Expression Valentin Durand De Gevigney

Pierre-Franc ¸ois Marteau

Arnaud Delhay

Damien Lolive

Video Latent Code Interpolation for Anomalous Behavior Detection 1 st

Keywords: component, formatting, style, styling, insert

Detecting an anomalous human behavior can be a challenging task. In this paper, we present a novel objective function for autoencoders which include a temporal component. Our method is a fully end-to-end semi-supervised approach for video anomaly detection. The autoencoder is trained to reconstruct a sample from a partial input, by interpolating latent codes obtained from this partial input. We show this approach improves over using usual autoencoder objective functions for video anomaly detection and achieves results close to the state of the art on a broad range of datasets. Our code is publicly available on github.

I. INTRODUCTION

Anomaly detection in video surveillance data streams is an overwhelming task due to the ever increasing volume of data that need to be processed: this volume basically follows the number of cameras that populate massively our streets and buildings. Automatizing the detection of anomaly is thus a crucial and unavoidable need today for optimizing cost and efficiency of the control surveillance tasks. However, the characterization and identification of anomalies is a difficult problem. In general, anomalies are quite rare events, present during a short time span. They resemble sometimes to weak signal, specifically when the event characterizing the anomaly occurs in the background of the scenes that are captured by the camera.

In this article we address the automatic detection of anomalies in video through a semi-supervised learning paradigm, for which mostly anomaly free videos are used to train the model. Our contribution is threefold:

1) We propose the design of an objective function for training temporal autoencoders using past and future information. We show that this objective function improves over using usual reconstruction objective functions. 2) We review commonly used datasets, providing complete information about these datasets in a centralized manner. We also propose labels for the Subway dataset. 3) We compare multiple metrics for computing the regularity score, using multiple common evaluation measures.

This research has been financially supported by the French Ministry of Defense -Direction Générale pour l'Armement (DGA) and the University of Bretagne Sud (UBS) under the MADMAX project.

We first address the related works and position our contribution within the scope of the state of the art methods. The second section details the design of our proposed architecture, while highlighting its main novelty and justifying our choices at the light of the problems we are aiming to solve. The third section presents the experimentation we have carried out. The fourth section aims to assess our model comparatively to state-of-the-art methods that challenge our contribution in this research domain. We finally conclude our study and present some perspectives that possibly extend this work.

II. RELATED WORK A. Video anomaly detection

Most of the time in deep learning approaches, video anomaly detection is performed within the semi-supervised learning paradigm: the training data are only made up of normal samples and the testing data are both normal and anomalous samples. Ideally, all anomalous samples are labelled and no unlabelled samples are left in the training data. Models are then trained on these normal samples, hoping they generalize well on normal samples contained in the testing data but not on anomalous samples.

Since deep learning based methods have proven to be popular and successful on anomaly detection [START_REF] Hasan | Learning temporal regularity in video sequences[END_REF], we only review major trends and leading methods entering in this subdomain.

Hasan et al. [START_REF] Hasan | Learning temporal regularity in video sequences[END_REF] proposed a 2D-convolutional autoencoder receiving handcrafted spatio-temporal features as inputs, namely Histograms of Oriented Gradients (HOG) and Histograms of Optical Flows (HOF) in order to learn temporal regularity in video sequences.

Hinami et al. [START_REF] Hinami | Joint detection and recounting of abnormal events by learning deep generic knowledge[END_REF] proposed a method that leverages the joint detection and recounting of abnormal events, the resulting models learns to classify concepts related to these abnormal events. However, this requires significantly more detailed labels, as well as labels for training data.

Fan et al. [START_REF] Fan | Video anomaly detection and localization via gaussian mixture fully convolutional variational autoencoder[END_REF] used two 2D-convolutional variational autoencoders (VAE), one on raw input frames for spatiality and one on Optical Flow for temporality. They then performed late fusion on the scores resulting from these two streams. This allows them to treat spatial and temporal anomalies mostly separately, which can be very relevant on datasets like UCSD Pedestrian, where cars are spatial and temporal anomalies for different reasons. The usage of a VAE also allows them to include uncertainty in the process, which is useful because a single situation has several likely outcomes.

Luo et al. [START_REF] Luo | A revisit of sparse coding based anomaly detection in stacked rnn framework[END_REF] proposed a temporally-coherent sparse coding (TSC), mapped to a stacked RNN. This TSC itself uses extracted features from a fixed encoder trained on UCF101. One of the advantages of using this sparse coding is that it makes the model learn a dictionary of normal events. They also add a temporal coherence to ensure that similar features give similar sparse codes. Since the dictionary learns normal events, they yield a better regularity score than abnormal events.

B. Predicting the future

An anomalous behavior can be defined as a behavior that could not be expected from historically observed behaviors. That is to say going from a normal state into a state that could not be predicted accurately. This is why some recent works focus on predicting the next state and not only reconstructing the current one.

The method proposed by Liu et al. [START_REF] Liu | Future frame prediction for anomaly detection-a new baseline[END_REF] uses a U-net generator to predict the next frame, based on previous frames. PSNR is then used to compute the regularity score of this frame. They train their model in an adversarial setup, also using an optical loss computed from the difference between generated and real Optical Flows evaluated on the next frames.

Zhao et al. [START_REF] Zhao | Spatiotemporal autoencoder for video anomaly detection[END_REF] proposed a 3D-convolutional autoencoder with two decoders. The first one aims at reconstructing input frames, while the second one aims at predicting future frames. This method is fully end-to-end, as it only requires raw input frames to be trained. The addition of the second decoder implicitly encourages the encoder to produce latent codes yielding temporal information, which is useful for detecting temporal anomalies. For anomaly detection, the second decoder is discarded and only reconstruction error is used to compute the regularity score. This work is also proof that 3Dconvolutions are suitable for video anomaly detection.

More recently, both Morais et al. [START_REF] Morais | Learning regularity in skeleton trajectories for anomaly detection in videos[END_REF] and Rodrigues et al. [START_REF] Rodrigues | Multitimescale trajectory prediction for abnormal human activity detection[END_REF] proposed methods based on skeleton poses to predict the next state based on previous states. Just like [START_REF] Zhao | Spatiotemporal autoencoder for video anomaly detection[END_REF], the method introduced by [START_REF] Morais | Learning regularity in skeleton trajectories for anomaly detection in videos[END_REF] aims at both reconstructing current states and predicting the next ones, this time using Gated Recurrent Units (GRU). Conversely, [START_REF] Rodrigues | Multitimescale trajectory prediction for abnormal human activity detection[END_REF] aims at predicting next states from current ones and reconstruct current ones from next ones, consequently proposing a bi-directional architecture.

Abati et al. [START_REF] Abati | Latent space autoregression for novelty detection[END_REF] defined a regularity score based on surprisal and reconstruction error. They use a 3D convolutional autoencoder and an autoregressive model. This autoregressive model receives latent codes from the encoder. The autoregressive model is trained jointly with this autoencoder, and measures surprisal, while the autoencoder provides the reconstruction error.

While the method presented here does not use an autoregressive model, it was originally designed to work with one. The initial intent was to use this autoregressive model to transform the latent code of a video, in order to predict the latent code for future frames. Since latent codes generated by unconstrained autoencoders do not necessarily capture well temporality, the presented method was made to alleviate this problem, so that the latent codes would be easy-to-transform inputs for a future autoregressive model. However, the proposed method (without the mentioned autoregressive model) shows very interesting capability to detect short temporal anomalies that we study in detail in this paper, and still shows capability to detect spatial anomalies.

This approach results in a simple 3D-convolutional autoencoder trained with a slightly different objective function. In short, our objective function makes the autoencoder act like a bi-directional autoencoder, similarly to [START_REF] Rodrigues | Multitimescale trajectory prediction for abnormal human activity detection[END_REF].

C. End-to-end methods

We note that previous works making use of handcrafted features such as Optical Flow, HOF, HOG, skeleton poses, etc. [START_REF] Hasan | Learning temporal regularity in video sequences[END_REF], [START_REF] Fan | Video anomaly detection and localization via gaussian mixture fully convolutional variational autoencoder[END_REF]- [START_REF] Liu | Future frame prediction for anomaly detection-a new baseline[END_REF], [START_REF] Morais | Learning regularity in skeleton trajectories for anomaly detection in videos[END_REF], [START_REF] Rodrigues | Multitimescale trajectory prediction for abnormal human activity detection[END_REF] usually yield better results than endto-end approaches [START_REF] Hinami | Joint detection and recounting of abnormal events by learning deep generic knowledge[END_REF], [START_REF] Zhao | Spatiotemporal autoencoder for video anomaly detection[END_REF], [START_REF] Abati | Latent space autoregression for novelty detection[END_REF].

While these handcrafted features are very relevant for surveillance footage for various reasons, they do not generalize well on other types of video data, such as face cam videos. For example, optical flow tends to produce unreliable results on face cam videos, while skeleton poses cannot be applied in the same way. It can also be noted that these handcrafted features cannot be applied to other modalities such as sound and text, through which anomalous behavior can also be observed.

