# Heating rate in a linear quadrupole trap

A. Poindron, J. Pedregosa-Gutierrez, C. Champenois  Aix-Marseille Université,
CNRS, PIIM, Marseille, France

###### Abstract

In radio-frequency trap, the temperature of ion ensembles converges towards a
hot equilibrium due to radio-frequency heating. This effect is detrimental to
the stability of trapped ensembles and is the justification of cooling. The
intensity of this radio-frequency heating increases with the amplitude of the
radio-frequency field $q_{x}$. Using an analytical empirical formula, we show
that the lifetime of the ion ensemble $t_{0}$ under cold condition increases
with $q_{x}$ according to a power law $t_{0}\propto q_{x}^{A}$, and does not
vary significantly for the several ion quantities $N$ tested. The temperature
of the explosive onset $B$ decreases linearly with $q_{x}$. We also show that
non-linear instabilities due to trapping parameters decreases $t_{0}$ and $B$,
and produce a local increase of heating rate for certain temperature ranges.

##  I Introduction

For the investigation of constituents of matter and their dynamical behaviour,
particle traps are an essential tool [1]. They are appreciated for their
ability to isolate a small amount of particles in a limited volume of space
where observations and interactions can be carried out. For the trapping of
charged particles, the use of radio-frequency (rf) fields is very convenient.
Nevertheless it introduces a forced motion in the ions dynamics which leads to
radio-frequency heating [2], an effect detrimental to the stability of trapped
ensembles and heating switching them from a cold equilibrium to a hot one [3].
Laser or sympathetic cooling can be used in order to bring the trapped ions to
a low temperature equilibrium, limiting the effect of rf heating to a minimum,
making ensembles of cooled ions suitable for many experiments where a high
level of precision is required such as in : micro-wave [4] and tera-hertz [5]
metrology, high precision spectroscopy [6], quantum information experiments
[7, 8, 9, 10], manipulation of cold molecular ions [11, 12, 13] or plasma
stopping power experiments [14]. Conversely, we recently identified a new
application for an ensemble of laser-cooled trapped ions as a detector for
giant molecular ions [15] where rf heating can be exploited as a beneficial
effect. In this principle, a molecular ion to be detected is introduced in a
laser-cooled trapped Ca+ ensemble, and triggers a modification of the
temperature of the ion ensemble, observable in its fluorescence. The radio-
frequency heating is used as an amplifier for the initial perturbation that
would be unable to induce a significant change in the ion ensemble temperature
alone. In both cases an analytical description of rf heating would be
beneficial for the design and operation of trapped charged particles
experiments but remains unavailable. In this article we propose to study the
temporal dynamics of rf heating through numerical simulations and aim at
providing an analytical expression for the thermal evolution as well as the
ensemble cold lifetime as a function of the rf amplitude. Previous numerical
works have been devoted to the study of the thermal evolution of trapped
ensembles of charged particles. First studies pointing out the relation
between rf heating and order-chaos transition were carried out around year
1990 [16, 17, 18] for only two-ion systems. In 1991 the thermal evolution of
ensembles up to 512 ions has been studied [19] during few hundreds of secular
period, limiting the study to temperature below 50 mK and to rf amplitude at
the limit of stability. In 2005, periodic edge conditions have been used to
study the thermal evolution at longer time scales [20], reaching 10K, but in
that case the study does not account for finite size effects which are non
negligible [21, 22]. In [23, 2] the rf heating are computed using an
equilibrium forced by a friction, thus without considering the dynamics. For
this article we propose to study the time-dependence of the temperature for
ion ensembles up to 1024 ions and temperatures up to 400 K. We propose an
analytical, empirical, function that can predict the cold lifetime of the ion
ensemble in the cold equilibrium for three ensemble populations and several rf
amplitudes. The knowledge of this cold lifetime is useful for the design and
operation of experiments where the cooling may be deactivated occasionally.
Also, this analytical function may allow to determine a threshold temperature
whose knowledge may help design experiments such as proposed in [15].

##  II Linear quadrupole trap

###  II.1 Trapping potential and motion equation

For those simulations, the trap parameters are the same as in our previous
article [3]. In a quadrupole linear Paul trap supplied with a radio-frequency
voltage $U_{rf}$ with angular frequency $\Omega=2\times 2\pi$ MHz and a static
voltage $U_{st}$ the potential within its internal radius $r_{0}$ is expressed
as

$\Phi(x,y,t)=\frac{U_{st}+U_{rf}\cos\Omega
t}{r_{0}^{2}}\left(x^{2}-y^{2}\right)$ (1)

with inner radius $r_{0}=2.5$ mm and $x$ and $y$ the two radial axis [15].

