# Fully Automated Image De-fencing using Conditional Generative Adversarial
Networks

Divyanshu Gupta1 Shorya Jain1 Utkarsh Tripathi1 Pratik Chattopadhyay1 Lipo
Wang2
1Department of Computer Science and Engineering, IIT(B.H.U), Varanasi-221005,
India
2School of Electrical and Electronic Engineering, Nanyang Technological
University, Singapore
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>
<EMAIL_ADDRESS>

###### Abstract

Image de-fencing is one of the important aspects of recreational photography
in which the objective is to remove the fence texture present in an image and
generate an aesthetically pleasing version of the same image without the fence
texture. In this paper, we aim to develop an automated and effective technique
for fence removal and image reconstruction using conditional Generative
Adversarial Networks (cGANs). These networks have been successfully applied in
several domains of Computer Vision focusing on image generation and rendering.
Our initial approach is based on a two-stage architecture involving two cGANs
that generate the fence mask and the inpainted image, respectively. Training
of these networks is carried out independently and, during evaluation, the
input image is passed through the two generators in succession to obtain the
de-fenced image. The results obtained from this approach are satisfactory, but
the response time is long since the image has to pass through two sets of
convolution layers. To reduce the response time, we propose a second approach
involving only a single cGAN architecture that is trained using the ground-
truth of fenced de-fenced image pairs along with the edge map of the fenced
image produced by the Canny Filter. Incorporation of the edge map helps the
network to precisely detect the edges present in the input image, and also
imparts it an ability to carry out high quality de-fencing in an efficient
manner, even in the presence of a fewer number of layers as compared to the
two-stage network. Qualitative and quantitative experimental results reported
in the manuscript reveal that the de-fenced images generated by the single-
stage de-fencing network have similar visual quality to those produced by the
two-stage network. Comparative performance analysis also emphasizes the
effectiveness of our approach over state-of-the-art image de-fencing
techniques.

##  1 Introduction

In recent times, due to the existence of inexpensive image capturing devices
such as smart-phones and tablets with sophisticated cameras, there is a steady
rise in the number of images captured and shared over the internet. Despite
these technological advances, often it is difficult to take a snapshot of the
intended object due to the presence of certain obstructions between the camera
and the object. For example, consider that a person wishes to capture the
image of an animal within a cage in a zoo. It is understandable that he/she
will not be able to capture a clear image of the animal from a distance due to
the presence of a fence or cage-bars in front. Till date, a number of research
articles on image de-fencing have been proposed in the literature, (e.g., Park
et al. (2010); Khasare et al. (2013); Jonna et al. (2015a, 2016); Liu et al.
(2008); Farid et al. (2016)). However, these methods are either semi-
automated, or are time-intensive due to involvement of complex computations.
Usually, image de-fencing is viewed as a combination of two separate sub-
problems: (i) _fence mask generation_ , which essentially clusters the image
region into two groups, i.e., fence and non-fence regions, and (ii) _image
inpainting_ , which deals with artificially synthesizing colors to the fence
regions to make the rendered image look realistic. This is explained with the
help of Figure 1.

Figure 1: (a) Input image with fence, (b) fence detection, (c) de-fenced image
after inpainting.

Conditional Generative Adversarial Networks (cGANs) (Reed et al. (2016); Zhang
et al. (2017); Huang et al. (2018)) have already demonstrated strong potential
in generating realistic images in accordance with a set of user-defined
conditions or constraints (Yeh et al. (2017); Brkic et al. (2017); Radford et
al. (2015); Chen et al. (2016)), and are possibly the best networks available
today for performing any image-to-image translation task. Since image de-
fencing can also be viewed as a sub-class of image-to-image translation
problems, we propose to use cGANs in our work as well.

To the best of our knowledge, the present paper is the first work on image de-
fencing that exploits the powerful generalization capability of GANs to
generate de-fenced images. Specifically, we propose two different GAN-based
de-fencing algorithms: (i) a two-stage network that consists of two sub-
networks to carry out the fence mask generation and image inpainting in
succession, and (ii) a single-stage network which directly performs image de-
fencing without any intermediate fence mask generation step. Experimental
results on a public fence segmentation data set (Du et al. (2018)) and our own
artificially created data set show the effectiveness of our work.

The rest of the paper is organized as follows: in Section 2, we briefly review
the related work in automatic fence detection, image inpainting and image de-
fencing. The problem formalization and the proposed cGAN based de-fencing
approaches are described in detail in Section 3. An extensive experimental
campaign is reported in Section 4. Finally, conclusions and future scopes for
research are highlighted in Section 5.

##  2 Related Work

As explained before, traditionally, the task of image de-fencing is viewed as
a two-step problem: (i) segmenting the fence in the image, and (ii) recovering
the eliminated area with plausible content via image inpainting. Hence, in
addition to reviewing the image de-fencing techniques in the literature, we
also study existing solutions to fence mask generation and image inpainting,
which are briefly described in the Sub-sections 2.1 and 2.2, respectively.
Finally, in Sub-section 2.3, we present a review of the state-of-the-art image
de-fencing techniques.

###  2.1 Fence Mask Detection

Fence mask detection is the process of segmenting an input image with fence
into two clusters, such that all the fence pixels are assigned a particular
cluster, and each of the other pixels is assigned a different cluster. A lot
of research has been done in the domain of regular and near-regular pattern
detection (Hays et al. (2006); Park et al. (2009); Lin and Liu (2007); Park et
al. (2010)). The work in Hays et al. (2006) used higher-order feature matching
to discover the lattices of near-regular patterns in real images based on the
principal eigen vector of the affinity matrix. Park et al. (2009) proposed a
method for detection of deformed 2D wallpaper patterns in real-world images by
mapping the 2D lattice detection problem into a multi-target tracking problem,
which can be solved within an Markov Random Field framework. In another work
by Park et al. (2008), the problem of near-regular fence detection was handled
by employing efficient Mean-Shift Belief Propagation method to extract the
underlying deformed lattice in the image. Mu et al. (2014) proposed a soft
fence-detection method using visual parallax as the cue to differentiate the
fence from the non-fenced regions.

###  2.2 Image Inpainting

Image inpainting is the process of restoration of the unfilled portions of an
image with appropriate plausible content/color. Image inpainting methods used
in the literature can be broadly divided into two categories: (a) diffusion
based methods (Bertalmio et al. (2003); Levin et al. (2008)) and (b) exemplar-
based methods (Criminisi et al. (2004); Xu and Sun (2010); Darabi et al.
(2012); Huang et al. (2014)). The former category of approaches uses
smoothness priors to propagate information from known regions to the unknown
region, while the latter category fills in the occluded regions by means of
similar patches from other locations in the image. Exemplar-based methods have
the potential of filling up large occluded regions and recreate missing
textures to reconstruct large regions within an image. But these methods are
unable to recover the high-frequency details of the image properly. To the
best of our knowledge, Context Encoder (Pathak et al. (2016)) is the first
deep learning approach used for image inpainting, in which an encoder is used
to map an image with missing regions to a low-dimensional feature space, which
is next used by the decoder to reconstruct the output image. Yang et al.
(2017) used a pretrained VGG network that minimizes the feature differences in
the image background, thereby improving the work of Pathak et al. (2016). Yeh
et al. (2017) proposed a GAN-based approach for image inpainting by applying a
set of conditions on the available data. Contextual attention (Yu et al.
(2018)) is another approach in which the missing regions were first estimated
followed by an attention mechanism to sharpen the results. Nazeri et al.
(2019) developed a two-stage adversarial model consisting of an edge generator
and image completion network. The edge generator network detects edges of
missing regions and is used by the image completion network as prior to fill
in the missing regions.