The usage of these handcrafted features also limits the amount of data the network has access to. While this helps by reducing the search space at first, it prevents the network to use crucial information that might have been lost in the process.

III. METHOD

In most contexts, detecting an anomalous human behavior comes down to detecting a temporal anomaly. In a semisupervised framework, the autoencoder-based approaches are well suited to detect abnormal behavior, since the reconstruction error is a particularly relevant scoring function. However, traditional autoencoding approaches are not necessarily well adapted for processing temporal information specifically. The model we propose is a regular 3D-convolutional residual autoencoder trained with an objective function that encourages the encoder to yield latent codes that capture normal temporal changes observed in stream inputs.

Since [START_REF] Zhao | Spatiotemporal autoencoder for video anomaly detection[END_REF] showed that a 3D fully convolutional autoencoder is a suitable basis, we also use it. We add residual connections to all convolutional layers (except the last one), like [START_REF] Abati | Latent space autoregression for novelty detection[END_REF] did. Like in [START_REF] Hinami | Joint detection and recounting of abnormal events by learning deep generic knowledge[END_REF], [START_REF] Zhao | Spatiotemporal autoencoder for video anomaly detection[END_REF], [START_REF] Abati | Latent space autoregression for novelty detection[END_REF], [START_REF] Chong | Abnormal event detection in videos using spatiotemporal autoencoder[END_REF], we design an end-to-end method, only using raw video frames as inputs. Similarly to [START_REF] Zhao | Spatiotemporal autoencoder for video anomaly detection[END_REF], the method we describe below implicitly encourages the encoder to produce latent codes yielding temporal information.

A. Volumes

In this paper, all the datasets we experiment on only contain one modality: video. Because we aim at detecting anomalous human behaviors, we built our method also considering multimodal datasets, like YouTube videos or EMO&LY [START_REF] Fayet | Emo&ly (emotion and anomaly): A new corpus for anomaly detection in an audiovisual stream with emotional context[END_REF]. In multi-modal datasets, we can for example have access to voice, which can allow us to better detect anomalous behaviors.

Video, voice and text can be aligned on the temporal axis but they don't usually share the same frequency, hence why we split our inputs. Inspired by [START_REF] Chong | Abnormal event detection in videos using spatiotemporal autoencoder[END_REF], we use the term volume to describe a section of a video. This way, all modalities can embedded and reshaped into a tensor with shape (N, dim modality ), then all modalities can be concatenated (on the last axis).

The main reason we proceed this way is to allow late fusion between modalities while keeping the size of the latent code low, which then requires less parameters, less memory and less processing power.

B. Objective function

Our method was designed to model the latent mechanisms that dynamically transform elements of our sequences over time. Since these mechanisms can be expressed as functions of time, we implicitly train our model to learn such mechanisms through a novel objective function.

Let LM be one of the latent mechanisms (e.g. walking), x be an input sequence (video in our case) and ∆ be a random value in [0, N -1]. We train our model to produce x ∆ such that:

x

∆ = LM (x 0 , x N -1 , ∆) (1)
More precisely, the encoder e is fed with a partial input, composed of two volumes: the first t frames (x 0 ) and the last t frames (x N -1 ), effectively producing two latent codes. The decoder d receives the result of a linear interpolation between these two latent codes, with a factor ∆. The autoencoder is then tasked to reconstruct x ∆ , only knowing x 0 and x N -1 .

Instead of using only one ∆, we can ask our model to output N volumes per training step. In this case, N ∆s are sampled linearly in [0, N -1]. We note that this requires significantly more processing power and memory than outputting only one volume at a time, and furthermore, it might not be suited for very large inputs.

In practice, the input x is split into N volumes of size t.

With e and d, the encoder and decoder respectively, let e n (x) be the latent code of the n th volume:

e n (x) = e(x n ), n ∈ [0, N -1] (2)
And let f n (x) be the interpolated latent code for the n th volume:

f n (x) = e N -1 (x) × n N -1 + e 0 (x) × (1 - n N -1 ) (3)
Then our objective function is defined by:

loss = 1 N N -1 n=0 ||d(f n (x)) -x n || 2 (4)
Fig. 1 represents how the model is trained using this objective function. Note that since this linear interpolation occurs on the latent codes, which are the outputs of several d(e n (x))

x 0 x 1 x N-2 x N-1 e e d d d d f 1 (x) f N-2 (x) d(f 0 (x)) d(f 1 (x)) d(f N-2 (x)) d(f N-1 (x))
e 0 (x) e N-1 (x) non-linear layers, it is able to represent more complex, nonlinear transformations in the input space.

C. Autoencoder

In this subsection, we detail the implementation of our autoencoder. We use 3-D convolutional residual blocks as described in [START_REF] Zhang | Fixup initialization: Residual learning without normalization[END_REF]. In this formulation of residual blocks, a single scalar is used at the end of the residual branch to multiply it. This formulation helps reducing the exploding and vanishing gradients problem and avoid using Batch Normalization. We bring one modification to this version, where we replace single scalar biases with vector biases usually found in convolutional networks. Both the encoder and the decoder use this structure, except that convolutions are replaced by transposed convolutions in the decoder. When performing downsampling (or upsampling), a convolution (or a transposed convolution) is added to the main branch to do this. Detailed implementation of a single residual block can be visualized in Fig. 2.

While we use rectified linear unit (ReLU) as the default activation function for most of the network, we find that it is necessary to employ a bounded activation function for the latent code. For the last layer of the encoder, the last ReLU is replaced by a sigmoid function or a hyperbolic tangent function. In the decoder, we observe better performance when the last activation function is completely removed.

Training schedule. We use a warmup schedule to train our model. The learning rate linearly increases each step until reaching the target learning rate after 1 epoch. We use it to avoid early-overfitting, as datasets like Subway contain a lot of motionless parts.

Data augmentation. To prevent overfitting even further, we apply random cropping/zooming. We first randomly select the size of our window. We then randomly position this window on the frame and apply cropping. The size of the window typically ranges between 90% and 100% of the original frame.

IV. EXPERIMENTS

We evaluate our method on six commonly used datasets for video anomaly detection, namely UCSD (Ped1 and Ped2) [START_REF] Mahadevan | Anomaly detection in crowded scenes[END_REF], Subway (Entrance and Exit) [START_REF] Adam | Robust real-time unusual event detection using multiple fixed-location monitors[END_REF], CUHK Avenue [START_REF] Lu | Abnormal event detection at 150 fps in matlab[END_REF] and ShanghaiTech Campus [START_REF] Luo | A revisit of sparse coding based anomaly detection in stacked rnn framework[END_REF]. Since datasets can widely differ from each others, we adapt some hyper-parameters for training and evaluate with different setups. Hyper-parameters are listed in supplementary materials.

While most previous works perform anomaly detection at the pixel or at the frame level [START_REF] Fan | Video anomaly detection and localization via gaussian mixture fully convolutional variational autoencoder[END_REF], [START_REF] Liu | Future frame prediction for anomaly detection-a new baseline[END_REF], [START_REF] Abati | Latent space autoregression for novelty detection[END_REF], we perform anomaly detection at the sequence level, where the length of each sequence is N * t. Since we aim to detect anomalous human behavior, we feel this is more appropriate.

In our experiments, we consider a sequence to be anomalous if the middle frame is anomalous, at the ground truth level. This approach lowered our results but we think this is more robust and less arbitrary than picking a specific percentage of frames.

A. Datasets 1) UCSD Pedestrian datasets.: The UCSD Pedestrian dataset is made of two parts: Ped1 and Ped2. In both parts, videos are taken from a stationary camera overlooking pedestrian walkways. Abnormal events are either the circulation of non-pedestrian objects (such as bikes and cars) or anomalous pedestrian motion patterns (such as walking on the grass).

UCSD Ped1 consists of 34 training videos and 36 testing videos. In addition to having frame-level labels for all 36 testing video, Ped1 also has pixel-level labels for 10 testing videos. All 70 videos have 200 frames. This dataset also contains a few corrupted frames.

UCSD Ped2 consists of 16 training videos and 12 testing videos. Ped2 has frame-level labels for all 12 testing videos. Each video has around 150 to 200 frames.

To our knowledge, the UCSD Pedestrian dataset is the most widely used dataset for video anomaly detection [START_REF] Hasan | Learning temporal regularity in video sequences[END_REF]- [START_REF] Zhao | Spatiotemporal autoencoder for video anomaly detection[END_REF], [START_REF] Rodrigues | Multitimescale trajectory prediction for abnormal human activity detection[END_REF]- [START_REF] Chong | Abnormal event detection in videos using spatiotemporal autoencoder[END_REF], [START_REF] Ravanbakhsh | Plug-and-play cnn for crowd motion analysis: An application in abnormal event detection[END_REF], [START_REF] Ravanbakhsh | Training adversarial discriminators for cross-channel abnormal event detection in crowds[END_REF].