The dynamics of an ion $i$ with mass $m$ in this potential is described by the
following equations :

$\displaystyle\ddot{u}_{i}+\left(-\frac{\omega_{z}^{2}}{2}\pm\frac{2QU_{RF}\cos{\Omega
t}}{mr_{0}^{2}}\right)u_{i}$
$\displaystyle\quad\quad\quad\quad=\frac{Q^{2}}{4\pi\epsilon_{0}m}\sum_{j=1,j\neq
i}^{N}{\frac{u_{i}-u_{j}}{|\bm{r}_{i}-\bm{r}_{j}|^{3}}}$ (2)
$\displaystyle\ddot{z}_{i}+\omega_{z}^{2}z_{i}=\frac{Q^{2}}{4\pi\epsilon_{0}m}\sum_{j=1,j\neq
i}^{N}{\frac{z_{i}-z_{j}}{|\bm{r}_{i}-\bm{r}_{j}|^{3}}}$ (3)

where $u_{i}$ stands for $x$ or $y$, and $\bm{r}_{i}=(x_{i},y_{i},z_{i})$,
$Q=z_{e}\times q_{e}=z_{e}1.6\cdot 10^{-19}$ C the particle charge,
$k_{C}=1/(4\pi\varepsilon_{0})$ and $\varepsilon_{0}$ the permittivity.
$a_{u}$ and $q_{u}$ are referred as stability parameters and defined as

$\displaystyle a_{x}$
$\displaystyle=-a_{y}=\frac{8QU_{st}}{mr_{0}^{2}\Omega^{2}}$ (4)
$\displaystyle q_{x}$
$\displaystyle=-q_{y}=\frac{4QU_{rf}}{mr_{0}^{2}\Omega^{2}}.$ (5)

In the case of a single ion trapped, the right-hand term of equation 2 cancels
and can be recast into the so-called Mathieu equation. In this case the
solution can be analytically derived and its stability determined as a
function of the parameters $a_{u}$ and $q_{u}$.

The confinement along the trap axis, z-axis, is done with a static potential
$U_{G}=m\omega_{z}^{2}z^{2}$ applied to the ends of each rod, generating a
quadratic potential in our segmented trap [15], characterised by the frequency
$\omega_{z}/2\pi=100$ kHz for a static potential applied of $U_{DC}=1$ V.

The secular frequencies are computed in the same manner as in [3], and the
trapping potential are chosen in order to obtain ion ensembles with unity
aspect ratios.

###  II.2 Temperature and heating rate

The temperature of the ion ensemble is related to the velocity $v_{i}$ of the
ions by the formula [24]

$\frac{3}{2}k_{B}T=\frac{1}{2}\frac{m}{N}\sum_{i=1}^{N}\overline{v_{i}}^{2}=\langle\overline{v_{i}}^{2}\rangle=\frac{1}{2}\frac{m}{N}\langle
V_{i}^{2}\rangle$ (6)

with $N$ the number of ions in the cloud, $k_{B}$ the Boltzmann’s constant,
and $\overline{v_{i}}$ the velocity of the ion $i$ over one rf period
$\tau_{rf}=500$ ns. Averaging over one radio-frequency period allows to smooth
out the micromotion induced by the radio-frequency field, and proves to
provide a satisfying averaged velocity for the measurement of the ensemble
temperature [25].

###  II.3 Radio-frequency heating

Because of radio-frequency heating, the temperature of an ensemble of charged
particles increase over time towards a high temperature equilibrium. Radio-
frequency heating is due the coupling introduced by the Coulomb forces,
allowing energy from the radio-frequency field to be transferred to the
Brownian motion of the ions [17, 19, 20]. One feature of this radio-frequency
heating is the so-called fast transition from low temperature to high
temperature equilibrium [3], refereed as an ”explosive onset” [16]. Heating
rate $H$ is defined as the temperature variation for a given unit of time.
Because temperature is computed so the micromotion is ignored, heating rate
can be understood as the time derivative of the temperature
$H=\mathrm{d}T/\mathrm{d}t$.

##  III Molecular dynamics simulations

Figure 1: Temperature evolution for $q_{x}=0.64$, $U_{DC}=15.4$ V. The blue
line is the temperature computed from the cycle average velocity of ions, the
dotted orange line is the temperature filtered with a 8th-order digital
Butterworth filter forward-reverse in time [26], the dashed red line is the
analytical fit of the temperature with function $\psi$.