###  2.3 Image De-fencing

The image de-fencing problem was first addressed in Liu et al. (2008), where
the fence patterns were segmented by means of spatial regularity, and the
fence pixels were filled in with suitable colors by applying an appropriate
inpainting algorithm (Criminisi et al. (2004)). Park et al. (2010) extended
the work of Liu et al. (2008) by employing multiple images for extracting the
information of occluded image data from additional frames. Park et al. (2010)
also used a deformable lattice detection method similar to that of Park et al.
(2009) discussed in Section 2.1. Khasare et al. (2013) proposed an improved
multi-frame de-fencing technique by using loopy-belief propagation
(Felzenszwalb and Huttenlocher (2006)). This method uses an image matting
(Zheng and Kambhamettu (2009)) for fence segmentation, but the main drawback
of this approach is that it involves significant user interaction and is
therefore not very suitable for practical purposes. Jonna et al. (2015b)
proposed a multimodal approach for image de-fencing in video frames, in which
the fence mask was first extracted in each frame with the aid of depth maps
corresponding to the color images obtained from a Kinect sensor, and next an
optical flow algorithm was used to find correspondences between adjacent
frames. Finally, estimation of the de-fenced image was done by modeling it as
a Markov Random Field, and obtaining its maximum a-posteriori estimate by
applying loopy belief propagation. Kumar et al. (2016) used signal demixing to
capture the sparsity and regularity of the different image regions, thereby
detecting fences, following which inpainting was performed to fill-in the
fence pixels with suitable colors. Farid et al. (2016) used a semi-automated
approach in which an user is requested to manually mark several fence pixels
in the image. A Bayesian classifier is next employed to classify each pixel as
fence or non-fence pixel based on the knowledge of the color distribution of
the marked pixels and the non-marked pixels. This approach is prone to human
error and also highly time-intensive.

Recently, a few deep learning based video de-fencing approaches have been
developed, e.g., the work by Jonna et al. (2015a) is a semi-automated approach
which first employs a CNN-based algorithm to detect the fence pixels in an
input image, and next use a sparsity based optimization framework to fill-in
the fence pixels. Jonna et al. (2016) utilized a pre-trained CNN coupled with
the SVM classifier for fence texel joint detection, and then connect the
joints to obtain scribbles for image matting. Du et al. (2018) presented an
approach for fence segmentation using fully convolutional neural networks
(FCN) (Long et al. (2015)) and a fast robust recovery algorithm by employing
occlusion-aware optical flow.

The main contributions of the paper are as follows:

  1. 1.

Developing for the first time fully automated and efficient image de-fencing
algorithms based on conditional Generative Adversarial Networks (cGANs).

  2. 2.

Proposing a two-stage image de-fencing network that involves a fence mask
generator and a image recovering network, each of which is based on cGAN.

  3. 3.

Making the algorithm more time-efficient by developing a single-stage end-to-
end cGAN network without any intermediate fence mask generation step. Edge-
based features along with the ground-truth of fenced de-fenced image pairs are
used to train the model so that it can generate high quality de-fenced images
even in the presence of a fewer number of layers compared to the two-stage
network.

  4. 4.

Performing extensive experimental evaluation, and also making the codes and
data set used in the experiments publicly available to the research community
for further comparisons.

##  3 Proposed Techniques for Image De-fencing using cGANs

The proposed cGAN-based two-stage and single-stage architectures for image de-
fencing are explained in detail in the following two sub-sections.

###  3.1 Two-stage Image De-fencing Network

The two-stage architecture shown in Figure 2 follows a work-flow similar to
that seen in most existing approaches, i.e., (i) fence mask generation and,
(ii) recovering the missing parts of the image behind the fence (refer to
Section 1). The difference from the existing techniques is that, we use
adversarial learning to carry out both these steps. More specifically, we use
a pair of cGANs, each consisting of a generator-discriminator pair, to perform
the two steps. The generator consists of a encoder network with seven down-
sampling layers, followed by a decoder network with seven up-sampling layers
as in Isola et al. (2017). The discriminator is a $16{\times}16$ Markovian
Discriminator, i.e, PatchGAN (Isola et al. (2017)), which classifies each
$16{\times}16$ patch in the image as real or fake and averages all the
responses to provide the final output. The proposed de-fencing algorithm is
discussed in Sections 3.1.1 and 3.1.2 by denoting ${D_{1}}$ and ${G_{1}}$ as
the discriminator and generator for the fence mask generator, and ${D_{2}}$
and ${G_{2}}$ as the discriminator and generator for the image recovering
network, respectively.

Figure 2: Two-stage image de-fencing network.

####  3.1.1 Fence Mask Generator

The task of the fence mask generator can be viewed as an image-to-image
translation problem where we convert a fenced image to a fence mask image. Let
$\mathrm{I}_{mask}$ be the ground-truth fence mask image, and
$\mathrm{I}_{fen}$ the input fenced image. During the training phase, the
generator takes the input as $\mathrm{I}_{fen}$, conditioned on
$\mathrm{I}_{mask}$ and predicts the fence mask image ${\mathrm{I}_{pred}}$.
Mathematically, the generator function can be represented as:

$\mathrm{I}_{pred}=G_{1}(\mathrm{I}_{fen},\mathrm{I}_{mask}).$ (1)

We use ${I_{mask}}$ and ${I_{pred}}$, conditioned on ${I_{fen}}$ as the input
of the discriminator, to predict the fence mask image as real or fake. The
network is trained only with the objective function comprising adversarial
loss and _L1_ loss, as shown next in (2):

$\min_{G_{1}}\max_{D_{1}}\mathrm{L}_{G_{1}}=\min_{G_{1}}(\alpha_{1}\max_{D_{1}}(\mathrm{L}_{adv,1}))+\beta_{1}(\mathrm{L}_{L1,1})),$
(2)

where $\alpha_{1}$ and $\beta_{1}$ are regularization parameters, with
$\alpha_{1}=1$ and $\beta_{1}=10$. The adversarial loss ($\mathrm{L}_{adv,1}$)
and _L1_ loss are defined in the following two equations:

$\mathrm{L}_{adv,1}=\mathbb{E}_{(\mathrm{I}_{fen},\mathrm{I}_{mask})}[\log(D_{1}(\mathrm{I}_{mask},\mathrm{I}_{fen}))]+\mathbb{E}_{(\mathrm{I}_{fen},\mathrm{I}_{pred})}[\mathrm{log}(1-D_{1}(\mathrm{I}_{pred},\mathrm{I}_{fen}))],$
(3)

and

$\mathrm{L}_{L1,1}=\mathbb{E}[\mathrm{\mid\mid}\mathrm{I}_{pred}-\mathrm{I}_{mask}\mathrm{\mid\mid_{1}}],$
(4)

where $\mathbb{E}$ denotes the expectation operator. The network is trained in
multiple epochs, and training is stopped when the absolute difference of the
value of loss function in two successive epochs is less than a small threshold
$\epsilon$. We consider the value of $\epsilon$ as $10^{-3}$.

####  3.1.2 Image Recovering Network

Let ${\mathrm{I}_{def}}$ be the ground-truth de-fenced image. The input fenced
image ${\mathrm{I}_{fen}}$ is masked with the fence mask image, which is
obtained by the fence mask generator, say $\mathrm{M}$, to generate
${\mathrm{\tilde{\mathrm{I}}}_{fen}}$, i.e.,
${\mathrm{\tilde{\mathrm{I}}}_{fen}}$ =
${\mathrm{I}_{fen}}{\odot}(1-\mathrm{M})$ representing unfilled image without
fences, where ${\odot}$ represents the Hadamard product. The image recovering
network, takes ${\mathrm{\tilde{\mathrm{I}}}_{fen}}$ as input, conditioned on
${\mathrm{\mathrm{I}}_{def}}$ to generate a de-fenced image
$\mathrm{\tilde{\mathrm{I}}}_{pred}$ filled with plausible content in the
unfilled part of ${\mathrm{\tilde{\mathrm{I}}}_{fen}}$ having the same
resolution as the input image, as shown in (5):

${\mathrm{\tilde{\mathrm{I}}}_{pred}}=G_{2}({\mathrm{\tilde{\mathrm{I}}}_{fen}},\mathrm{I}_{def}).$
(5)

The image recovering network is trained until convergence by a joint objective
function based on Nazeri et al. (2019) that considers adversarial loss,
perceptual loss, style loss and _L1_ loss, along with the SSIM loss (Wang et
al. (2004), Zhao et al. (2017)). The adversarial loss function for $G_{2}$ is
defined as:

$\mathrm{L}_{adv,2}=\mathbb{E}_{(\tilde{\mathrm{I}}_{fen},\mathrm{I}_{def})}[\log(D_{2}(\mathrm{I}_{def},\tilde{\mathrm{I}}_{fen}))]+\mathbb{E}_{(\tilde{\mathrm{I}}_{fen},\tilde{\mathrm{I}}_{pred})}[\mathrm{log}(1-D_{2}(\tilde{\mathrm{I}}_{pred},\tilde{\mathrm{I}}_{fen}))].$
(6)