2) Subway datasets.: The Subway dataset is made of two parts: Entrance and Exit. In both parts, videos are taken from a surveillance camera in a subway station. Authors provide timestamps for anomalies, defined as events that would interest a security guard such as entering the subway by the exit, or entering without payment.

Subway Entrance consists of a 1h36m long video and we use the first 18 minutes for training. These 18 minutes do not contain any anomaly. Subway Exit consists of a 43m long video and we use the first 10 minutes for training. These 10 minutes do not contain any anomaly.

This dataset does not directly contain frame-level labels, but rather timestamps at which abnormal events occur. We find that authors evaluating their models on this dataset often use different annotations as explained in [START_REF] Luo | A revisit of sparse coding based anomaly detection in stacked rnn framework[END_REF].

Multiple works seem to use labels introduced by [START_REF] Kim | Observe locally, infer globally: a space-time mrf for detecting abnormal activities with incremental updates[END_REF], as they all report the exact same number of events (66). We find that these labels lack accuracy, as some large sections of the video are labeled as abnormal while nobody appears on camera. We also find them to sometimes lack relevance, as these labels also include a lot of events categorized as loitering. We think considering events like loitering as abnormal to be subjective, as such consideration would not be useful if applied to the real world.

It is also worth noting that a person loitering closely to the camera can produce a significant amount of reconstruction errors, this is also true for people passing quickly under the camera. This makes these events easy to detect, and be categorized as anomalies because they would be flagged as false alarms otherwise. Unless we make an error of interpretation, we feel this is a case where the task seems to have been shaped for the method.

In our case, we manually define short windows around events like entering with no payment, or going back up the stairs. This makes our definition of anomalies very close to the definition of original authors [START_REF] Adam | Robust real-time unusual event detection using multiple fixed-location monitors[END_REF]. These labels are listed in supplementary materials.

In this paper, we compare our model on these three ways of defining labels (from the original authors [START_REF] Adam | Robust real-time unusual event detection using multiple fixed-location monitors[END_REF], from [START_REF] Kim | Observe locally, infer globally: a space-time mrf for detecting abnormal activities with incremental updates[END_REF] and ours). Since original authors only provide the frame at which anomalous events occur, we define short windows around these timestamps.

3) CUHK Avenue dataset.: The CUHK Avenue dataset contains 16 training videos and 21 testing videos. Videos come from a fixed camera at human height. Anomalies include throwing objects, loitering and running. Authors provide pixellevel labels for all testing videos. 4) ShanghaiTech Campus dataset.: The ShanghaiTech Campus dataset contains 330 training videos and 107 testing videos. Videos come from 13 different surveillance cameras and covers a wide spectrum of human-related anomalies. Authors provide both pixel-level and frame-level labels for all testing videos.

B. Metrics

Usually, in previous works using autoencoders, different metrics are used to compare the input and the output of the autoencoder in order to compute the regularity score. We investigate the usage of several metrics and compare them.

The metrics we evaluate include: Mean squared error (MSE), mean absolute error (MAE), negative Structural Similarity [START_REF] Wang | Image quality assessment: from error visibility to structural similarity[END_REF] (SSIM), negative Peak Signal to Noise Ratio (PSNR). MSE and MAE are used in two different ways: with and without interpolation 1 . When not using interpolation, our model behaves like a regular autoencoder, generating latent codes for each input volume.

Cosine similarity. A special note should be made for the cosine similarity (CS), as we do not use it to compare frames directly. Instead, we compute the cosine similarity between the interpolated latent codes, and the regular latent codes. Since we are performing interpolation on the temporal axis, we are only temporal anomalies (when using cosine similarity). We find this is particularly important in the framing of anomalous human behavior detection. It is also worth noting that a parallel can be drawn with [START_REF] Abati | Latent space autoregression for novelty detection[END_REF], where the latent code likelihood is used to determine surprisal.

C. Sliding window

To perform anomaly detection, we slide a window of size L = N * t, which is the total length of our input sequences. This sliding window is moved with a stride of 1. The sample evaluated by the sliding window is considered to be abnormal if the central frame of the sliding window is abnormal.

V. RESULTS

In this section, we first compare multiple measures to compute a regularity score. Secondly, we compare our results to the same autoencoder, without our objective function for training, on the UCSD Pedestrian 2 dataset. Thirdly, we compare our best results to the state of the art. Fourthly, we compare our models on the different ways to annotate the Subway Entrance dataset.

A. Ablation study 1) Choice of metric.: As stated before, we evaluate several metrics to compute our regularity score. We compare them in this section, using the area under the following curves (AUC) : Receiver Operating Characteristic (ROC) and Precision-Recall (PR). We also compute Equal Error Rate (EER) from the ROC curve and Average Precision (AP) from the PR curve.

As it can be seen in results we present in Tables I, II and, III, all regularity scores are fairly consistent with each others. We find we cannot select a single metric for all dataset, as these six metrics all have good theoretical basis and their ranking changes depending on the dataset. Additionally, ROC, PR, EER and AP mostly point a single metric for a given dataset, suggesting the pointed metric is a robust choice for the given dataset.

1 When using interpolation, -i is added after the initials. Results are presented in Table IV. These results show our objective function improves over using the usual MSE in our setup by a significant margin. Exit Entrance [START_REF] Hinami | Joint detection and recounting of abnormal events by learning deep generic knowledge[END_REF] 0.922 [START_REF] Zhao | Spatiotemporal autoencoder for video anomaly detection[END_REF] 0.923 0.912 0.771 [START_REF] Chong | Abnormal event detection in videos using spatiotemporal autoencoder[END_REF] 0.899 0.874 0.803 0.940 0.847 [START_REF] Abati | Latent space autoregression for novelty detection[END_REF] 0.954 0.725 Ours 0.790 0.933 0.823 0.714 0.932 0.806 [START_REF] Hasan | Learning temporal regularity in video sequences[END_REF] 0.810 0.900 0.702 0.807 0.943 [START_REF] Liu | Future frame prediction for anomaly detection-a new baseline[END_REF] 0.831 0.954 0.849 0.728 [START_REF] Luo | A revisit of sparse coding based anomaly detection in stacked rnn framework[END_REF] 0.922 0.817 0.680 [START_REF] Feng | Learning deep event models for crowd anomaly detection[END_REF] 0.925 0.630 [START_REF] Fan | Video anomaly detection and localization via gaussian mixture fully convolutional variational autoencoder[END_REF] 0.949 0.922 [START_REF] Sabokrou | Deepanomaly: Fully convolutional neural network for fast anomaly detection in crowded scenes[END_REF] 0.902 0.904 [START_REF] Ravanbakhsh | Plug-and-play cnn for crowd motion analysis: An application in abnormal event detection[END_REF] 0.957 0.884 [START_REF] Ravanbakhsh | Training adversarial discriminators for cross-channel abnormal event detection in crowds[END_REF] 0.968 0.955 [START_REF] Rodrigues | Multitimescale trajectory prediction for abnormal human activity detection[END_REF] 0.922 0.829 0.760 [START_REF] Morais | Learning regularity in skeleton trajectories for anomaly detection in videos[END_REF] 0.734 Ours 0.790 0.933 0.823 0.714 0.932 0.806 1 ShanghaiTech.

B. Comparison with previous works

In this sub-section, we compare our results with those of previous works. All reported results of previous works were directly taken their respective papers. We separate results from end-to-end methods from others, as end-to-end methods usually do not perform as well and because using end-to-end models has advantages (as explained above).

As most previous works evaluate their methods using the area under ROC curve (auROCc), we compare our results using this metric. Since we compute several regularity scores using several metrics, we only indicate the best one for each dataset.

For the Subway Entrance dataset, we use labels from [START_REF] Kim | Observe locally, infer globally: a space-time mrf for detecting abnormal activities with incremental updates[END_REF] to allow comparison. Results are presented in Table V.

C. Subway Entrance labels comparison

Lastly, in this sub-section, we compare the three different ways to annotate the Subway Entrance dataset we mentioned. For all three experiments, we use the same method, with the same hyper-parameters and weights. The only difference is the way the dataset is annotated.

We only report the best results for each way, which was MSE-i for the original labels and ours, and MAE-i for those introduced by Kim et al. [START_REF] Kim | Observe locally, infer globally: a space-time mrf for detecting abnormal activities with incremental updates[END_REF]. Results are presented in Table VI.

D. Sliding window

While using a stride of 1 to move our sliding window is more thorough, using a bigger stride can be necessary to allow real-time detection of anomalies, depending on the hardware. We perform an experiment with a stride of L on the Subway Entrance dataset (L being the total length of the input). We find that our anomaly detection results, using this bigger stride, are close to using a stride of 1, with the relative difference between metrics being between 0% and 4%, as it can be seen in table VII. Initially, to perform anomaly detection on the Subway Entrance dataset with a stride of 1, it takes about 6 hours and 32 minutes, while the duration of the dataset is about 55 minutes. When using a stride of L (L = 32), it takes about 11 minutes, which is well under the 55 minutes of the dataset, thus showing real-time can be achieved with our model.