###  III.1 Parameters

The numerical simulations are carried out with a molecular dynamics program
based on velocity-Verlet algorithm [15], integrating Coulomb repulsion and
electric trapping forces, but neither laser cooling nor friction. Ensemble of
$N=[256,512,1024]$ ions are simulated for each of the set of trapping
parameters in table 1, initially for a total of 27 different conditions. Some
additional condition have been tested to refine the results when required. The
trapping voltages are chosen so the trapping potential is spherical.

$q_{x}$ | $0.54$ | $0.56$ | $0.58$ | $0.60$ | $0.62$
---|---|---|---|---|---
$a_{z}$ | $5.55\cdot 10^{-2}$ | $6.04\cdot 10^{-2}$ | $6.56\cdot 10^{-2}$ | $7.12\cdot 10^{-2}$ | $7.71\cdot 10^{-2}$
$q_{x}$ | $0.64$ | $0.66$ | $0.68$ | $0.70$ |
$a_{z}$ | $8.35\cdot 10^{-2}$ | $9.04\cdot 10^{-2}$ | $9.77\cdot 10^{-2}$ | $1.05\cdot 10^{-1}$ |
Table 1: Trapping parameters for the first systematical set of simulations.

While the simulation time is expected to increase with $N$, it turns out
$q_{x}$ is the main parameter affecting wall time, because the smaller $q_{x}$
the longer the simulation. In order to keep the simulations under two hours,
no simulation is done with $q_{x}<0.54$ and $N>1024$. Additional conditions
were rendered to study the behaviour of the system around $q_{x}=0.62$ where
an instability is found [27]. The simulation time step $\tau_{simu}$ is taken
as the highest value for which no significant change is visible when it is
taken smaller. In this article the time step is taken so there are
$n_{t}=1000$ time step in one radio-frequency cycle
$\tau_{simu}=2\pi/(n_{t}\Omega)$.

###  III.2 Analytical empirical formula

The sigmoid shape of the temperature evolution in semilog-y representation
(Fig. 1) inspired the choice for the analytical function used to fit the data.
Elementary logistic or arctangent functions have been tested, but showed a
poor ability to fit the temperature evolution, which translated into
inconsistent determinations of cold lifetimes as a function of the rf
amplitude. A more general sigmoid function with 5 parameters is used in this
article (Eq. 7) [28], as follows :

$\psi=A\frac{t-t_{0}}{\left(C+|t-t_{0}|^{\gamma}\right)^{1/\gamma}}+B$ (7)

with $A$ the amplitude of the function and $B$ the value of $\psi$ at
$t=t_{0}$. $C$ and $\gamma$ are parameters related so $A/(C^{-1/\gamma})$ is
the value of $\mathrm{d}\psi/\mathrm{d}t$ at $t=t_{0}$.
$\mathrm{d}\psi/\mathrm{d}t$ is maximum for $t=t_{0}$. This function exhibits
a fast transition between two levels with an inflection point of coordinates
$(t_{0},B)$. $t_{0}$ is the timing of the inflection point, related to the
timing of the explosive onset in this article, and $B=T(t=t_{0})$ the
temperature at which this explosive onset occurs.

Because the temperature exhibits fast oscillations, unrelated to radio-
frequency and secular motion, it is filtered before applying the fit. The
filter is an 8th-order digital Butterworth low-pass filter, forward-reverse in
time to ensure no time shift is induced [26] as with a Savitzky-Golay for
instance. The cut frequency of this filter is chosen equal to the double of
the highest of the first order secular frequencies
($\omega_{x},\omega_{y},\omega_{z}$).

It is not satisfying to use $t_{0}$ directly as the timing of the explosive
onset because the initial temperature varies with $N$ for a fixed set of
numerical parameters. A reliable cold lifetime $\Delta t$ should only depend
on the initial temperature when its dependency regarding the initial
temperature would be studied. In the case of this article, the cold lifetimes
are studied as a function of the trapping parameters and the population. The
cold lifetimes are then computed by measuring the time difference between the
two following events : the ensemble reaches $T_{threshold}=10$ mK and the
explosive onset. This can be written as $\Delta t=t_{0}-t(T=T_{threshold})$.

###  III.3 Heating rate

Radio-frequency heating is a phenomenon significantly occurring in long-time
scale with respect to the radio-frequency period. Rather than carrying on a
time derivate of the temperature sampled at the radio-frequency period it is
more relevant to derivate the heating rate from a window-averaged temperature.
Then the temperature is first averaged over a given number of radio-frequency
periods $n_{t}$ before time derivation is applied. Furthermore, because the
radio-frequency sampled temperature exhibits significant oscillation at short
time scale unrelated to radio-frequency heating, averaging ensures that those
oscillations are neglected with respect to the long term variations due to
radio-frequency heating.