The perceptual loss term (Johnson et al. (2016)) $\mathrm{L}_{perc}$, computes
the differences between the high-level feature representations between the
ground-truth and the generated images extracted from a pre-trained CNN. If the
predicted image label is dissimilar from the actual image label, a higher
penalty is imposed through this loss term. Mathematically, the perceptual loss
is defined as follows:

$\mathrm{L}_{perc}=\mathbb{E}[\sum_{i}\frac{1}{N_{i}}\mid\mid\mathrm{\vec{a}_{i}}(\mathrm{I}_{def})-\mathrm{\vec{a}_{i}}(\tilde{\mathrm{I}}_{pred})\mid\mid_{1}],$
(7)

where $\mathrm{\vec{a}_{i}}$ is the activation map of the $i^{th}$ layer of a
pre-trained VGG-19 network. We also use the style loss (Gatys et al. (2016)),
which determines the difference between the style representations of two
images. The style representation of an image at a particular layer is given by
the gram matrix $\mathrm{G}$, and each element of this matrix represents the
inner product between a pair of vectorized feature maps at the given layer.
For the vectorized feature map of size $C_{j}\times H_{j}\times W_{j}$, the
style loss is mathematically defined as follows:

$\mathrm{L}_{sty}=\mathbb{E}_{j}[\mid\mid\mathrm{{G_{j}}^{\vec{a}}}(\tilde{\mathrm{I}}_{pred})-\mathrm{{G_{j}}^{\vec{a}}}({\mathrm{I}}_{def})\mid\mid_{1}],$
(8)

where $\mathrm{{G_{j}}^{\vec{a}}}$ is the a
$\mathrm{C_{j}}\times\mathrm{C_{j}}$ gram matrix corresponding to feature map
$\mathrm{\vec{a}_{j}}$. The _L1_ loss function is computed as follows:

$\mathrm{L}_{L1,2}=\mathbb{E}[\mathrm{\mid\mid}\tilde{\mathrm{I}}_{pred}-\mathrm{I}_{def}\mathrm{\mid\mid_{1}}].$
(9)

For obtaining visually pleasing images from the generator, we also incorporate
a structural similarity loss term (Wang et al. (2004), Zhao et al. (2017)) as
shown in (10), which indicates the differences in the luminance, contrast, and
structure between the generated de-fenced image and the ground-truth de-fenced
image.

$\mathrm{L}_{SSIM}=\frac{1}{N}\sum_{p}(1-\mathrm{SSIM(p)}),$ (10)

where, $p$ refers to a particular pixel position, and

$\mathrm{SSIM(p)}=\frac{2\mu_{x}\mu_{y}+C_{1}}{{\mu_{x}}^{2}{\mu_{y}}^{2}+C_{1}}.\frac{2\sigma_{xy}+C_{2}}{{\sigma_{x}}^{2}{\sigma_{y}}^{2}+C_{2}},$
(11)

refers to the structural similarity index magnitude between ground-truth and
the generated image at pixel position $p$. In the above expression, $\mu_{x}$
and $\mu_{y}$ represent mean intensities in the neighborhood of $p$, while
$\sigma_{x}$ and $\sigma_{y}$ represent standard deviations for two non-
negative image signals $x$ and $y$, respectively, $\sigma_{xy}$ represents the
co-variance of $x$ and $y$, and $C_{1}$ and $C_{2}$ are constants. Appropriate
values for $C_{1}$ and $C_{2}$ to compute the SSIM loss can be found in
https://github.com/keras-team/keras-
contrib/blob/master/keras_contrib/losses/dssim.py.

The overall loss function for the image recovering network is henceforth
computed as:

$\min_{G_{2}}\max_{D_{2}}\mathrm{L}_{G_{2}}=\min_{G_{2}}(\alpha_{2}\max_{D_{1}}(\mathrm{L}_{adv,2})+\beta_{2}(\mathrm{L}_{L1,2})+\gamma(\mathrm{L}_{perc})+\delta(\mathrm{L}_{sty})+\eta(\mathrm{L}_{SSIM})),$
(12)

where $\alpha_{2}$, $\beta_{2}$, $\gamma$, $\delta$ and $\eta$ are
regularization parameters. In our experiments, we use $\alpha_{2}$=0.1,
$\beta_{2}$=10, $\gamma$=2, $\delta$=1 and $\eta$=1.

###  3.2 Single Stage End-to-End Image De-fencing Network

Figure 3: Single-stage image de-fencing network.

Use of two generators makes the image de-fencing process time-intensive. To
reduce the response time, we propose to use a single end-to-end architecture
with a single generator-discriminator pair for translating the input image
with a fence structure directly to its de-fenced version without any fence
generation step in between. Since only a single generator is used here, the
single-stage network will have fewer number of layers compared to the two-
stage network described in Section 3.1. Presence of fewer layers in a
convolutional neural network has a tendency to loose significant contextual
information. To boost up the performance of the single-stage network, we
propose to train the model with the given ground-truth fenced de-fenced image
pairs as well as with an edge map of the fenced image given by the Canny
filter. We observe that appending the Canny edge map along with the input
fenced image facilitates high quality image de-fencing even in the presence of
fewer number of layers. The network architectures for the generator and
discriminator are similar to that of the image recovering network in Section
3.1.2. Also, an objective function similar to (12) has been used to train the
single-stage network until convergence.

##  4 Experiments and Results

###  4.1 Data Set and System Description

We use three Graphics Processing Units (GPUs) to train the models out of which
one is Nvidia Titan Xp (with 12GB RAM, total FB memory as 12196 MB and total
BAR1 memory as 256 MB), and the other two are Nvidia GeForce GTX 1080 Ti (with
11 GB RAM, total FB memory as 11178 MB and total BAR1 memory as 256 MB). The
experimental protocols are briefly discussed next. For training the two-stage
image de-fencing network, the fence segmentation dataset provided by Du et al.
(2018) is used along with a synthetically generated data set formed by adding
artificial fence structures on a set of images from the Pascal VOC dataset
(Everingham et al. (2010)). For training the image recovering network, we also
created an artificial data set by using images from the Pascal VOC dataset
(Everingham et al. (2010)) and the COCO dataset (Lin et al. (2014)). The data
set for training the single-stage end-to-end image de-fencing network is also
constructed in a similar manner by applying random fence structures on a set
of images from Pascal VOC data and COCO data. The test set consists of a total
of 245 images and is formed by selecting images from the above-mentioned
public data sets as well as some images captured by our research team. Before,
making a forward pass through the network, the dimensions of each training and
test image is made equal to 256$\times$256.

###  4.2 Experiments with Two-Stage Image De-fencing Network

Figure 4 shows the qualitative performance of the two-stage image de-fencing
network by means of a sample set of fenced images. The first row in the figure
represents the input, the second row represents the output of the mask
generator, the third row corresponds to the input to the image recovery
network, and finally the last row shows the output of the image recovery
network.

Figure 4: Qualitative results for the two-stage image de-fencing network.

It is seen from the figure that the output results are visually quite
appealing.

###  4.3 Experiments with Single-Stage Image De-fencing Network

As discussed in Section 3.2, in a bid to reduce the response time of image de-
fencing further, we propose an efficient single-stage image de-fencing
network. In the fourth row of Figure 5, the outputs given by the proposed
single-stage de-fencing network (with supervision of canny edge map) are shown
on eight different test images. The first and second rows of the figure
respectively depict the input image and the corresponding ground-truth, while
the third row shows the images generated by single-stage image de-fencing
network without extra supervision of canny edge maps, fifth row shows the
images generated by the two-stage de-fencing network discussed in Section 3.1.

Figure 5: Qualitative results by the single stage end-to-end image de-fencing
network.

The qualitative results clearly depict that the output images given by the
proposed single stage image de-fencing network are comparable with that of the
two-stage de-fencing network.