VI. DISCUSSION

While we evaluate our method specifically on video, its design allows it to be applied to any type of temporal sequences. For example, by changing 3D-convolutions to 1D or 2Dconvolutions, we can apply it to text (with word embeddings), sound or MFCC, for instance.

Our model is only well suited for short anomalies. As our model takes inputs of length L, increasing this size also increases requirements in memory and reduces the likelihood of convergence. This makes it impractical for longer sequences (and longer anomalies). This is why we intend to experiment with an autoregressive model, as mentioned before, building on the basis laid out in this paper. Instead of predicting the present from the near past and the near future, this autoregressive model will aim at predicting the future on longer durations, hence allowing the detection of longer anomalies.

We also argue that our model is conceptually simpler, compared with most previous works such as GAN-based models [START_REF] Liu | Future frame prediction for anomaly detection-a new baseline[END_REF], [START_REF] Ravanbakhsh | Training adversarial discriminators for cross-channel abnormal event detection in crowds[END_REF], autoregressive models [START_REF] Abati | Latent space autoregression for novelty detection[END_REF], and others models such as [START_REF] Luo | A revisit of sparse coding based anomaly detection in stacked rnn framework[END_REF], [START_REF] Rodrigues | Multitimescale trajectory prediction for abnormal human activity detection[END_REF]:

1) Our model is not in an adversarial setup. While GANs might produce more detailed output, they can also require a significant amount of time to tune hyperparameters in order to have a stable training.

2) Our model only uses one encoder and one decoder, and the autoencoder only needs to be able to process temporal data. From there, it can take any shape or form, which makes it very adaptable. This makes our approach very versatile, as it can be applied to any type of temporal data, assuming they can be described using (1). 3) Our model will converge and yield consistent results without the usage of Batch Normalization [START_REF] Ioffe | Batch normalization: Accelerating deep network training by reducing internal covariate shift[END_REF], making training stable across multiple trials. In supplementary materials, we provide curves for the loss of multiple trials, using the same hyper-parameters and random initialization. Our comparison between reconstruction metrics and latent code cosine similarity shows that the complete model also detects spatial anomalies. This is useful in datasets like UCSD Pedestrian, where cars not only move faster than pedestrians, but also look very different. However, detecting a car (or any anomalous object) and detecting an anomalous human behavior are two distinct tasks and we aim at the later one. The regularity scores obtained from reconstruction error and cosine similarity can also be merged together, as in [START_REF] Abati | Latent space autoregression for novelty detection[END_REF] to provide a regularity score, thus exploiting surprisal and reconstruction error. We provide in supplementary materials results obtained this way.

All experiments were performed on a single GeForce RTX 2080 Ti, which has 11Go of memory. All training took between 3 hours and 12 hours. Time required to train and test our method is provided in supplementary materials. We did not observe significant changes in our results when increasing the stride used for our sliding window, this is why we two durations for testing, as increasing the stride lowers the required time to perform anomaly detection.

VII. CONCLUSION

In this paper, we propose a method for video anomaly detection that relies on representing normal behaviors as functions of time. Our main contribution is the conditioning of the autoencoder, using our objective function, to produce latent codes that can be interpolated in the temporal axis.

While we do not achieve state-of-the-art, we show multiple evidences of the benefits of using our architecture and objective function:

1) Using our objective function improves over using the usual MSE objective function, as shown in Table IV. 2) We obtain comparable results to the state of the art on all datasets, demonstrating its ability to generalize well, as shown in Table V. 3) When evaluating the cosine similarity on latent codes, we observe it is a reliable metric to compute the regularity score, as shown in Tables I, II and III. While cosine similarity between latent codes does not yield better results than reconstruction errors, it shows that these representations can be directly compared. In this paper, we explore and evaluate several metrics to compute the regularity score. Our results show that, depending on the dataset, some metrics can be clearly superior to the others, making this exploration necessary for future works.

Our results also show that choosing a metric for the regularity score is mostly straightforward on a given dataset. Our results also show that on some occasions, the ranking of those metrics will depend on the method used to rank them. Ultimately, if this happens, it will come down to the needs of the application to dictate how to rank these metrics.

We also reviewed datasets commonly used for video anomaly detection (UCSD Pedestrian 1 and 2, Avenue, Shang-haiTech, Subway Entrance and Exit). We also discussed about annotations used for Subway Entrance and provide new annotations that we feel are more appropriate for real world applications. Finally, we evaluated our method on these different annotations to provide a fair comparison.

Lastly, we showed that the stride can be increased if necessary, to provide a valuable speed-up, as the results obtained when using a stride of 1 and a stride of 32 for the sliding window are very similar (see Table VII).

VIII. FUTURE WORKS

The proposed approach opens up interesting leads for future works. Firstly, more work can be done on latent codes. We noticed that anomalous behaviors will often be auto-encoded to incoherent videos: for example, people going the wrong way on the Subway datasets will be decoded as going the right way (and moved instantly at the start of each volume). While we observe this incoherence from a semantic level, it often produces less reconstruction errors than more people having a normal behavior, hence the interest to find a better suited metric to detect these anomalies.

More complicated tasks are also worth investigating. For example, using different volumes as inputs, which would change the time between the start and the end of the video.

Also, latent codes produced by our method could be used in more complex models, like autoregressive models that would aim to predict the next volume, or multi-modal models using latent codes to reduce dimensionality. Finally, we think it could be worth trying to use our model in an adversarial setup, where the discriminator would help producing more detailed outputs.

Fig. 1 .

 1 Fig. 1. (a) Our autoencoder for one volume. (b) Our autoencoder used with latent code interpolation for N volumes. Weights are shared across volumes. e and d stand respectively for the encoder and decoder parts.

Fig. 2 .

 2 Fig. 2. Scheme of a single residual block.

TABLE I METRICS

 I COMPARISON FOR THE UCSD PEDESTRIAN DATASETS.

		Metric	ROC	EER	PR	AP
		MSE	0.773 0.273 0.825 0.824
		MAE	0.746 0.316 0.803 0.802
		MSE-i	0.775 0.301 0.832 0.831
	Ped 1	MAE-i 0.753 0.312 0.813 0.813
		SSIM	0.725 0.346 0.791 0.790
		PSNR	0.788	0.272	0.836 0.835
		CS	0.790	0.290	0.854 0.852
		MSE	0.873 0.236 0.984 0.972
		MAE	0.933 0.165 0.993 0.982
		MSE-i	0.869 0.209 0.974 0.973
	Ped 2	MAE-i 0.877 0.203 0.977 0.975
		SSIM	0.873 0.167 0.986 0.976
		PSNR	0.879 0.243 0.985 0.972
		CS	0.898 0.186 0.978 0.977
			TABLE II
	METRICS COMPARISON FOR THE SUBWAY DATASETS.
		Metric	ROC	EER	PR	AP
		MSE	0.791 0.261 0.554 0.551
		MAE	0.803 0.255	0.582 0.580
		MSE-i	0.798 0.268 0.540 0.536
	Entrance	MAE-i 0.806 0.245	0.558 0.556
		SSIM	0.802 0.275 0.564 0.562
		PSNR	0.792 0.259 0.564 0.562
		CS	0.725 0.313 0.403 0.400
		MSE	0.923 0.169 0.399 0.394
		MAE	0.932 0.144	0.439 0.433
		MSE-i	0.908 0.167 0.231 0.229
	Exit	MAE-i 0.919 0.164 0.318 0.317
		SSIM	0.916 0.153	0.468 0.462
		PSNR	0.924 0.168 0.402 0.394
		CS	0.919 0.161 0.277 0.268
			TABLE III
	METRICS COMPARISON FOR THE CUHK AVENUE AND SHANGHAITECH
		CAMPUS DATASETS.
		Metric	ROC	EER	PR	AP
		MSE	0.812 0.255 0.598 0.597
		MAE	0.799 0.284 0.607 0.605
		MSE-i	0.796 0.286 0.577 0.575
	Avenue	MAE-i 0.777 0.310 0.566 0.564
		SSIM	0.723 0.336 0.508 0.506
		PSNR	0.823 0.254 0.618 0.615
		CS	0.755 0.318 0.517 0.514
		MSE	0.692 0.353 0.629 0.628
		MAE	0.678 0.360 0.609 0.608
		MSE-i	0.688 0.364 0.620 0.619
	ShanghaiTech MAE-i 0.674 0.367 0.596 0.595
		SSIM	0.711 0.341 0.646 0.644
		PSNR	0.703 0.349	0.646 0.644
		CS	0.688 0.365 0.617 0.601
	2) Training without our objective function.: We compare
	our model trained with our objective function to the same
	model trained with the MSE objective function. All others
	hyper-parameters are the same, including the total number of
	training steps.