##  IV Results

###  IV.1 Temperature evolution

Temperature evolution of trapped ensembles exhibits a bistable behaviour as
described in [3]. Figure 1 shows two temperature evolutions for two ensembles
sizes and similar trapping parameters. Ions are initialized below $10^{-2}$ K
before the explosive onset occurs within few milliseconds. The temperature of
the ensembles reaches $100$ K after a delay similar to the delay between
$10^{-2}$ and $1$ K.

###  IV.2 Cold lifetime

All temperature evolutions from simulated conditions were fitted with the
function $\psi$. The ensembles lifetime $\Delta t$ for each condition are
displayed in Fig. 2 against the Mathieu parameter $q_{x}$. For each ensemble,
$\Delta t$ vs. $q_{x}$ exhibits an affine behaviour in a loglog
representation. This data is fitted with an affine function $\log\Delta
t=p\log q_{x}+q$ which allows to express $\Delta t$ as a power law of $q_{x}$
so that $\Delta t=rq_{x}^{p}$. Values of $p$ and $r=10^{q}$ are presented in
table 2. It is not guaranteed the linear fit can extrapolate beyond the
simulated range of parameters, but it already provides an idea of ensembles
lifetimes. In particular, looking at the range from $q_{x}=0.66$ to
$q_{x}=0.70$ it is possible to see the slope may be different than in the
other part of the data set. When the lifetime goes beyond the ms, the
explosive onset may occur too soon for the fit to properly render the first
low temperature plateau.

Figure 2: Ensemble lifetime $t_{0}$ as a function of Mathieu parameter $q_{x}$. The dashed lines are affine fits to the corresponding data (colour code). N | $256$ | $512$ | $1024$
---|---|---|---
p | $-20.8$ | $-18.9$ | $-16.4$
r | $7.96\cdot 10^{-8}$ | $2.02\cdot 10^{-8}$ | $9.11\cdot 10^{-7}$
Table 2: Parameters for the fit of $t_{0}$ vs. $q_{x}$, for three ensembles of
ions.

###  IV.3 Explosive onset temperature

The temperature at which the explosive onset occurs is given by the parameter
$B=T(t=t_{0})$, presented in figure 3. Globally the temperature of the
explosive onset decreases linearly with $q_{x}$ in a linear. In the context of
our trapped ensemble used as a molecular ion detector [15], this temperature
can be related to the trigger threshold of the detector. Indeed, once the
ensemble overcomes this temperature, the rf heating becomes dominant with
respect to laser cooling [3] and temperature reaches much higher orders of
magnitude, providing a detection signal in the fluorescence of the ensemble
[15]. This trigger temperature can be then converted into energy transferred
from the projectile to the cloud. For instance, in a $N=1024$ ^40Ca+ ion
ensemble, an explosive onset temperature of $B=1$ K is equivalent to an energy
of $132$ meV.

Figure 3: Cloud temperature $B$ at $t=t_{0}$ as a function of Mathieu
parameter $q_{x}$. The dashed lines are affine fits to the corresponding data
(colour code).

###  IV.4 Non-linear behaviour

At $q_{x}=0.62$ for $N=1024$ ions, it is possible to see that the ensemble
lifetime before explosion is a third of the lifetime for similar conditions in
the vicinity. At such parameters the temperature of the explosive onset is 10%
lower than for close $q_{x}$. In the context of our detector this is of
particular interest because it allows the detector to be more sensitive.
Additionnal simulation between $q_{x}=0.61$ and $q_{x}=0.63$ are carried out
(Fig. 4). It shows that this extra sensitivity is achieved for $q_{x}=0.62\pm
0.01$, where $q_{x}$ only varies by 2% in relative value. This margin is very
wide regarding the precision of radio-frequency drives, thus it is possible to
set the parameters in this area in order to make the ensemble more susceptible
to a molecula ion. The existence of local conditions with significantly
different outcomes in term of stability was already something visible in our
previous study of the interaction of a trapped ensemble with a molecular ion
[15]. It may be related to non-linear instabilities [27]. In this case, the
explosive onset having a lower temperature as around allows to trigger more
easily the detection with an injected molecular ion.