##  5 Conclusions and Future Work

In the present manuscript, we explore the applicability of conditional
Generative Adversarial Networks (cGANs) for image de-fencing in two different
settings: (i) a two-stage image de-fencing network which employs a fence mask
generator network and an image recovering network in succession, and (ii) a
single-stage image de-fencing network, which uses a single generator to render
the de-fenced image from the original fenced image and its edge map.
Experimental results show that both the proposed methods can produce de-fenced
images with high visual quality, but the later approach is more advantageous
if a fast response is desired. Comparison with state-of-the-art techniques
also emphasize the effectiveness of employing GANs in the image de-fencing
task. In future, it may be studied how to make the algorithm more time-
efficient, so that it can be applied for real-time video de-fencing. Another
challenging area of research is how to effectively de-fence images with
irregular or repeated fence structures, which the present work and also other
existing techniques are unable to handle properly.

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# Curious Rhythms: Temporal Regularities of Wikipedia Consumption

Tiziano Piccardi1111Work done while at EPFL., Martin Gerlach2, Robert
West3222Robert West is a Wikimedia Foundation Research Fellow.

###### Abstract

Wikipedia, in its role as the world’s largest encyclopedia, serves a broad
range of information needs. Although previous studies have noted that
Wikipedia users’ information needs vary throughout the day, there is to date
no large-scale, quantitative study of the underlying dynamics. The present
paper fills this gap by investigating temporal regularities in daily
consumption patterns in a large-scale analysis of billions of timezone-
corrected page requests mined from English Wikipedia’s server logs, with the
goal of investigating how context and time relate to the kind of information
consumed. First, we show that even after removing the global pattern of
day–night alternation, the consumption habits of individual articles maintain
strong diurnal regularities. Then, we characterize the prototypical shapes of
consumption patterns, finding a particularly strong distinction between
articles preferred during the evening/night and articles preferred during
working hours. Finally, we investigate topical and contextual correlates of
Wikipedia articles’ access rhythms, finding that article topic, reader
country, and access device (mobile vs. desktop) are all important predictors
of daily attention patterns. These findings shed new light on how humans seek
information on the Web by focusing on Wikipedia as one of the largest open
platforms for knowledge and learning, emphasizing Wikipedia’s role as a rich
knowledge base that fulfills information needs spread throughout the day, with
implications for understanding information seeking across the globe and for
designing appropriate information systems.

## Introduction

Human life is driven by strong temporal regularities at multiple scales, with
events and activities recurring in daily, weekly, monthly, yearly, or even
longer periods (Kreitzman and Foster 2011). The cyclical nature of human life
is also reflected in human behavior on digital platforms. Understanding and
modeling temporal regularities in digital-platform usage is important from a
practical as well as a scientific perspective: on the practical side,
understanding user behaviors and needs is critical for building effective,
user-friendly platforms; on the scientific side, since online behavior
reflects user needs, studying temporal regularities of platform usage can shed
light on the structure of human life itself and is thus consequential for
sociology, psychology, anthropology, medicine, and other disciplines. For
instance, in information science, time has long been recognized as a crucial
contextual factor that drives human information seeking (Savolainen 2006). The
study of traces recorded on digital platforms has yielded novel insights about
circadian rhythms (Aledavood et al. 2022; Pintér and Felde 2022; Althoff et
al. 2017; Murnane et al. 2015; Chalmers et al. 2011; Kumar Swain and Kumar
Pati 2020; Leypunskiy et al. 2018) and periodic fluctuations in alertness
(Abdullah et al. 2016), mood (Dodds et al. 2011; Golder and Macy 2011), focus
(Mark et al. 2016), musical taste (Park et al. 2019; Heggli, Stupacher, and
Vuust 2021), purchase habits (Gullo et al. 2019), and ad engagement (Saha et
al. 2021).

With regard to both aspects—practical and scientific—Wikipedia constitutes a
particularly important online platform to study: On the practical side,
Wikipedia is one of the most frequently visited sites on the Web, such that a
better understanding of user behavior can potentially lead to site
improvements with consequences for billions of users. On the scientific side,
Wikipedia is not just yet another website; it is the world’s largest
encyclopedia, where each page is about a precise concept. Temporal
regularities of Wikipedia usage thus have the potential to reveal regularities
of human necessities, telling us what humans care about, and what they are
curious about, at what times. Some temporal regularities of Wikipedia usage
are already known: e.g., Wikipedia’s overall usage frequency, as well as the
length of sessions, varies by time of day (Piccardi et al. 2023), as do users’
reasons for reading Wikipedia (Singer et al. 2017; Lemmerich et al. 2019).
These studies have, however, glanced at temporal regularities merely
superficially and in passing while focusing primarily on other aspects of
Wikipedia usage. The most related to our work is a study that showed that
Wikipedia editing follows daily and weekly regularities (Yasseri et al. 2012),
but the study was limited to editing behavior. One reason why previous studies
have not been able to analyze reading, rather than editing, behavior to date
is that, as opposed to edit logs (where editors’ geo-locations can be
approximated via logged IP addresses), geo-located reading logs are not
publicly available. Rather, Wikipedia’s public hourly pageview
logs333https://dumps.wikimedia.org/other/pageviews/readme.html report only
Coordinated Universal Time (UTC) without specifying the reader’s local time.
Especially in large language editions such as English, which are accessed from
many countries in different timezones, this constitutes a major limitation.

We overcome this limitation by working with a non-public dataset of English
Wikipedia’s full webrequest logs, enriched with timezone information inferred
from user IP addresses, which allows us to timezone-correct all timestamps and
thus to faithfully study, for the first time, temporal regularities of
Wikipedia reading at hourly granularity. We characterize how information
consumption on the platform varies by time of day and how time interacts with
other contextual properties, such as article topics and reader country. Adding
to previous studies on the consumption and popularity of Wikipedia content, we
provide insights into the daily temporal rhythms that drive Wikipedia usage.
Specifically, we address the following research questions:

RQ1

Strength of rhythms: How strongly is Wikipedia consumption driven by periodic
rhythms?

RQ2

Shapes of rhythms: What are the typical shapes of Wikipedia consumption
rhythms?

RQ3

Correlates of rhythms: How do topical and contextual factors determine
Wikipedia consumption rhythms?

Regarding RQ1, we find that fluctuations in Wikipedia’s total access volume
are largely explained by a diurnal baseline rhythm corresponding to the human
circadian wake–sleep cycle. Crucially, however, individual articles deviate
systematically from the baseline rhythm, with deviations themselves following
periodic diurnal patterns.

Regarding RQ2, principal component analysis reveals that individual articles’
access rhythms are heavily driven by a small number of prototypical temporal
signatures, but that article-specific rhythms do not cluster into distinct
groups, but vary smoothly along a continuum.

Regarding RQ3, regression analysis shows that temporal regularities in article
access volume vary systematically by article topic, access method (mobile vs.
desktop), and reader country. The latter is the strongest determinant of
access rhythm, whereby different countries’ interests in English Wikipedia
fluctuate in idiosyncratic periodic patterns over the course of the day. In
terms of topic, to a first approximation, stem and history & society articles
tend to be more popular early in the day, and media articles later in the day,
with culture articles being less concentrated in time.

Taken together, these findings further our understanding of how human
information needs vary in space and time, and can serve as a stepping stone
toward the informed design of improved information systems, on Wikipedia and
beyond.

## Related Work

Temporal rhythms in digital traces. Temporal patterns using digital traces
have been explored in a large variety of topics. Consumption logs can bring
invaluable insight into our understanding of how time impacts human
activities. For example, mobile phone traces can help characterize daily
rhythms (Aledavood et al. 2022) and expose insights about our circadian rhythm
(Pintér and Felde 2022), which may be difficult to study otherwise. Analyzing
the temporal dynamics of digital traces can also uncover biological and
cognitive rhythms during the day, such as sense of alertness (Abdullah et al.
2016), chronotypes (Althoff et al. 2017), wellness (Zhou et al. 2023b), and
focus (Mark et al. 2016). Individual temporal rhythms can also serve as
predictors of medical conditions that need attention (Doryab et al. 2019).
Social media data, like Twitter (Murnane et al. 2015; Chalmers et al. 2011;
Grinberg et al. 2013), and messaging apps, like WhatsApp (Kumar Swain and
Kumar Pati 2020), can be used as large-scale sensors revealing insights about
sleeping patterns (Leypunskiy et al. 2018), and happiness fluctuations (Dodds
et al. 2011), with variations across cultures (Golder and Macy 2011). Time of
day also impacts our choices in terms of musical taste (Park et al. 2019;
Heggli, Stupacher, and Vuust 2021), purchase habits (Gullo et al. 2019), and
ad engagement (Saha et al. 2021).