TABLE IV COMPARISON

 IV OF OUR MODEL WITH AND WITHOUT OUR OBJECTIVE FUNCTION FOR THE UCSD PEDESTRIAN DATASET.

		Method	ROC	EER	PR	AP
		AE	0.865 0.226 0.974 0.971
		IAE	0.933 0.165 0.993 0.982
				TABLE V
	RESULTS (ROC) ON ALL DATASETS. TOP: COMPARISON WITH
	END-TO-END METHODS. BOTTOM: COMPARISON WITH OTHER METHODS.
	Method	Ped1	Ped2	Avenue	ST 1

TABLE VI COMPARISON

 VI OF THE DIFFERENT WAYS TO ANNOTATE THE SUBWAY ENTRANCE DATASET, USING OUR MODEL. ONLY THE BEST RESULTS ARE INDICATED (SEE SECTION V-C).

	Labels		ROC	EER	PR	AP
	Original [14]	0.855 0.227 0.140 0.140
	Kim et al. [18] 0.806 0.245 0.558 0.556
	Ours		0.834 0.230 0.204 0.203
			TABLE VII
	RELATIVE DIFFERENCE OF ANOMALY DETECTION RESULTS ON THE
	SUBWAY ENTRANCE DATASET BETWEEN DIFFERENT STRIDES (1 AND L).
	Metric	Stride ROC EER	PR	AP
	MSE	∆	0%	0%	3% 3%
	MAE	∆	1%	3%	2% 1%
	MSE-i	∆	1%	2%	3% 2%
	MAE-i	∆	0%	0%	2% 0%
	SSIM	∆	1%	0%	0% 0%
	PSNR	∆	0%	1%	3% 4%
	CS	∆	0%	4%	0% 2%


come

Introduction: Masculinity and Politik

by Christopher Fletcher IRHiS (UMR 8529) CNRS / Université de Lille, F-59000 Lille, France What do we mean by politics [Politik]? The concept is extremely broad and includes every kind of independent leadership activity. We can speak of the foreign exchange policies of the banks, the interest rate policy of the Reichsbank, the politics of a trade union in a strike; we can speak of educational policy in a town or village community, the policies of the board of management of an association, and even of the political manoeuvrings [Politik] of a shrewd wife seeking to influence her husband. Needless to say, this concept is far too broad for us to consider this evening. Today we shall consider only the leadership, or the exercise of influence on the leadership, of a political organization, or in other words a state. [START_REF] Weber | Politics as a Vocation[END_REF] When Max Weber set out to consider Politik in the broadest possible terms at the start of a lecture delivered in 1919, it went without saying that almost every area of 'political' life would be monopolized by men. Despite the recent expansion of the franchise in post-revolutionary Germany to permit women to vote and to stand for election, both the 'politics' and the 'policy' of private and national banks and of management boards remained the monopoly of adult males, and trade unions and public office were overwhelmingly dominated by men. 2 Only in more local and more informal arenas, ones closer literally to home, such as educational policy, religious life and the domestic sphere itself, did Politik cease to be almost exclusively masculine.

For two millennia and more before Weber spoke, formal political authority in Europe was normally and ideally in the hands of adult males. Normally because this was most often the case and because this formed a norm whose regularity served as proof of its naturalness. Ideally because male authority was felt to be the ideal and female authority the aberration. This is not to say that women at all social levels did not exercise informal authority and especially 'power through the family', much like Weber's 'shrewd wife'. [START_REF] Mcnamara | The Power of Women through the Family in Medieval Europe: 500-1100[END_REF] Nor is it to set aside the numerous occasions where women have exercised formal political authority: in medieval and early modern Europe, for example, in which women frequently wielded authority as independently influential noblewomen, as queens regent or as queens regnant. [START_REF] Kowaleksi | Femmes, pouvoir et société dans le haut Moyen Âge[END_REF] All the same, female power, despite its ubiquity, was perceived until very recently as a kind of a recurrent contradiction, a paradox which refused to go away. 5 In particular, the norm and the ideal that formal political power would be masculine created vulnerabilities for powerful women which adult male rulers did not experience. This state of affairs was arguably intensified by the gradual process of formalisation which Weber sketched out influentially in the meat of his lecture. As Weber tells this story, the 'means of administration' and particularly the monopoly of legitimate violence which were now in the hands of the state had once been distributed amongst many different actors and groups, from powerful nobles to city states. [START_REF]For this coinage see Weber[END_REF] These 'means' had first been gradually absorbed by kings and princes, in particular by assuming the role of the agents of public authority, the authority of the res publica or common good once claimed exclusively by Roman emperors. According to Weber, monarchs then in turn found their power gradually sapped by the administrators they needed to govern such an extensive and elaborate apparatus. These administrators were alienated from the means of administration at their disposal, in the sense that, like the functionaries of a large company, they managed these resources but did not own them. The 'state' in its full form thus came into being: an ensemble of administrative, fiscal and judicial apparatus which different groups might seek to control. This was 'politics' in Weber's narrow sense: the competition for control of formal institutions possessed of a monopoly of legitimate violence. [START_REF]Weber's powerful theorisation of an ideal type of 'politics' defined by its dependence on an equally idealised 'state' was very much a product of its time[END_REF] These developments also had significant gendered consequences which Weber did not identify. A recurring theme in European politics between the Roman Empire and the contemporary world is the move by different political actors to mobilize the res publica, the common good or the public weal. [START_REF]De Bono Communi: The Discourse and Practice of the Common Good in the European City (13 th -16 th centuries)[END_REF] Kings and princes as much as city administrations invoked their public authority, in the sense of their authority deriving from their role as the protectors of the welfare of the people, to justify their rights to administer justice, to legislate, to raise taxation and to wage war. This did not mean that all rights of justice, legislation, taxation and violence were legitimated in this way, far from it, but it did introduce a form of political authority which was significantly different from power justified by private right, hereditary status or custom. The more public authority was perceived as public, in the sense of serving the common good of the people, the less acceptable it was that informal influence or even the rights of particular individuals or groups should play a role in policy or politics. One central aspect of these developments which historians have not explored is that government in the name of the common weal was more overwhelmingly masculine than any form of rule that had come before it. [START_REF]Although in the context of the French revolution, see D. Outram, The Body and the French Revolution: Sex, class and political culture[END_REF] Women's informal influence and even formal political authority continued, of course, but because the political authority of the 'state' was based not on individual status, custom or collective privileges but on the absolute good of the res publica, these forms of female power, even whilst they continued, were now perceived as an even more uncomfortable aberration. For centuries, this was not perceived as a difficulty: the only problem was that women did still ostensibly wield power, and ways had to be found to justify these states of exception. Only in the eighteenth and nineteenth centuries did the exclusion of women from formal politics begin to seem unacceptable to some. The slow admission of women into electoral democracy was perceived as the cure for this malady, yet it is clear that in the vast majority of modern Western democracies it has still not proved effective. 'Politics' conceived of as the politics of the state may no longer be ideally or even exclusively the preserve of men, but it remains an overwhelmingly masculine domain. [START_REF] Pateman | The Disorder of Women: Democracy, feminism and political theory[END_REF] It is in this context that the present 'handbook' seeks to make a contribution. The chapters in this book explore from multiple angles and over a long period the mechanisms by which the maleness of formal political power has been established and maintained across successive generations. They examine how these mechanisms have marked European political culture over the long term, and still marks it today. It is clear that to pursue these issues we cannot, like Max Weber, begin by limiting ourselves to the kind of formal political institutions familiar from the European nation states of the past two or three centuries. If politics is the struggle to exercise leadership over 'a political organization, or in other words a state', then an analysis of masculinity and political culture could confine itself to the analysis of the influence of gendered ideas and values over the kind of politics which takes place in representative institutions or within the apparatus of the state. This is certainly one legitimate approach to the study of masculinity and political culture, and many contributions to the present volume take it as their central theme. [START_REF] Verjus | Le bon mari: Une histoire politique des hommes et des femmes à l'époque révolutionnaire[END_REF] Nonetheless such a line of analysis quickly becomes problematic if it is pursued exclusively. In pre-industrial contexts especially, where the means of coercion were less effective, where communications were not as developed, and where judicial and fiscal machinery required the cooperation of non-state agents to work, the study of politics cannot be limited to the study of the state. [START_REF]For crucial developments in the emergence of the 'state' between the thirteenth and the fifteenth century, see[END_REF] To understand the interaction between the maleness of power and the nature of politics over the longue durée, we need to begin with a broader definition of political culture than has so far been applied in studies of masculinity and politics in the relatively recent past.