Figure 4: (Top) Ensemble lifetime $\Delta t$ as a function of Mathieu
parameter $q_{x}$ for values around $q_{x}=0.62$. The dashed line is the fit
from figure 2. The dotted line is a guide to the eye. (Bot) Explosive onset
temperature $B$ as a function of $q_{x}$ for the same values around
$q_{x}=0.62$. The dashed line is the fit from figure 3. The dotted line is a
guide to the eye.

##  V Conclusion

Typically, the fit provides a very consistent information on the explosive
onset timing ($t_{0}$). By carefully avoiding to include parts of the
temperature data where the evolution do not account for the radio-frequency
heating we are studying, it is also possible to benefit from the information
about the temperature at which explosive onset occurs ($B$). Ideally, an
analytical formula derived from the microscopic understanding of the ensemble
behaviour will also provide the same informations, but the determination of
such time-dependent formula for the temperature evolution is a challenge [29,
2], and answering to this problem requires a microscopical theory that our
synthetical approach can’t elude. Perhaps it is possible to elaborate a more
representative sigmoid function once derived provides a more representative
heating rate than the one we propose. Nevertheless, our method already
provides a very good estimate of the lifetime of the cloud, which is a very
crucial information for some experiments where trapped ions must be kept
stable in cold temperature while cooling is sporadically interrupted.

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# TrollSpot: Detecting misbehavior in commenting platforms

Tai Ching Li  University of California - Riverside900 University
AveRiversideCA92557<EMAIL_ADDRESS>,  Joobin Gharibshah  University of
California - Riverside900 University AveRiversideCA92557<EMAIL_ADDRESS>,
Evangelos E. Papalexakis  University of California - Riverside900 University
AveRiversideCA92557<EMAIL_ADDRESS>and  Michalis Faloutsos  University of
California - Riverside900 University AveRiversideCA92557<EMAIL_ADDRESS>
(2018)

###### Abstract.

Commenting platforms, such as Disqus, have emerged as a major online
communication platform with millions of users and posts. Their popularity has
also attracted parasitic and malicious behaviors, such as trolling and
spamming. There has been relatively little research on modeling and
safeguarding these platforms. As our key contribution, we develop a systematic
approach to detect malicious users on commenting platforms focusing on having:
(a) interpretable, and (b) fine-grained classification of malice. Our work has
two key novelties: (a) we propose two classifications methods, with one
following a two stage approach, which first maps observable features to
behaviors and then maps these behaviors to user roles, and (b) we use a
comprehensive set of 73 features that span four dimensions of information. We
use 7 million comments during a 9 month period, and we show that our
classification methods can distinguish between benign, and malicious roles
(spammers, trollers, and fanatics) with a 0.904 AUC. Our work is a solid step
towards ensuring that commenting platforms are a safe and pleasant medium for
the exchange of ideas.

††journalyear: 2018††copyright: rightsretained††conference: WSDM workshop on
Misinformation and Misbehavior Mining on the Web; 2018; Marina Del Rey, CA,
USA††doi: 10.475/123_4††isbn: 123-4567-24-567/08/06

##  1\. Introduction

Any successful medium eventually attracts abusive behaviors, and commenting
platforms is no exception. Over the last decade, commenting on news articles
has emerged as a new form of highly social interaction. First, a small number
of companies facilitate the backend management of comments for a wide range of
websites. We use the term commenting platform to refer to such platforms,
which include Disqus (Disqus, 2015), LiveFyre (LiveFyre, [n. d.]), and
IntenseDebate (Intense Debate, [n. d.]). Second, commenting is an intense
activity for many users, who can spend many hours daily at it.

We list a set of definitions that we use in this paper. A user is defined by a
platform account, which enables her to leave comments to articles on a website
that uses the commenting platform. A user may leave multiple comments for an
article, which leads us to define the engagement of a user for that article.
An engagement has a time duration and intensity in terms of number of
comments. In lack of a better term, when two users comment on the same
article, we say that they collaborate and we use the term collaboration to
describe this activity. We use the term collaboration intensity referring the
number of articles for which two users collaborate.

The key question in our work is: Can we automatically detect malicious users
in these commenting platform? Specifically, we frame the problem as follows.
The input is the commenting information of the users. This includes: the
author of the comment, the time it was posted, and information on the article
it was posted for. The goal is to identify malicious behaviors and users.
Detecting parasitic and abusive behaviors is a critical building block for
ensuring that these platforms serve their primary purpose, which is the honest
and safe exchange of opinions among readers.