Interactions with Wikipedia, too, are affected by time. Previous studies
describe how consumption patterns reveal information about seasonal
fluctuations in mood (Dzogang, Lansdall-Welfare, and Cristianini 2016) at the
population scale and how editors’ temporal patterns exhibit culture-specific
differences (Yasseri, Sumi, and Kertész 2012). It has also been noted that
modeling Wikipedia temporal readers’ needs has implications for technical
improvements and could be exploited to develop scalable infrastructure adapted
to reading patterns (Reinoso et al. 2012).

Wikipedia reader behavior. Given Wikipedia’s central role in the Web
ecosystem, there is increasing attention to characterizing reader behavior.
Previous work investigated the reasons that lead readers to consume Wikipedia
content (Singer et al. 2017), finding differences by time and country
(Lemmerich et al. 2019). Complementary studies focus on consumption dynamics
(Ratkiewicz et al. 2010; Ribeiro et al. 2021; Lehmann et al. 2014;
TeBlunthuis, Bayer, and Vasileva 2019) and interaction with various article
elements, such as citations (Maggio et al. 2020; Piccardi et al. 2020),
external links (Piccardi et al. 2021), and images (Rama et al. 2021).
Significant attention is also dedicated to navigating from page to page to
understand the mechanism that allows users to move across content in a natural
setup (Piccardi et al. 2023; Piccardi, Gerlach, and West 2022; Trattner et al.
2012; Helic et al. 2013; Singer et al. 2014; Lamprecht et al. 2017;
Gildersleve and Yasseri 2018; Dimitrov et al. 2019) or in lab-based settings,
such as wiki games (West, Pineau, and Precup 2009; West and Leskovec 2012b;
Helic 2012; West and Leskovec 2012a; Scaria et al. 2014; Koopmann et al.
2019). Our work complements these findings by focusing on the shape of
temporal regularities, which have not been analyzed in detail before.

Information needs and curiosity. Our work relates broadly to more theoretical
work on information needs. The formulation of information needs was initially
popularised by Wilson (Wilson 1981) and the resulting information models
refined over the years (Wilson 1997, 1999). Information needs have also been
linked to concepts in biology by comparing the need for information to the
need for food (Machlup 1983). This idea is formalized in information foraging
theory (Pirolli and Card 1999), which has developed behavioral models
describing humans in the information space as predators relying on mechanisms
such as information scent (Chi et al. 2001) to find what they need (Suh et al.
2010; Mangel et al. 2013; Rotman et al. 2011). More recent work (Lydon-Staley
et al. 2021; Zhou et al. 2023a) investigates the mechanism of online
consumption by focusing on the role of curiosity, using Wikipedia as the
reference platform and finding substantial differences in how humans explore
information networks.

## Data

Our study relies on the access logs of English Wikipedia, collected over four
weeks (1–28 March 2021) on the servers of the Wikimedia Foundation. These
server logs, stored for a limited time, describe the requests received by the
server when readers access the site, capturing the title of the requested
article, the time the request was made, the user’s IP address and geo-location
(approximately inferred from the IP address), and more.

In this study, we focus only on the traffic generated by human readers by
discarding all bots. In order to ensure anonymity, we prepare the data as
follows. First, we consider only requests for articles (namespace 0), ignoring
requests for pages in other namespaces (e.g., talk pages), and we consider
only requests originating from external websites, ignoring requests made from
other Wikipedia pages. The restriction to incoming traffic from external
websites better captures the (exogenous) information needs that cause users to
visit Wikipedia, rather than (endogenous) information needs that are caused by
visiting Wikipedia. Additionally, we refine the logs by removing sequential
loads of the same page from the same client because they could be an artifact
of the browser (Piccardi et al. 2023), not representing a real intention to
visit Wikipedia.

We anonymize the data by removing all sensitive information such as IP
addresses, user-agent strings, fine-grained geo-coordinates, and all requests
from logged-in users (3% of the pageloads). Finally—and crucially for our
purposes—we align all requests by converting timestamps to the user’s local
time using timezone information available in the logs.

After these steps, we retain 3.45B pageloads associated with 6.3M articles. We
represent the number of pageloads of article $a$ in hour $h$ of the week
(averaged over the four weeks) by $n_{a}(h)$, i.e., each article is
represented by a 168-dimensional time series, with one entry for each of the
$168=24\times 7$ hours per week.

Article properties. ORES (Halfaker and Geiger 2019), Wikipedia’s official
article scoring system, offers a classifier for labeling articles with topics.
The labels are organized in a two-level taxonomy manually derived from
WikiProjects444https://en.wikipedia.org/wiki/Wikipedia:WikiProject (groups of
editors who self-organize to work on specific topical areas). We applied the
classifier to all articles in our dataset and, for each article, obtained a
probability for each of 38 topics, grouped into five top-level topics: stem,
culture, history & society, media (originally included in culture, but
promoted to a top-level topic for our study), geographical. Note that each
article is independently scored for each topic, so topic probabilities do not
sum to 1 for a given article.

Access properties. For each pageload, we retain two contextual properties of
the request: access method and user country. The access method indicator
specifies if the user loaded the article from a desktop or a mobile device,
such as a smartphone or tablet. The user country is estimated by geo-locating
the IP address associated with the request.

Figure 1: Top: Total number of pageloads from external origin by hour of the
week, averaged over four weeks. Bottom: Idem, stratified by desktop and
mobile.

Baseline rhythm. Fig. 1 (top) shows the total number of pageloads per hour of
the week (averaged over the four weeks considered). The consumption rhythm
follows a diurnal pattern, with the lowest access volume between 4:00 and 5:00
from Monday to Saturday and between 5:00 and 6:00 on Sunday, and with a sharp
increase in traffic from 18:00 every day of the week, consistently reaching
its peak at 21:00. When broken down by access method (Fig. 1, bottom),
different device types are associated with different patterns, with mobile
devices driving the increase in evening traffic. Similarly, access from
desktop devices, likely more dependent on working rhythms, shows a small
reduction around 12:00 and 18:00 and reduced activity on weekend mornings.

Denoting the number of pageloads in hour $h$ by $N(h)=\sum_{a}n_{a}(h)$ and
normalizing $N(h)$ to be a distribution over the 168 hours of a week, we
obtain what we term Wikipedia’s baseline rhythm
$\Pr(h):=N(h)/\sum_{h^{\prime}=0}^{167}N(h^{\prime})$.

Divergence from the baseline rhythm. In addition to Wikipedia’s overall access
volume (Fig. 1), we are interested in studying temporal access volume
regularities for individual articles $a$, by analyzing article-specific
distributions over hours,
$\Pr(h|a):=n_{a}(h)/\sum_{h^{\prime}=0}^{167}n_{a}(h^{\prime})$. Individual
articles’ rhythms $\Pr(h|a)$ are heavily driven by the overall baseline rhythm
$\Pr(h)$ dictated by human wake–sleep patterns. Therefore, to study article-
specific rhythms in isolation from the baseline rhythm, we remove the latter
by computing the hourly divergence $D_{a}(h)$ of $a$’s rhythm $\Pr(h|a)$ from
the baseline rhythm $\Pr(h)$ via pointwise division:

$D_{a}(h)=\frac{\Pr(h|a)}{\Pr(h)}=\frac{n_{a}(h)/\sum_{h^{\prime}=0}^{167}n_{a}(h^{\prime})}{N(h)/\sum_{h^{\prime}=0}^{167}N(h^{\prime})}.$
(1)

A divergence greater [less] than 1 indicates that in hour $h$, article $a$
receives more [less] attention than expected from the baseline rhythm, whereas
a divergence of 1 implies that a global weekly rhythm fully determines $a$’s
consumption.

Given the skewed distribution of article popularity, to avoid data sparsity
issues, we keep only articles with at least 1,000 pageloads over the four
weeks considered, or 35 pageloads per day on average. After applying this
filter, we retain 439K articles, accounting for 83.8% (2.89B pageloads) of
English Wikipedia’s traffic.