Nor is the need for a broad conception of 'politics' limited to the study of the pre-modern past. It is clear that even when contemporary Europe is in question, a state-based approach to politics is not sufficient for an effective analysis of political authority and gender. Critics of modern liberal democracy on left and right, from Weber and Carl Schmidt [START_REF] Schmidt | La logique des champs' in his Réponses[END_REF] to Pierre Bourdieu 14 and Pierre Rosanvallon [START_REF] Rosanvallon | La contre-démocratie: La politique à l'âge de la défiance[END_REF] have noted the inadequacy of any vision of politics which restricts itself to the 'occasional' politics of the ballot box, to the institutions of electoral democracy or the activities of the modern state. [START_REF] Weber | Politics as a vocation[END_REF] It is thus all the more necessary to take a broad view of political culture which takes in not only the state-centred vision of politics put to the fore by Weber, but also all those areas of Politik which he identified but chose not to discuss. After all, one aim of the earliest studies of gender history was to disrupt the division between public and private which placed men in the former sphere and women in the latter. [START_REF] Davidoff | Family Fortunes: Men and Women of the English Middle Class, 1780-1850[END_REF] It thus seems only natural to turn around Weber's casually sexist aside about the scheming wife in order to insist that gender relations in the household are indeed an important kind of politics, and that any global vision of the political culture of a given society must include them also. [START_REF]For recent explorations of the relationship between masculine domestic and political virtue in early modern England[END_REF] Gender historians and political historians have often had an uneasy relationship in recent decades. It remains the case both that gendered approaches to political history have had difficulty finding acceptance within that broader field, and that historians of gender have proved wary of straying into political history. Certainly, if one compared the aims and methods of gender historians and political historians before the 1970s, it would appear difficult to reconcile them. Yet it is true that even as gender history was emerging, so political history was gradually undergoing a transformation which could be traced back to initiatives begun some decades before. [START_REF]For a short survey of these developments[END_REF] Prosopographical methods brought the study of politics closer to social history than it had ever been, consciously distancing modern research from the excessively institutional and legal perspective of earlier writers. Already by the 1980s, political history and gender history were not so distant in their methods. The growing andPolitical Culture in Europe (London: Palgrave Macmillan, 2018), pp. 1-16. DOI: 10.1057/978-1-137-58538-7 interest in cultural history touched both sub-disciplines at the same times and in a similar fashion. The concept of 'political culture' in particular has made it possible to push back the boundaries of political history to cover not only the political thought found in learned and not-so learned treatises, but also the unspoken assumptions and expectations of different social groups about how government ought to work. [START_REF] Carpenter | Introduction: Political Culture, Politics and Cultural History' in The Fifteenth Century IV: Political Culture in Late Medieval Britain[END_REF] The time thus seems ripe to bring gender history and political history together, taking both politics and gender equally seriously.

Reasons of good practice and the state of current research thus encourage a broad definition of politics and a long range of study. It is for these reasons that a handbook dedicated to masculinity and political culture includes not only studies of masculinity in representative institutions and the gendered nature of the expansion of the electoral franchise, for example, but also studies of the action of class and authority in the life of a judge and 'closeted' homosexual in late nineteenth-and early twentieth-century Strasbourg, or of the significance of gendered notions of honour and right action for the elites of fifteenth-century Spanish towns. 21 In seeking to understand how the normal and ideal maleness of power has affected European political culture over the very long term, the contributors to this volume have ranged widely beyond the state, all whilst keeping to Weber's central concern with 'leadership' and with 'influence'. One result is that the present volume is avowedly a 'handbook' and not a 'textbook'. It aims to offer a wide-ranging selection of specialist studies, designed to be accessible to the non-specialist, but privileging access to the best recent research.

What might perhaps surprise specialist readers more than this broad conception of political culture is the use of the term 'masculinity'. 'Masculinity' is one of those dangerous words for the researcher which combines both a technical usage and broad, often unacknowledged modern associations. 22 Both in the popular psychology of the modern day and in much of the specialist literature, it is common to consider that adult males have a need to 'prove their masculinity' by aggressive action, and above all by sexual activity. [START_REF] See Esp | Manhood in the making: Cultural concepts of masculinity[END_REF] The contributors to this volume, although many of them do consider sexuality, have not found this to be a helpful model for understanding the cases they consider. Instead, they are closer in their methodology to the sociologist Raewyn Connell, whilst adapting and refining her work for application to societies and cultures which are in some cases very distant from the contemporary, Western, Anglophone case studies which she considers.

Connell has been widely influential, perhaps especially amongst historians, because of the usefulness of the pluralising conception of 'masculinities' first developed in her works. Thinking of 'masculinities' instead of 'masculinity' serves to catch the way in which the fact of being a man will not be lived in the same way by a factory worker, for example, than by an office clerk, all whilst accepting certain commonalties of male bodily experience. 24 For historical purposes, however, Connell's analysis requires some adaptation, not least because her use of the concept of 'masculinities' brings together several phenomena which are not analytically identical. These phenomena can usefully be distinguished as different understandings of what 'a masculinity' is. First, 'a masculinity' might be said to refer to a set of norms, values or forms of behaviour which are emphatically linked to acting 'manly' or 'like a man'. Such a 'masculinity' asserts its compulsory and ideal nature by seeking to link a set of social norms or behaviours to deep-running cultural and linguistic assumptions. When somebody asserts that such-and-such an action is 'manly' they are not only making a judgement in accordance with shared social norms, they are also drawing on a set of accepted uses of the word 'manly' in the language they use and the culture they share with their interlocutors. In Europe, many of these accepted uses stretch back into ancient Roman language and culture, [START_REF] Dumas | Sire, uns hom sui : Transgression et inversion par rapport à quelle(s) norme(s) dans l'histoire des masculinités médiévales?[END_REF] and it is only in relatively recent times that sexual activity has come to be seen as the defining quality of 'masculinity'. In the Latin language, to act 'viriliter' is to be strong and vigorous, and more specifically to stand one's ground and not retreat in a combat situation. 26 These values might be invoked in a real battle, or metaphorically in a mental attitude which shows steadfastness or constancy. The same values lie behind the multiple referents of the Latin 'virtus', which refers not only to what we call virtue, but also to steadfastness which is both physical and psychological, all with a clear reference to the fact of being a 'vir' (a 'man'). [START_REF] For 'virtus' | Roman Manliness: Virtus and the Roman Republic[END_REF] The use in European vernaculars of words such as 'manly', 'manhood' and equivalent words including 'virtue' has long been heavily influenced by this common cultural heritage. Certainly, the range of potential applications of such concepts is very large. They might be stretched, for example, to cover the qualities of moral virtue, [START_REF] Kuefler | The Manly Eunuch: Masculinity, Gender Ambiguity and Christian Ideology in Late Antiquity[END_REF] or even credit worthiness. [START_REF] Shepard | Manhood, credit and patriarchy in early modern England, c. 1560-1640[END_REF] Nonetheless, these values are not infinitely malleable. It would be comic, even ungrammatical, to clean one's teeth like a man, but to fight or to suffer adversity like a man seems linguistically uncontroversial. Just so, the deep running associations attached to manhood in European culture permit certain forms of behaviour to be more easily denoted as fitting for adult males than others.

Second, and as a variant of the first approach, a 'masculinity' might also be a set of characteristics or behaviours routinely associated with males in a positive or negative fashion, although without this necessarily being linked to all men. Fatherhood is thus 'a masculinity' without it being experienced by all men. The sexual excess and other negative characteristics held to characterise young men in medieval culture can also be considered to be a 'masculinity'. [START_REF] Moss | An Orchard, a Love Letter and Three Bastards: The Formation of Adult Male Identity in a Fifteenth-Century Family' in What is Masculinity[END_REF] Slightly paradoxically, from this point of view even 'effeminacy' is a masculinity, since it is a set of characteristics which can only meaningfully be applied to a man. Third, 'a masculinity' might also denote a set of norms, ideals or practices which an historian or sociologist can identify as being either exclusively or usually applicable to adult males, even though the social actors in question are unaware of this and might even deny it. Practices like blood brotherhood in medieval Iceland concern only males, but this is nowhere explicitly stated. 31 The individuals who assumed the role of the grey-suited technocrat or 'professor' in post-war Italian politics were all men, and yet their political self-presentation eschewed overt identification between their political persona and their masculinity. 32 Yet from an analytical point of view the figure of the chess-playing professor is just as much a masculinity as, for example, the emphatically masculine military self-presentation adopted by Nazi politicians in the early 1930s. 33 Indeed, it is a characteristic of many masculinities to deny that this is what they are, perhaps especially in politics.