Commenting platforms have attracted little attention so far with only few
exceptions (Cheng et al., 2015)(Cheng et al., 2017). Most work on modeling and
misbehavior detection focuses on Online Social Networks (OSNs), and blogs. In
Section 6, we survey the key related areas including: (a) detecting abusive
behaviors and malware propagation in OSNs(Chu et al., 2012)(Morstatter et al.,
2016); (b) modeling online user behavior(Ferraz Costa et al., 2015) (Devineni
et al., 2015) (Gu et al., 2016)(Gharibshah et al., 2017) (Rawassizadeh et al.,
2016); and (c) analyzing text of online users(Sculley and Wachman,
2007)(Mishne et al., 2005)(Sureka, 2011).

We propose a systematic comprehensive methodology to identify malicious users
on commenting platforms to enable: (a) interpretable, and (b) fine-grained
classification of malicious behavior. We claim four key novelties in our work.

a. A behavior-based classification. We propose two classification methods, the
first one use typical Random Forest classifier yet another one introduces a
two-stage classification approach. In this method, we map: (a) observable
features to behaviors, and (b) behaviors into user roles, using unsupervised
and supervised learning respectively.

b. A comprehensive multidimensional feature set. We combine 73 features from
four different dimensions of user interactions: (a) social interaction or
user-user interaction, (b) engagement or user-article interaction, (c)
temporal features, and (d) linguistic features.

c. Fine-grained malicious role identification. Our approach goes beyond a good
versus bad determination to a more fined-grained classification of misbehaving
roles. Here, we focus on three roles: (a) spammers, (b) trolls, and (c)
fanatics, which are defined in the next section. However, it is easy to
introduce more roles as long as appropriate ground truth is available.

d. Interpretable classification. The results of our approach are
interpretable, since they are behavior-centric. A system administrator can
better understand or tweak the definition of, say, a spammer, by looking at
the behaviors that constitute its definition (e.g. high number of repeated
text across articles, low engagement per article).

Our study is grounded on nearly 7 million comments from nearly 200K users over
9 months from Discus, which is arguably the largest commenting platform. Here
we highlight some interesting result from our study.

a. Identifying misbehaving users with 0.904 AUC. Our classifier can
efficiently identify misbehaving users and it outperforms the baseline we
compare with.

b. The role classification result achieves 80.8% overall accuracy.

c. We find patterns of misbehaving users from their interpretable latent
behavior. An example latent behavior indicates that making longer comments and
using capital letters more frequently is a sign of misbehaving users, and the
later the active hour of a users, the more likely they are to misbehave.

d. Large scale study. About 0.9% of total users in our data-set are
misbehaving users, and CNBC has the largest percentage of misbehaving users
which is 1.48%. Only 15% of the misbehaving users exhibit a cross-website
behavior.

##  2\. Data collection and definitions

Disqus is one of the most widely-used commenting service provider today with a
billion unique visitors a month and installed by more than two and a half
million sites, including ABC News, Rolling Stone, IGN, Bloomberg and more.

Data Collection. We collected data from Disqus through its Application
Programming Interface (API). The API can be used to collect all the comments
for a given article, and for all the articles of a given website. However, the
functionality of collecting all the comments for a given user would have been
useful for our study, but it became unavailable in 2014 for privacy reasons.

Using the website-centric API, we collect data from four popular websites: (a)
CNBC News, (b) ABC News, (c) Bloomberg Views and (d) Breaking News - a Disqus
channel. The first three are well-known news websites and the last one is the
most popular channel on Disqus. A channel is similar to a newsfeed, whose
articles are selected by the users that participate in that channel. We
collect all comments posted at articles published on these 4 sources in
between Nov 1st 2015 and July 31st 2016. The dataset consists of: (a) 286,275
articles, (b) 6,994,693 comments and (c) 201,112 unique users, (d) 1,705,667
engagements.

Establishing the ground truth of misbehaving users. A key challenge in our
work is the need for ground truth of misbehaving users. Fortunately, Disqus
enables users to report misbehaving comments and the number of reports a
comment received is provided by Disqus API. In our 7M comments, we have 66.4k
comments reported as “bad/inappropriate" by the community. We will further
discuss this in Section 4 and show how we leverage this to identify
misbehaving users.

Roles of misbehaving users and ground truth. We identify and attempt to detect
three different roles of misbehaving users: trolls, spammers and fanatics.
These are inherently difficult to define, so we resort to human feedback.

We define three malicious roles below. We show here the definitions that we
gave our evaluators, as we explain in Section 4.

  1. (1)

Trolls. Users who make inflammatory or inappropriate comments for the sole
purpose of upsetting other users and provoking a response.

  2. (2)

Spammers. Users who repeatedly make similar comments in the same or multiple
articles.