## RQ1: Strength of Rhythms

We start by quantifying the strength of temporal regularities in Wikipedia
consumption patterns. Taking a signal processing approach, we decompose a time
series $x(h)$ of interest (e.g., $x(h)=\Pr(h)$ or $D_{a}(h)$) into its
frequency components via the Fourier transform, which represents $x(h)$ as a
weighted sum of sinusoids of all possible frequencies. We denote the weight
(Fourier coefficient) of frequency $f\in\\{0,\dots,167$} by $\hat{x}(f)$. We
then measure the contribution of each frequency $f$ to time series $x(h)$ (or,
equivalently, to $\hat{x}(f)$) via the so-called energy spectral density
$E(f)$, which captures the fraction of $x(h)$’s total variance (or energy)
explained by each frequency $f$:

$E(f)=\frac{|\hat{x}(f)|^{2}}{\sum_{f^{\prime}=0}^{167}|\hat{x}(f^{\prime})|^{2}}.$
(2)

Baseline rhythm. Using $x(h)=\Pr(h)$ lets us study temporal regularities in
the weekly baseline rhythm. Fig. 2 (top) plots the variance $E(f)$ explained
by each frequency component $f$ of the baseline rhythm $\Pr(h)$ (mean-centered
across $h$ in order to discard the constant offset term corresponding to
$f=0$). As previously anticipated by Fig. 1, the dominant frequency
corresponds to a 24-hour cycle ($f=7$). The daily and half-daily cycles ($f=7$
and 14; wavelengths 24 and 12 hours) together explain 96.2% of the variance
(74.8% and 21.4%, respectively). When split by access method, the pattern on
mobile is more predictable, with daily and half-daily cycles explaining 94% of
the total variance for mobile, vs. 87% for desktop.

Article-specific rhythms. To measure the strength of article-specific daily
rhythms that do not depend on the overall baseline rhythm $\Pr(h)$, we next
repeat the above analysis, but now with $x(h)=D_{a}(h)$ (again mean-centered
across $h$). We obtain the energy spectral density $E(f)$ for each article $a$
and average it over $a$ in order to measure the average strength of frequency
$f$ in divergences $D_{a}(h)$ from the baseline rhythm, plotted in Fig. 2
(bottom). We see that, even after removing the overall baseline rhythm, still
22.3% of the variance is explained by a combination of the cycles of
wavelengths of 24 (16.5%) and 12 (5.8%) hours. This means that the individual
articles’ access volume rhythms are not just driven by the change in the
overall number of pageloads throughout the day/week, but are also strongly
determined by article-specific factors.

To summarize, investigating RQ1, we found that overall Wikipedia consumption
follows a strong baseline day–night rhythm, but also that individual articles
considerably deviate from this baseline rhythm. The deviations themselves also
largely follow diurnal patterns.

Figure 2: Top/blue: Contribution of each frequency to baseline rhythm $\Pr(h)$
of Wikipedia access volume (measured as the fraction of total variance
explained). Bottom/red: Contribution of each frequency to article-specific
divergence $D_{a}(h)$ from baseline rhythm (Eq. 1) (computed per article $a$,
then averaged over articles).

(a) Daily pattern

(b) Divergence

Figure 3:  Daily access volume of two articles with different topics: stem
(dashed blue) and media (dotted red). (a) Normalized time series $\Pr(h|a)$.
(b) Divergence $D_{a}(h)$ of $\Pr(h|a)$ from the overall baseline rhythm
$\Pr(h)$ (cf. Eq. 1).  Figure 4: Four principal components of the daily access
volume time series, capturing 73.6% of total variance.

(a) $k$-means clusters

(b) STEM vs. Media

Figure 5: (a) Top: UMAP projection of access volume time series for 10K random
articles, with colors representing clusters obtained with $k$-means for
different values of $k=2,3,4$. Bottom: Centroids reconstructed from their
first four principal components. (b) A subset of the same 10K articles, with
colors representing topics (stem and media).

## RQ2: Shapes of Rhythms

Answering RQ1, we established that the consumption pattern of articles
exhibits daily regularities even after removing the weekly baseline rhythm.
Next, we investigate the shape of these patterns. Since the daily rhythm
(wavelength 24 hours) was found to be the strongest by far, we henceforth
focus on the daily instead of the weekly cycle; i.e., we now have
$h\in\\{0,\dots,23\\}$ instead of $\\{0,\dots,167\\}$, with averages taken
over 28 days instead of over four weeks.

Fig. 3 shows examples of the resulting daily time series for two articles $a$
associated with different topics (stem and media). Fig. 3 shows the shape of
the normalized daily access volume time series $\Pr(h|a)$, and Fig. 3 shows
their divergence $D_{a}(h)$ from the daily baseline rhythm $\Pr(h)$.

### Principal Components

To investigate prototypical article consumption behaviors, we extract the
principal components describing the daily divergence time series $D_{a}(h)$ of
article $a$. For this purpose, we stack the individual divergence time series
$D_{a}(h)$ in a $439\text{K}\times 24$ matrix $D$ whose rows correspond to $a$
and whose columns correspond to $h$. We mean-center $D$ column-wise and
compute its singular value decomposition (SVD) $D=U\Sigma V^{T}$. The
(orthogonal) columns of $V$, then, are the principal components of $D$,
capturing prototypical divergence time series. Individual articles’ divergence
time series $D_{a}(h)$ can be approximated as linear combinations of the top
principal components. $\Sigma$ is a diagonal matrix whose $i$-th entry
represents the standard deviation of the data points (rows of $D$) when
projected on the $i$-th principal component. Using the elbow method, we find
that the first four principal components provide a good representation of
consumption behavior, accounting, respectively, for 39.2%, 19.7%, 10.2%, and
4.5% of the total variance, jointly capturing 73.6% of the total variance.

Fig. 4 shows the first four principal components of $D$. Since each component
can contribute positively or negatively to the reconstruction of the rows of
$D$ (since principal components are sign-invariant), we depict each component
in its positive and negative variant (dark and light). The first and strongest
component (PC1) captures the distinction between articles that receive more
attention during the day versus evening/night (or vice versa), with two
turning points around 7:00 and 21:00. The second component (PC2) describes
patterns with a strong positive or negative contribution in the morning, with
a peak around 5:00, which is reversed in the late hours of the day. The third
principal component (PC3) captures a consumption pattern that peaks positively
or negatively in the early morning and evening. Finally, the fourth principal
component (PC4) models a similar behavior with the strongest contribution
around 4:00 and in the early evening.

### Clustering

Next, we aim to identify groups of articles with similar temporal access
patterns via clustering. As clustering tends to work better in low dimensions,
we start by obtaining low-dimensional time series representations by
truncating $U$ (obtained via SVD) to the first four columns $U_{1:4}$
(corresponding to projections on the first four principal components) and
approximating article $a$’s divergence time series $D_{a}(h)$ via the $a$-th
row of $U_{1:4}$. We then cluster the rows of $U_{1:4}$ using $k$-means and
search for the optimal number $k$ of clusters using the average silhouette
width and sum-of-squares criteria. Both criteria indicate $k=2$ as the optimal
number of clusters, suggesting that the articles cannot easily be separated
into distinct groups. This intuition is supported by Fig. 5, which shows the
clusters obtained for $k=2,3,4$. The upper plots show a UMAP (McInnes, Healy,
and Melville 2018) reduction in two dimensions of the four principal
components used to cluster the articles. The visualization is based on a
sample of 10K random articles, color represents cluster assignments, and
centroids are marked as black dots. The lower plots show the centroid of each
cluster, reconstructed from the first four principal components. These plots
support the intuition that consumption behaviors do not separate into
different groups but distribute along a continuum.555Silhouette scores
obtained by grid-searching the number of principal components and clusters do
not improve the separation. Density-based clustering yields the same
conclusions.

On the right side of each of the three scatter plots, we see articles popular
during daytime. In contrast, on the left, we see articles popular during the
evening/night. This partition becomes more evident when increasing the number
of clusters. With three clusters, the data on the left separate into an
additional group (green) containing articles popular during the night.
Similarly, adding the fourth cluster isolates a set of articles (red) popular
in the early morning.

To summarize, investigating RQ2, we found that Wikipedia articles’ access
rhythms are driven by only few prototypical basis patterns (e.g., day vs.
night). Individual articles’ access patterns can be captured as weighted
combinations of those basis patterns, yet they do not cluster into distinct,
well-separated groups, but vary along a smooth continuum.