Finally, 'a masculinity' might be a set of ideals, behaviours or practices which is implicitly associated with adult maleness in a particular group or period without this always being explicitly linked to manhood, although such a link was recognised in certain circumstances. In some contexts, it is the unspoken nature of these norms which might enable, for example, a patrician member of the Victorian House Commons to identify expressions of emotion on the part of a working class MP as unmanly, whereas the latter believed himself to be demonstrating manly authenticity. [START_REF]See further below, Griffin. Cf. the ambiguous role of tears and emotional expression in the seventeenth century, discussed by B. Capp[END_REF] In other contexts, such norms could be enunciated explicitly. In early modern England, for example, anxieties generated by differing norms of masculinity in different social groups created a market for manuals of correct comportment which enable outsider males to 'pass'. [START_REF] Shepard | Meanings of Manhood in Early Modern England[END_REF] Didactic or moralistic texts might also seek to rectify masculine comportments which they took to be lax or corrupted, although in this case we have to be careful to assess just how widely accepted their strictures might be. [START_REF] Fletcher | Manhood, youth and politics[END_REF] This final kind of 'masculinity' thus lies somewhere between the first emphatic variety of masculinity and our third category of masculine norms or practices which we can identify as characteristically male without this being acknowledged by contemporaries. Instead, this final variety of 'masculinity' denotes a 'habitus' which is known to be characteristic of men in a given society or social group, although this is not always made explicit. 37 The contributions to this volume thus explore masculinity taken as a broad field of study whilst permitting the authors to treat phenomena which take in any or all of these different approaches to 'a masculinity' as their subject matter allows. What brings them together is less a single theoretical viewpoint and more a common concern with the interaction between competing masculinities and changing forms of political culture. 38 It is this ecumenical approach which has made it possible to assemble in one volume studies of masculinity and political culture in contexts stretching from ancient Rome to the contemporary West. Read as a whole they make it possible to perceive broad developments without the implicit teleology which has marked recent attempts to trace the history of particular cultural phenomena such as 'virilité' from antiquity to the present day, [START_REF]Histoire de la virilité[END_REF] or the tendency to excessive schematization which has dogged, for example, attempts to periodize the history of masculinity in the British Isles. [START_REF] For A Critique | Man's Estate: Landed Gentry Masculinities, 1660-1900[END_REF] Instead what emerges is a slowly evolving palette of concepts and practices linked to ideal or deviant manhood which have played different roles in a broad variety of European political cultures. Sometimes appeals to emphatic or explicit masculinities have proved crucial in policing the boundaries of acceptable political activity and in particular its normal and ideal association with adult males. At others, the non-explicit nature of gendered practices has allowed these same boundaries to shift as pragmatic considerations dictated, admitting women and even eunuchs into the circle of masculine power.

The essays contained in this handbook each consider how, in different periods, gendered concepts and gendered practices have impinged on the exercise of political authority and influence. The volume opens with two contributions which consider the complex relationship between ideals of male patrician comportment and the broader culture of masculinity in the Roman Empire before and after Christianisation. For Cyril Dumas, the sexualised symbolism and phallic imagery which were ubiquitous in pagan society should not be seen as erotic in purpose, but rather as the flipside of a culture in which patrician men's claims to authority were conditional on the control of their bodies and on the subordination of sexual activity to reproduction. Mathew Kuefler continues this story into the later Roman Empire and past its fall in the West. Roman political and masculine values which had been revitalised and redirected by Christianity now found themselves under renewed pressure from the more overtly military masculine ideals of barbarian invaders and increasingly by formerly barbarian members of the Roman army. This revived tensions between the need to demonstrate status by conspicuous display and the need to show a hard, simple, manly exterior. Both Dumas and Kuefler consider the often difficult interaction between masculine ideals and political norms in a society which closely linked the virtues of public life to the characteristics of an ideal adult male.

The overt linkage between masculinity and political power was not always so straightforward, however. In exceptional circumstances, in late antiquity or in the Middle Ages, gendered norms could be overcome to permit individuals to assume forms of authority from which they would normally be excluded. In different contexts, social practices essential for the exercise of political authority were not perceived as especially masculine even though they were heavily associated with being a man. Georges Sidéris considers how, in the late fourth century, the eunuch Eutropius was able, as a result of political circumstances, to overcome the normal exclusion of eunuchs from military command to lead a successful campaign in 396-7 and to attain the consulship in 399. Only retrospectively, after Eutropius's disgrace, did it become legally impossible for a eunuch to attain the summits of political power. Laurence Leleu, meanwhile, considers how women who assumed positions of power in the tenth-century Ottonian empire, such as the Empress Theophano, could be praised without difficulty and without a sense of inversion, ascribing them the ideal virile qualities of male rulers. Accusations of soft effeminacy could be used just as effectively against male political actors. Finally, Pragya Vohra examines the nature of Icelandic kinship groupings which, in a society without any formal governmental institutions, were one of the primary means by which political actors could achieve their ends. In contrast to the late Roman or Ottonian empire, structures such as blood brotherhood, while overwhelmingly concerning relationships between men, were not perceived as such. In Iceland, the maleness of political power did not play the same kind of ideological role which it did in early medieval continental Europe.

In the political cultures of central and later medieval Europe norms of masculinity continued to provide a powerful group of themes with which political actors, whether they be churchmen, townsmen or nobles, could positively present their own actions or undermine the actions of their opponents. Matthew Mesley explores the ambiguous position of the bishops of twelfth and thirteenth century Germany with regards to norms of political authority. In early work on medieval masculinity, churchmen tended to be treated as fundamentally different from laymen, on account of their theoretical exclusion from sexual activity. Only recently has attention been drawn to how clerics had much in common with their social equals amongst the laity. This article extends this investigation to elite churchmen, focussing on the theme of masculine fidelity in the career Adolf of Altena, bishop of Cologne. Hippólita Rafael Oliva Herrer examines how, in the Iberian peninsula from the later thirteenth until the fifteenth century, ideals of masculinity which had initially been set out most clearly in clerically authored guides for rule known as 'mirrors for princes' increasingly came to play a role in the definition of good rule, even at the level of the ideal behaviour of the mayor of a town. Urban leaders could gain legitimacy, notably in comparison to noble leaders, by demonstrating self-control and the upright and honourable behaviour of an established householder. Finally, Hugo Dufour considers the contrasting ways in which the leaders of different factions in the political upheavals of the late fourteenth-and fifteenth-century France managed the relationship between their own masculinity and authority, or used gendered terms to attack their opponents. Burgundian propagandists made use of topoi of excessive, warlike masculinity or sexually sinful effeminacy to smear their opponents, leaving for posterity the image of the Louis, duke of Orléans as a luxurious dandy. The austere tomb monument he commissioned presents his manhood very differently, in contrast to the magnificent but traditional manliness projected by the tomb of his enemy, John the Fearless.

Early modern historians, and perhaps especially those working on the British Isles, have long included gender and more recently masculinity in their account of society. The contributions of Susan Doran and Ann Hughes build upon this work with two essays focused on specifically British examples which consider how different masculinities negotiated with one another in political culture in the sixteenth and seventeenth centuries. Susan Doran argues that although the reigns of Edward VI, Mary I, Elizabeth I and James I all put conventional ideas of masculine rule under pressure in different ways -first through the rule of a minor, then a queen regnant with an absentee husband, then an unmarried woman, and finally a man who often did not conform to gender norms of masculinity -the political culture of the day adapted to accommodate this variety, even if Charles I later felt the need to restore the image of monarchical masculinity. Ann Hughes, meanwhile, considers how the civil war both enhanced and placed under pressure existing conceptions of male rule. The war disrupted the perception of the king as father, but added new charge to the linkage between elite masculinity and public office, on the one hand, and the right to bear arms, on the other. She considers how both 'cavalier' and 'roundhead' models of political activism developed, sometimes in explicit contrast to the growing possibility for female agency which had emerged in the religious and political upheavals of the 1640s and 1650s. Both Doran and Hughes suggest the broad continuities in gendered ideology despite the political upheavals of this period. It seems less that social change led to a crisis of masculinity, and more that political and social upheaval made explicit and implicit norms of masculine authority all the more valuable in the attempt to establish political legitimacy. Ideals of manhood in the eighteenth and nineteenth centuries in some ways had much in common with their pre-modern forebears. Vigour, honourable conduct and self-control continued to be associated with ideal manhood, whilst effeminate changeability, sexual excess and luxury were still portrayed as the roots of political vice. Nonetheless, behind these deep continuities, there were also profound changes, and, on occasion, explicit attempts to question the established gender order. On the one hand, the shocks of the late eighteenth and early nineteenth centuries, from political revolutions to industrialisation, could provoke a critique of traditional gender values; on the other, it could equally well lead to their reassertion.

Matthew McCormack and Henry

French consider the interplay of these transformations in Britain eighteenth and nineteenth-century Britain, exploring how large scale political and cultural shocks had an impact on the personal and political lives of individual men. McCormack takes a synthetic perspective, considering how historians have begun to integrate masculinities into their analysis of the political culture, from political representation, to the history of the body, the emotions and material culture. Henry French focuses this account through a study of the career of one politician, William Windham (1750-1810). During his own lifetime and in the immediate aftermath of his death, Windham's reputation was high, and he was celebrated for his commitment to his own vision of the right course of political action, even when this led him to disconcerting political choices and changes of position. With the publication of his personal diary in the mid-nineteenth century, this reputation was drawn into question, with the revelation of his vigorous selfexamination, hypochondria, and doubts about his own abilities. French reconsiders 'weathercock Windham's' posthumous fortunes to portray a man who was, in part, a victim of the changing focus of nineteenth century ideals of masculinity, away from authenticity and towards self-control.