  3. (3)

Fanatics. Users who exhibits an extreme and uncritical enthusiasm in religion
or politics.

##  3\. Features and user behavior

In this section, we identify and study features that relate to user behavior
on the Disqus platform. Although studying each of these features in depth is
of independent interest, the goal is to identify meaningful features that can
help us detect misbehavior. Due to space limitations, we can only provide
highlights of the features and their distributions. In Table 1, we outline the
features that we use in Section 4.

We study the behavior of users along four dimensions: (a) engagement behavior
(user-article interaction), (b) social behavior (user-user interaction), (c)
temporal behavior, and (d) linguistic properties.

[b]

Table 1. The overview of the 73 features we use per Dimension

Dimension |  Features |  Count
---|---|---
Engagement |  number of engagements, engagement duration*, engagement intensity* |  7
Social |  degrees, number of maximal cliques, number of triangles (in different level of collaboration intensity) |  17
Temporal |  number of comments made in 24-hour slots, highly-active hour |  25
Linguistic |  number of words*, number of sentences*, percentage of capital letters*, readability metrics, number of URLs |  24

  * *

We use several statistical versions (mean, maximum and minimum) of the feature
per engagements, user or comment.

###  3.1. Engagement behavior

Figure 1. Engagement behavior: Distribution of intensity and duration of
engagements.

We quantify the engagement (user - article interaction) with 7 different
features. Six of them are derived from two major properties: The engagement
duration is the time interval between the first comment and the last comment
user makes on the article. If the user leaves only one comment, we consider
this as zero length interval. The engagement intensity is the total number of
comments user makes on the article.

Engagement duration: 90% last for less than 10 hours, but some can be as long
as half an year. In Figure 1, we plot the Cumulative Distribution Function
(CDF) of the duration (top x-axis) for all 1.7M engagements. We find that 90%
of engagements last less than 10 hours and have less than 7 comments.
Interestingly, we find 106 engagements which last for more than half year!

Engagement intensity: 90% have less than 7 comments, but 0.06% have more than
100 comments. In Figure 1, we plot the CDF of the intensity (bottom x-axis)
for all engagements. We find that 90% of them have less than 7 comments, while
1,151 (0.06%) of them have more than 100 comments.

High intensity is correlated with misbehavior. The observations above raise
the question: is unusually high engagement intensity associated with
misbehavior? Preliminary manual inspection suggests that these engagements
contain many reported (by the community) comments. We quantify the correlation
between engagement intensity and the total number of reported comments in the
engagement and we find a Pearson correlation coefficient $\rho=0.53$. This
suggests that engagement intensity should be a good metric in our
classification.

###  3.2. Social Behavior

We propose 17 features to model the social interaction of the users, which we
define as the posting of comments to the same articles.

Single-article collaboration Threshold: $\theta$ comments. We say that two
users collaborate in one article, if they each post at least $\theta$ comments
on that article. For $\theta=1$, the graph become very dense, and the analysis
is both slow and less informative. In the remaining of this work, we use a
threshold $\theta=2$.

User-user collaboration intensity and threshold: $\lambda$ articles. The
collaboration intensity is the number of articles that two users collaborate
for a given threshold $\theta$. To study collaborations at different levels of
intensity, we introduce the collaboration intensity threshold $\lambda$, which
we use below.

We define the undirected weighted collaboration graph $G_{\lambda}=\langle
V_{\lambda},E_{\lambda}\rangle$ of collaboration intensity $\lambda$ where:

  1. (1)

$V_{\lambda}$ is a set nodes $v$, representing users.

  2. (2)

$E_{\lambda}$ is the set of edges, where edge $e_{ij}$ between nodes $v_{i}$
and $v_{j}$ exists, if and only if the collaboration intensity of the users
exceeds the threshold of $\lambda$ articles. The edge weight $w(e_{ij})$ is
set to the collaboration intensity.

The collaboration graph (for $\theta=2$ and $\lambda=0$) has 95,527 users and
roughly 21 millions edges, an average degree of 440.7 and a median degree of
137. Note that we do not include users with zero degree in this graph.

In Figure 2, we plot the CDF of the user degrees (bottom x-axis) and the edge
weight distributions (top x-axis). We see that 90% of the users have degree
lower than 1,054, the max degree goes to 26,318: this user collaborates with
more than 27% of users in the graph! The figure also shows that 90% of the
edges have weights less than 2. Although it is not easy to gauge from the
plot, we find 12,374 edges with weight over 64, 1,779 edges with weight over
128 and 65 edges with weight over 256. In other words, there are 65 pairs of
users who have collaborated on more than 256 articles.