## RQ3: Correlates of Rhythms

In this section, we investigate what factors correlate with the shape of daily
consumption. We focus on three factors: article topics, access method, and
user country.

Fig. 5 offers initial evidence that article topics are associated with daily
access patterns. The plot represents the subset of articles from Fig. 5 with
topic media or stem. By coloring the data by topic (red for media, blue for
stem), we can notice a natural separation akin to the clustering with $k=2$
clusters (Fig. 5, left). Note that the topic was not considered during
clustering; the separation happens only based on the shape of access patterns.
Articles about stem are on the right side, indicating a pattern aligned with
more attention during daytime, whereas articles about media cover the right
side, associated with evening and night consumption.

Going deeper, we analyze prototypical shapes of access volume time series via
regression analysis, quantifying the relationship of each factor (topics,
access method, country) with time, and measuring the influence of each factor
in an ablation study.

Figure 6: Linear regression coefficients of the topics most associated with
each of the four main principal components of article access volume time
series. Figure 7: Linear regression coefficients of the interaction between
topics and hour. Background colors represent top-level topics: stem (green),
media (yellow), culture (blue), history & society (red) and geographical
(gray). For each top-level topic, specific topics are sorted alphabetically.
Red bands represent 95% confidence intervals. Figure 8: Linear regression
coefficients of the interaction between country and hour (left, gray
background, sorted by the total access volume), and between device and hour
(rightmost plot). Yellow area in rightmost plot represents typical working
hours in Western countries. Red bands represent 95% confidence intervals.

### Principal Components and Topics

In an initial analysis, we leverage the principal components introduced
earlier for RQ2 and investigate the relationship between topics and access
patterns using four linear regressions, one per top principal component. Given
an article $a$, we predict the projection $U_{ai}$ of its divergence time
series $D_{a}(h)$ onto the $i$-th principal component using $a$’s topics as
binary predictors.

Fig. 6 shows a summary of the coefficients obtained by fitting the four
regressions. The first principal component, capturing the day–night rhythm,
separates articles about STEM from those about entertainment (also cf. Fig.
5). Articles associated with topics such as comics & anime, films, and
television show a negative association with this principal component,
suggesting nighttime popularity, whereas the temporal patterns of articles
about chemistry, mathematics, and physics show a positive association,
suggesting daytime popularity. The second component, associated with higher
activity in the early morning and a drop during the evening, shows that the
topics associated most positively with this pattern are libraries &
information, radio, and philosophy & religion. On the other side of the
spectrum, films, television, and food & drinks are most negatively associated
with this pattern (i.e., low activity in the early morning, spike during the
evening). Finally, the third and fourth principal components, showing peaks in
the early morning and during the evening, are most positively associated with
radio and food & drink, respectively.

### Temporal Variation of Correlates

Next, we are interested in the prototypical access volume time series
associated with each level of each factor (topics, access method, user
country). A naive way of accomplishing this would be to first restrict the
data to the respective factor level (e.g., requests for biology articles only,
or requests from Canada only) and then compute access volume time series for
the restricted data only. This approach is, however, compromised by the fact
that the various factors contribute differently to the observed access
pattern. Thus, in order to disentangle the factors, we employ linear
regression.

Model. We prepare the data as follows. First, we decompose each article $a$’s
divergence time series $D_{a}(h)$ by country and access method. To avoid data
sparsity issues, we limit ourselves to the 20 countries with the most
pageloads. This step generates, for each article, 40 daily time series (20
countries, two access methods) describing the divergence of the attention to
$a$ from a specific country and access method vs. the global baseline rhythm
$\Pr(h)$. We explode each time series into 24 samples, such that each article
is represented by 960 data points describing its divergence from the baseline
rhythm for each combination of 20 countries, two access methods, and 24 hours.
We then model divergence (transformed via the natural logarithm, to make the
model multiplicative) as a linear combination of country, access method,
topics, and hour of the day. Additionally, since we are interested in modeling
the relationship between country, access method, and topics with time, we
include interaction terms between each of these three factors with the hour-
of-the-day indicator. We represent all binary predictors via deviation coding,
which lets us interpret the coefficients associated with each level as
differences from the grand mean, which is itself captured by the intercept
(since differences are taken in log space, they correspond to ratios with the
grand mean in linear space). With this setup, we keep the time series composed
of at least 100 pageloads during the four-week period of study and fit a
linear regression using a random sample of 30K articles. The obtained model
fits the data with $R^{2}=0.181$.

Coefficient analysis. Sorting (by hour) the 24 interaction coefficients of
each factor level with hour of the day allows us to characterize the typical
temporal shape of each factor level (in terms of its deviation from
Wikipedia’s baseline rhythm) when controlling for all other factors.

Fig. 7 shows the temporal shapes of the topics organized in the five top-level
topical groups. The plot shows how articles about stem topics, such as
chemistry, physics, and mathematics, tend to receive more attention than
average during the daytime and a visible reduction outside the typical working
hours. On the other hand, articles about films, television, and biography have
an inverted shape, with less consumption than average during the day and a
substantial increase during the evening. Interestingly, the shapes of the
temporal patterns suggest that content about video games, comics & anime,
internet culture, military, and society are consumed by night-active readers,
with relative consumption peaking during the night.

On the contrary, articles about radio, libraries & information, and
philosophy, are more preferred in the early hours of the day. Some of the
shapes, especially the ones associated with stem articles, show a reduction of
attention around noon, suggesting that they might be affected by the lunch
break when people’s attention moves to other content types. This is
corroborated by the fact that attention on articles about food sees an
increase during common meal times.

Next, Fig. 8 shows the interaction coefficients of country by time. Some
countries share similar daily patterns. For example, readers from the United
States, Germany, Netherlands, and Nigeria tend to consume Wikipedia more than
average in the early morning. This behavior is inverted for readers from
India, Ireland, Italy, and Spain, who during the same hours consume less
content than average. Meanwhile, other countries, such as Malaysia, Singapore,
Brazil, Russia, and Pakistan, show higher consumption during the night.
Furthermore, some countries, like the Philippines, Italy, France, and Spain,
also reveal shared habits, such as a reduction of information consumption
around noon, possibly associated with lunchtime.

Finally, the rightmost plot of Fig. 8 shows the coefficients of the
interaction of access method with time, in particular, the shape of the
consumption from desktop devices. As already observed by breaking down the
baseline rhythm by device in Fig. 1, access from desktop devices is above the
global average in the central hours of the day, between 9:00 and 17:00.

(a) stem

(b) media

(c) culture

(d) history & society

Figure 9: Typical access times of topics. Lines represent the coefficient time
series of Fig. 7, and bold crosses the average times per topic. The dotted
line marks the global baseline rhythm $\Pr(h)$. Yellow area shows typical
working hours in Western countries. geographical is included in history &
society to compress the visualization.

### Typical Access Times of Topics

We now aim to summarize each topic-wise time series of Fig. 7 concisely in a
single number describing at what time of day articles from the respective
topic are particularly popular. In order to obtain point estimates of “average
time”, the simple arithmetic mean is unsuitable, given the circular nature of
time (e.g., the average between 23:00 and 1:00 should be 0:00, not the
arithmetic mean of 12:00), so we use the angular mean instead (essentially an
arithmetic mean in the 2D plane described by a clock’s hands). Fig. 9 shows
the topic-wise time series of Fig. 7 in a circular fashion as light-colored
curves, and average times as bold crosses, with one panel per top-level topic
(where a cross’s closeness to the origin captures the variance of the
respective time series). We observe that articles about stem (except for
space) tend to garner particularly much attention during working hours between
8:00 and 14:00. On the other hand, media is, on average, consumed more during
the evening and night. radio is an exception in this group, peaking in the
early morning, as visible in Fig. 7, bringing its daily average to around
10:00. Articles about books are at the limit of the typical working hours,
with average access in the late afternoon around 17:00. Differently from the
previous two groups, articles about culture tend to have high variance and
have average times spread over the day. Even in this case, entertainment
topics such as fashion, internet culture, and comics & anime are concentrated
during the night, with average access after midnight. Finally, content about
history & society shows an average consumption split into two groups, night
vs. working hours, with society, military, and transportation concentrated
during the late evening and night, and business & economics, history, and
education during the day.