Acceptance and submission to ideals of masculine authority, leading to a recurring sense of failure and inadequacy, were not the only possibilities available in the late eighteenth and nineteenth centuries. In the wake of the political, social and economic transformations of these years, it was also newly possible to perceive the gender order for the ideological construction that it was. Opposition and subversion brought with them consequences which were sometimes political, sometimes social. Victoria Russell considers the development of the Romantic critique of norms of masculinity and femininity, which although at first highly politicised, found its longer term success in the quietist form of social and educational reform, insisting on the gender-neutral nature of the majority of human intellectual characteristics. Allison Goudie, meanwhile, considers the ambiguous reception of Antonio Canova's statue of Ferdinand IV of Naples, commissioned in 1800, widely interpreted as 'Ferdinand IV in the guise of Minerva'. As such, it encodes a critical stance towards the involvement of Ferdinand's wife, Maria Carolina, in government. Even traditional conceptions of masculinity could be used to question established authority in circumstances of profound political and social upheaval.

Sexuality, too, opened up the possibility of distance from and criticism of the established political order, even when this critique remained latent. Régis Schlagdenhauffen thus considers the personal diary of the Franco-German jurist Eugène Wilhelm (1885-1951). Wilhelm exercised the authority of a judge, condemning homosexuals amongst other deviants, all whilst continuing homosexual relationships, sometimes over several decades, with men who might be considered to be members of the underclass. His diary is a further witness to the ambiguous interplay between sexuality and political authority. Dominic Janes notes how a variety of Bloomsbury intellectuals, and in particular Lytton Strachey and John Maynard Keynes, were able to distance themselves from contemporary masculine norms to critique performances of masculinity by prominent public figures, notably the participants in the peace conferences in the aftermath of the First World War.

By the early twentieth century, the criteria by which masculinity was defined were no longer something that could be taken as given. This led to phenomena of critique, but also of reactionary reassertion could itself be innovative. Christopher Dillon describes how, during the Nazi takeover of 1930 to 1934, there was a difficult and hesitating interaction between the controlled, authoritarian masculinities of traditional conservatives and the violent, beer hall masculinity of emergent National Socialism. He reveals that although propaganda portrayed this interaction as a simple victory of Nazi virility over Weimer emasculation, the development of Nazi masculinity during this period was actually more hesitant and internally conflictual than might at first appear. Nazi self-presentation had to struggle both with the homosexuality of several of its prominent members within an overtly homophobe movement, and with the non-correspondence between Hitler's dandyish lifestyle and the manly austerity of his public image.

The two final contributions to the volume consider the interplay between norms of masculinity and changing forms of political culture up to the present day, considering how masculinities affected the ability to be an effective political agent. Ben Griffin examines the extent to which the 'gentlemanly' masculinity which had enabled professional and middle class men to be absorbed into the parliamentary political class without excessive friction in the late nineteenth and early twentieth centuries stood in the way of the later integration of women and working class men. He considers how far parliamentary culture succeeded in adapting to these changes, focusing on the problems which MPs, and especially male Labour MPs, experienced in navigating between the masculine ideals of their supporters and those of the Houses of Parliament. Finally, Stephen Gundle considers the continuing competition of different masculinities, still attendant on the overwhelmingly male-dominated nature of politics, in Italy from the Second World War to the 1990s. Gundle places the particular masculinity of Silvio Berlusconi in historical perspective, examining how the post-war model of a competent, business-like political masculinity was nonetheless still haunted by the ghost of Mussolini's hyper-masculinity. The collapse and transformation of the political culture which supported these conflicted masculinities casts new light both on Berlusconi's own contradictory masculinity and the significance of his rise, and on the importance of gender and masculinity for the study of modern Italian politics.

In the case studies brought together in this volume, stretching over two millennia, different political cultures have interacted in different ways with a wide variety of norms associated in whole or in part with adult maleness. Sometimes these norms have been deployed for political ends, sometimes they have structured politics without the participants necessarily being aware that this was happening. In certain circumstances masculine norms have been critiqued or left aside for political purposes, at other moments they have been re-asserted for political ends. What emerges above all is that masculinity has constantly played an important role in the configuration of political life, from the Roman Empire to the present day. This volume shows how historians who concentrate on the intersection between masculinity and political culture can make a vital contribution to our understanding of both the history of gender and the history of politics.

  Institutional deposit of pre-copy-edited version. Please consult and cite: Christopher Fletcher, 'Introduction: Masculinity and Politik' in Christopher Fletcher, Sean Brady, Rachel E. Moss and Lucy Riall, eds., The Palgrave Handbook of Masculinity and Political Culture in Europe (London: Palgrave Macmillan, 2018), pp. 1-16. DOI: 10.1057/978-1-137-58538-7

  Institutional deposit of pre-copy-edited version. Please consult and cite: Christopher Fletcher, 'Introduction: Masculinity and Politik' in Christopher Fletcher, Sean Brady, Rachel E. Moss and Lucy Riall, eds., The Palgrave Handbook of Masculinity and Political Culture in Europe (London: Palgrave Macmillan, 2018), pp. 1-16. DOI: 10.1057/978-1-137-58538-7

  Institutional deposit of pre-copy-edited version. Please consult and cite: Christopher Fletcher, 'Introduction: Masculinity and Politik' in Christopher Fletcher, Sean Brady, Rachel E. Moss and Lucy Riall, eds., The Palgrave Handbook of Masculinity and Political Culture in Europe (London: Palgrave Macmillan, 2018), pp. 1-16. DOI: 10.1057/978-1-137-58538-7

  Institutional deposit of pre-copy-edited version. Please consult and cite: Christopher Fletcher, 'Introduction: Masculinity and Politik' in Christopher Fletcher, Sean Brady, Rachel E. Moss and Lucy Riall, eds., The Palgrave Handbook of Masculinity and Political Culture in Europe (London: Palgrave Macmillan, 2018), pp. 1-16. DOI: 10.1057/978-1-137-58538-7

  Institutional deposit of pre-copy-edited version. Please consult and cite: Christopher Fletcher, 'Introduction: Masculinity and Politik' in Christopher Fletcher, Sean Brady, Rachel E. Moss and Lucy Riall, eds., The Palgrave Handbook of Masculinity and Political Culture in Europe (London: Palgrave Macmillan, 2018), pp. 1-16. DOI: 10.1057/978-1-137-58538-7

  Institutional deposit of pre-copy-edited version. Please consult and cite: Christopher Fletcher, 'Introduction: Masculinity and Politik' in Christopher Fletcher, Sean Brady, Rachel E. Moss and Lucy Riall, eds., The Palgrave Handbook of Masculinity and Political Culture in Europe (London: Palgrave Macmillan, 2018), pp. 1-16. DOI: 10.1057/978-1-137-58538-7

  Institutional deposit of pre-copy-edited version. Please consult and cite: Christopher Fletcher, 'Introduction: Masculinity and Politik' in Christopher Fletcher, Sean Brady, Rachel E. Moss and Lucy Riall, eds., The Palgrave Handbook of Masculinity and Political Culture in Europe (London: Palgrave Macmillan, 2018), pp. 1-16. DOI: 10.1057/978-1-137-58538-7


Keywords:

Lack of diversity of the input data

The New York Times, "Many Facial-Recognition Systems Are Biased, Says U.S. Study", By Natasha Singer & Cade Metz,. 2019 7

Algorithmic bias

Lack of diversity of the team 8

Data privacy

Quartz, "Using a fitness app taught me the scary truth about why privacy settings are a feminist issue". R. Spinks, 2017. Standards for data sharing

11

Raw data

Derived data

Results

Raw data

Data preparation

Derived data

Data integration

Analysis

•

  Variability in single-lab studies ○ Across subjects ○ Across scans • Variability in single-lab studies ○ Across subjects ○ Across scans • Variability in multi-lab studies ○ All of the above plus ○ Across machines ○ Across sites ○ Across acquisition protocols Levels of variability • Variability in single-lab studies ○ Across subjects ○ Across scans • Variability in multi-lab studies ○ All of the above plus ○ Across machines ○ Across sites ○ Across acquisition protocols • Variability in data integration studies ○ All of the above plus ○ Across preparation protocols ○ Across analysis protocols • Variability in single-lab studies ○ Across subjects ○ Across scans • Variability in multi-lab studies ○ All of the above plus ○ Across machines ○ Across sites ○ Across acquisition protocols • Variability in data integration studies ○ All of the above plus ○ Across preparation protocols ○ Across analysis protocols

Image credits: Sculpture by Malin Bjornsdotter "Cerebia", OHBM Brain Art SIG

Data integration

Analysis Data preparation

Data integration

Analysis Data preparation

A brain imaging study

We need bigger and representative samples

Towards data integration in brain imaging

@cmaumet

Towards large-scale brain imaging studies

Camille Maumet

Sculpture by Malin Bjornsdotter "Cerebia", OHBM Brain Art SIG