level image information).
Different pretrained networks provide different relevant/nuisance attribute splits.
We found that pretrained weights obtained from supervised classification on external datasets such as ImageNet, tend to emphasize the main object featured in the center of the image, and are more invariant to other attributes. Representations Original Gaussian Noise
Contrastive
JPEG A glossary of the augmentations used to create the nuisance factors in Tab.6: An original image, Gaussian noise augmentation, Contrastive augmentation, and JPEG Compression augmentation. learned by self-supervised pretraining on external datasets are affected both by the dataset and by the augmentation used for its contrastive learning.
Therefore they may have difference inductive biases.
Augmentations.
Different methods may require augmented images to be similar or dissimilar to the original image (Chen et al., 2020; Tack et al., 2020).
This choice tends to have a strong effect on the results.
E.g., a network trained to be rotation invariant, may fail when the relevant attributes include the image orientation angle.
Our approach only uses simple augmentations such as Gaussian blurring, saturation and crops.
We expect these augmentations not to restrict the anomalies detectable in the vast majority of cases.
In general, augmentations should be carefully inspected when deploying anomaly detection methods in practice.
Removing nuisance attributes with generative models.
Recently, generative models e.g. StyleGAN (Karras et al., 2019) have been able to learn very powerful representations for several data types, particularly images of faces.
Their representations exhibit a certain level of disentanglement (Wu et al., 2021).
When available, such models can be utilized for removing nuisance attributes in a similar approach to ours.
C C OMPARED M ETHODS
DN2 (Reiss et al., 2021).
A simple but effective approach fully reliant on pretraining. It uses an ImageNet-pretrained network to extract representations for each image.
Each test image is scored using k NN density estimation similarly to our approach. MeanShifted (Reiss & Hoshen, 2021).
A recent method that achieves state-of-the-art performance on standard anomaly benchmarks. It uses a modified contrastive learning loss to adapt its feature to the normal train set.
This method uses the same pretrained network as our method to initialize the features. It then uses a k NN for anomaly scoring.
CSI (Tack et al., 2020).
A strong self-supervised anomaly detection method that does not rely on pretraining.
It uses two types of augmentations: fine augmentations simulating positive contrastive loss samples, and domain shifts simulate negative samples. Anomaly scoring is performed using an ensemble of similarity scores based on the learnt features.
SimCLR (Chen et al., 2020).
An ablation of our approach that trains a single contrastive loss rather than a different contrastive loss for each domain. We score the anomalies similarly to our approach.
D I MPLEMENTATION D ETAILS D. D ISENTANGLEMENT MODULE
We use most of the parameters as in the DCoDR paper (Kahana & Hoshen, 2022) for our disentanglement module.
All images were used in a 64 × 64 resolution.
For the contrastive temperature, we use τ = 0 .
1 for all the datasets.
We scale down the loss L rec by a factor of 0 . 3 . [Figure]
Architecture.
We used a ResNet50 encoder pretrained on image classifications.
In accordance with previous works, we add 3 fully-connected layer to the encoder for the SmallNorb dataset (Gabbay & Hoshen, 2019; Kahana & Hoshen, 2022).
For the perceptual loss of the generator we used a VGG network pretrained on ImageNet.
Optimization.
We use 200 training epochs.
In each batch we used 32 images from 4 different nuisance classes (a batch size of 128 , in total).
We used a learning rates of 1 · 10 − 4 and 3 · 10 − 4 for the encoder and generator (respectively).
Augmentation.
We used Gaussian blurring (kernel_size = 5 , σ = 1 ), high contrast (contrast = (1 . 8 , 3 . 0) ), and high saturation (saturation =
(1 . 8 , 3 . 0) ) for our augmentation.
For Edges2Shoes we used only Gaussian Blurring.
For the SimCLR (Chen et al., 2020) contrastive learning (both in our approach and the baseline), we follow DCoDR by only augmenting the original image once, and comparing the augmented and the original views encodings.
This in contrast to SimCLR which compares two augmented views instead. Baselines.
We ran all the baselines using the same ResNet50 backbone network we used.
As
CSI (Tack et al., 2020) performance deteriorated when using ResNet50, we ran it with the original ResNet18 backbone used by the authors.
As we aim to detect anomalies without relying on any labelled anomalous samples, we used all the baselines with their default parameters. As DCoDR (Kahana & Hoshen, 2022) uses different temperature parameter for each dataset, we used τ = 0 . 1 for all datasets.
D. S CORING MODULE
We use faiss (Johnson et al., 2019)
k NN implementation, using k = 1 .
E D ATASETS
We label each sample as either normal , true anomaly , or pseudo-anomaly as detailed below.
We include only true anomalies and pseudo-anomalies in the test set, and split the normal samples between the training set and the test set ( 85% / 15% train/test split).
To simulate anomalies in the dataset, we first designate true anomalies as described in Sec.5.
We then chose combination of normal classes and the nuisance attribute to designate pseudo anomalies.
We used the following random combinations for pseudo anomalies:
Cars3D
: We define true anomalies as images of 5 (randomly selected) car models.
The nuisance attributes are defined in Tab.5.