### Strength of Correlates: Ablation Study

Finally, we investigate each factor’s influence on temporal access rhythms by
estimating the strength of the interaction between each factor and time in an
ablation study. Using the fitted model described above, we proceed as follows.
We use a held-out dataset of 10K random articles not used in model-fitting to
assess the $R^{2}$ fit after permuting all the interaction terms of the factor
being investigated. This approach, typically used to estimate feature
importance in machine learning (Breiman 2001; Fisher, Rudin, and Dominici
2019), has the advantage of keeping the model fixed—thus, no $R^{2}$
adjustment is required—and measuring the impact of removing the correlation
between the selected feature and the dependent variable.

The original model has an $R^{2}$ fit of 0.181. When permuting the interaction
terms of “time by topic”, the $R^{2}$ drops to 0.055 (reduction by 69%); when
permuting “time by access method”, the $R^{2}$ is 0.040 (reduction by 78%);
and finally, when permuting “time by country”, the $R^{2}$ score is
$-0.0298$666A negative $R^{2}$ is possible on a held-out set, indicating that
a flat line approximates the data better than the model. (reduction of 116%).
A permutation of all three factors reduces the $R^{2}$ to $-0.429$. These
observations suggest that all factors are essential for the prediction and
indicate that the interaction of time with the readers’ country plays the most
important role.

To summarize, in answering RQ3, we found that temporal regularities in the
popularity of Wikipedia articles vary in important and systematic ways by
topic, access method, and user country, and that, out of these, user country
has the strongest influence.

## Discussion

Summary of findings. In this study, we conducted the first large-scale study
on temporal rhythms of information consumption on Wikipedia, based on a new
timezone-corrected dataset of hourly-aggregated pageviews where the reader’s
local time was inferred from Wikipedia’s webrequest logs.

First, we showed that the overall information consumption exhibits daily
rhythmic patterns, with the strongest components having periods of 24 and 12
hours, respectively. We further showed that the consumption of individual
articles follows specific rhythms that cannot be explained by Wikipedia’s
overall wake–sleep baseline rhythm. Rather, each article reveals a specific
consumption fingerprint throughout the day.

Second, we provided a systematic description of the principal shapes of the
different rhythms of the individual articles. We find that the main shape
distinguishes articles that are read disproportionally more during the day
than during the night (and vice versa). We do not, however, find distinct
clusters of shapes but, instead, observe a continuum of different rhythms of
information consumption.

Third, we show systematic differences in consumption patterns based on the
reader’s context (country or device) or the article’s topics. We showed that
articles of specific topics are associated with specific rhythmic patterns.
For example, articles on stem and media naturally separate into two clusters
related to rhythms with disproportional attention during the day and night,
respectively. More generally, this leads to markedly different “average” times
when articles from different topics are accessed. We also showed that
pageloads from mobile vs. desktop devices are driven by substantially
different 24-hour rhythms, with mobile pageloads showing an almost twofold
increase in the evening hours compared to the day, which is absent for desktop
devices. Lastly, we also find substantial variation in the access patterns
across different countries.

Implications. Our work shows that context is an important element to consider
when trying to understand how information on Wikipedia is consumed. This has
several implications.

Diversity of information needs. Wikipedia as a platform fulfills multiple
information needs. These needs vary not only with geographic location, such as
country (Lemmerich et al. 2019), but also with time of day when a reader
accesses the platform. In order to serve these needs, we need to consider the
heterogeneity of Wikipedia’s audience in space and time. Additionally, given
the extension of topics that Wikipedia covers and its large adoption, our
study offers insights into what content people consume online during the day,
at a scale generally accessible only to search engines and Internet providers,
with implications for design beyond Wikipedia.

Cultural diversity. Given the diversity of Wikipedia access rhythms across
countries (Fig. 8), future work could revisit our results from an
anthropological perspective, e.g., in order to pinpoint cultural differences
in the daily rhythm of information needs—or curiosity—across the globe. For
instance, we are fascinated by the fact that the rhythm of (English)
Wikipedia’s popularity in the U.S. is nearly exactly opposed to that in Spain,
and that India and Pakistan—two countries that once were one—have entirely
different rhythms of English Wikipedia consumption. Wikipedia logs offer a
window into where in the world people care about what, when, and we anticipate
that studying access time series while accounting for the interaction of
country by topic (which we omitted here) has enormous potential for
understanding global patterns of needs for knowledge.

Metrics for information needs. The popularity of an article (i.e., pageloads)
is often used as an indicator for its relevance (Wulczyn et al. 2016) or a
covariate used for stratification in the analysis of articles (Piccardi et al.
2020). In our context, this corresponds to only looking at the volume of the
consumption pattern and ignoring its shape throughout the day. In contrast,
our approach focuses on the shape of the consumption pattern revealing
substantial differences between articles. Thus, using the total number of
pageviews (volume) as a single relevance metric will likely miss nuances about
how these articles are useful to the reader. Complementary metrics capturing
the usage of articles, such as the shape, describe important properties that
might act as confounding factors, and other studies should consider them in
stratified analyses. In addition, they could also be directly useful for
editors providing additional information about the audience of articles,
potentially helping to bridge the gap reported in the misalignment between
supply and demand of articles (Warncke-Wang et al. 2015).

Customization. These results should be taken into account when building tools
to support users in finding and accessing relevant information (e.g.
Wikipedia’s search or recommendations such as
RelatedArticles777https://www.mediawiki.org/wiki/Extension:RelatedArticles) or
to customize their online experience. For example, on average offering
information about a movie in the morning has less value than in the evening.
Similarly, understanding the content that draws more attention at a different
time of the day has implications for designing systems to engage potential
editors when they are more inclined to contribute to specific content.

Infrastructure optimization. As observed in previous work (Reinoso et al.
2012), these findings are valuable for optimizing the Wikimedia
infrastructure. Given the scale of Wikipedia, optimizing data caching and
load-balancing to reflect the actual needs of the consumers across space and
time can offer significant benefits for the platform’s performance.

Limitations and future work. Our analysis may have some data limitations,
although we argue that it is unlikely they would alter our main findings and
conclusions. For example, despite the best efforts of the Wikimedia
infrastructure team in developing heuristics to detect bots, the data may
still contain some automated traffic. Similarly, country and timezone are
identified using the IP address of the request, which may be sensitive to the
use of VPNs. Other aspects that may influence our findings are unobserved
external factors such as biases introduced by search engines. Since the large
majority of Wikipedia traffic originates from search engines (Piccardi et al.
2023), search engine results varying with the time of the day would also
impact visits to Wikipedia.

One concrete limitation of our study that we aim to address in future work is
focusing only on the English edition of Wikipedia. Readers from non-English-
speaking countries consuming content from this edition may be a biased
population. Future work should extend our study to multiple languages to
compare information behaviors worldwide. Also, future work should study how
individual-level (as opposed to population-level) information needs change
during the day, possibly combined with demographic data, such as age or
education (Kulshrestha et al. 2020). In our case study, this was not possible
due to privacy constraints.

Another limitation of this study is the potential impact of external factors.
The readers’ behavior could be affected by extended temporal cycles, including
annual trends or worldwide occurrences, such as the mobility restrictions
imposed during the COVID-19 pandemic (Ribeiro et al. 2021). Consequently,
further research should explore these patterns over a period extending beyond
the four-week duration of this study.

Moreover, future work should explore the shape and strength of temporal
rhythms on other platforms beyond Wikipedia, especially on search engines,
which tend to be the first resource we turn to when we need information
online. In this sense, studying search engines can offer a complementary view
to our findings. Ultimately, we hope that our study can help pave the way to
better serve the needs of Wikipedia readers and Web users in general.

Ethical considerations. Server logs may contain sensitive information with
implications for the privacy of users. In this work, we pay special care to
ensure the researchers access only anonymized records, excluding activities of
logged-in users and editors that may be linked through public data. Our
findings describe aggregated behaviors that represent a minimal risk for
privacy violations. We believe the benefit of presenting them outweighs the
potential risks.

## Acknowledgements

We would like to thank Leila Zia and Brandon Black for insightful discussions
and for reviewing an initial draft of this paper. West’s lab is partly
supported by grants from Swiss National Science Foundation (200021_185043,
TMSGI2_211379), Swiss Data Science Center (P22_08), H2020 (952215), Microsoft
Swiss Joint Research Center, and Google, and by generous gifts from Facebook,
Google, and Microsoft

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