[Table]
SmallNorb: Each image is synthetically constructed from several attributes: object type, camera azimuth, camera elevation and lighting.
The object types come from different categories such as animals, people, planes, trucks and cars. To simulate our anomalies we randomized a single object class (e.g. deer) from each category type. We define the camera azimuth angles as our nuisance attribute. For each azimuth angle value we randomize a single object class, and assign samples of that type and camera angle as pseudo-anomalies.
The nuisance attributes are defined in Tab.6.
[Table]
Edges2Shoes: The images in this dataset are labelled in terms of image type (sketch vs. photo), shoe type, and other attributes (we use labels from the UT-Zappos50K dataset (Yu & Grauman, 2014)).
We assign all images with shoe type ‘slippers’ as a true anomaly.
We assign all photos of type ‘sandal’, and all sketches of type ‘boot’ as pseudo-anomalies.
The nuisance attributes are defined in .
[Table]
We included all of the psuedo anomalies to the test set.
E. C OMPUTE R ESOURCES
The entire project used in total 3000 hours of NVIDIA RTX A5000 GPU (including development, testing and comparisons).
All resources were supplied by a local internal cluster. E. R UNTIME
Although k NN has runtime complexity linear in the number of training data, it can be sped up using
K means or core-set techniques (as done in SPADE (Cohen & Hoshen, 2020) or PatchCore (Roth et al., 2021)). In practice, the wall-clock runtime of the retrieval stage of our approach is minimal, even without such speedups (>3500 images per second for the SmallNorb dataset). E. L ICENSE Our technical approach is based on the DCoDR paper(Kahana & Hoshen, 2022) with SOFTWARE
RESEARCH LICENSE detailed here 2 . The implementation uses the PyTorch and faiss (Johnson et al., 2019) packages. PyTorch Uses a BSD-style license, as detailed in their license file 3 . faiss uses
MIT License . The CLIP(Radford et al., 2021) network we used for automatic labelling uses MIT License . SimCLR (Chen et al., 2020) used by DcoDR and as a baseline uses Apache License .
LICENSE
We performed an additional experiment where we select pseudo-anomalies from a range of values, instead of considering just one viewing angle for each class as pseudo-anomaly.
Here, for a set ofrandom classes we randomly select a range of 36 degrees in azimuth, which we remove from the train set, and treat as pseudo anomalies.
We report the results for the SmallNorb dataset Tab.8.
We can see our method still preforms well under this setting.
[Table]
G A BLATION STUDY
We further extend our ablation study in Tab.9.
We provide two versions of our methods, without one or more of its components.
(i)
First, we validate the need for our use of labels for the nuisance factor.
As in the main text [Table] SimCLR trains a single contrastive loss, similar to Eq. [Table]
but when treating the entire training set as coming from the same single label (ii) Second, No Rec presents our method without using the reconstruction loss (Eq.5).
Similarly to (Kahana & Hoshen, 2022), it works well in some cases [Table] but is not stable across datasets.
Especially, in datasets such as Edges2Shoes where invariance is very hard to achieve because the domain shifts are dominant.
[Table]
H T YPICAL S TATISTICAL E RROR IN E XPERIMENTAL R ESULTS
We ran 3 repetitions of our approach for each experiment.
The consistency of the results is presented in Tab.10.
I I NVARIANCE AND I NFORMATIVENESS
We use an MLP, as a practical estimator for the nuisance attribute given the code embedding (Tab.11).
As “Optimal” invariance we report the accuracy of predicting the nuisance attribute when no information is available at all.
Although our invariance is far from optimal, it is significantly [Table] [Table] better than the invariance achieved by the competing methods.
We note that on the SmallNorb dataset
[Table]
other methods achieve better invariance than our method.
However, they are also very low in
Informativeness, suggesting that neither nuisance nor relevant attributes are represented with their encoder.
[Equation]
classifier nuisance attributes normal samples D
Result: An anomaly score S t for each test image /
* Preprocessing: */ for x i ∈ D train do n i ← C ( x i ) end /
* Training: */ while Not converged: do
L con =
(cid:16) log (cid:80) x i ,x j 1 ( n i = n j ) e sim (cid:0) ( f ( x i ) ,f ( x j ) (cid:1)(cid:17) /
* x i , x j ∈ D train are arbitrary normal samples */
L rec = (cid:80) x i ,N ℓ perceptual (cid:16) x i , G (cid:0) f ( x i ) , n i (cid:1) (cid:17) L aug = − sim (cid:16) f (cid:0)
A 1 ( x i ) , A 2 ( x i ) (cid:1)(cid:17)
F, G ← arg min F,G ( L con + L rec + L aug ) /* SGD */ end /* Compute representations for all training samples: */
T = { f ( x ) | x ∈ D train } /* Anomaly scoring a test sample x t : */ f t = f
( x t )
S ( x t ) =
k NN_Distance ( f t , T )
K C OMPARISON OF DENSITY ESTIMATION METHODS
Following previous anomaly detection works, we set the value of k to 1 (Cohen & Hoshen, 2020).
The results for different values of k are shown in the Tab.
K. We also compare to alternative density estimation methods (Breunig et al., 2000; Chen et al., 2001).
[Table]