Capturing the collaboration groups: triangles and cliques. We quantify the
local connectivity of the users using the number of maximal cliques and
triangles in which a user participates. Both these metrics capture how densely
connected the neighbors of that user are. Figure 2 shows the distribution of
triangles and maximal cliques of user in graph, for $\lambda$ equals to 128.
We do not count "trivial" cliques of size two. We see that 50% of users have
less than 27 triangles on the neighborhood, 90% of have less than 376, but
there are 1% with more than 868 triangles. We also see that 90% of users have
less than 51 maximal cliques and there are 8 users, who participate in more
than 186 cliques which is more than 50% of all maximal cliques in the graph.
These highly collaborative users are suspicious and this encouraged us to
consider both these features for misbehavior detection.

Figure 2. Social behavior: (a) the CDF of the user degrees (bottom x-axis) and
the edge weight distributions (top x-axis), (b) CDF of the number of cliques
and triangles of user in the $G_{128}$ collaboration graph.

###  3.3. Temporal behavior

We quantify the temporal behavior of users with 25 features.

Most users exhibit persistent behavior: daily and weekly. We use the time and
day of the week plot to understand the temporal behavior of the users. The
plot shows the number of comments in each hour-of-day and day-of-week as a
heat-map. Figure 3 shows this behavior for all the users, but individual users
exhibit similar daily and weekly behavior, as we will see below. On the x-axis
(hour-of-day), we see that the commenting activities increase at the beginning
of day in the east coast as annotated in the plot, the peak hours cross the
noon period of both east and west coasts then drop sharply after that. Given
the news websites we are studying, it is reasonable to assume a US-centric
user majority. In y-axis (day-of-week), the activity increases at the start of
the week, peaks in the middle, and drops before the weekend. Combining the two
observations, we see that Disqus users post most of their comments during the
common work-hours in the week. Note that the same pattern is also observed on
other social networks, like Facebook (Warren, 2010) and Twitter (Sysomos,
2014).

The plot lead us to the following hypothesis:

Hypothesis: A typical user makes most of her comments in a period of 3-4 hours
in a day.

Figure 3. Temporal behavior. (a) Time and day of the week plot. (b) The
distribution of highly-active hours of users.

The highly-active hours of users commenting behavior. To assess the validity
of our hypothesis, we would like to answer the question: how many hours a day
does a user spend commenting? Determining this hides subtleties as: (a)
patterns can vary from day to day, and (b) it could be that many hours have
non-zero activity due to averaging over a long period. Thus, we opt to capture
how “focused" or "spread" is the commenting activity of the user. We define
highly-active hours to be the minimum number of hours, during which the user
makes more than 50% of their total comments during a day on average.

Highly-active hours is less than 4 hours for 96.7% of the users. The
distribution of the users’ highly-active hours is shown in Figure 3. The plot
shows that 96.7% of users have highly-active hours less than four hours, which
matches our hypothesis. Interestingly, we find 368 users who have more than 8
highly-active hours, a significantly wider spread. Upon inspection, many of
these users have non-trivial activity over 14 hours in a day. This wide range
of behaviors suggests that highly-active hours can be a useful metric for our
classification.

###  3.4. Linguistic properties

Figure 4. Linguistic property: number of words in a comment

We identify and study 24 linguistic features from the text of the posts, such
as the length of the comment, several metrics readability, number of URLs, but
discuss only a two metrics.

Only 1.9% of comments contain URLs. We naturally consider the existence of
URLs in a comment as a feature in our classification: their presence can
indicate ad-oriented spamming. We find that only 1.9% of all comments contain
one or more URLs. We also find that only 1.7% of the users have ever posted
more than 3 comments containing URLs. In fact, our interaction with the data
suggests that often users will use URLs as references in support of their
opinions.

Length: 91% of comments have less than 100 words. The length of a comment is a
good metric for the interest and the time a user is willing to spend
expressing her opinion about the article. In Figure 4, we plot the
distribution of the number of words in a comment in three different ways: (a)
across all comments, (b) the average comment length per user, and (c) minimum
comment length per user. We see that 91% of comments have less than 100 words,
while roughly 20% of the comments with less than 10 words. Interestingly, we
also find 14,838 (0.002%) comments with more than 500 words, which is roughly
equivalent to 1.5 pages (per wordstopages.com with Times New Roman, 12 font-
size, single-spacing): the comment is the size of small article!

Lengthy comments are more likely to be spam. We examine the lengthy comments
(>500 words) and find out that 47% of them are verbatim copies of at least one
other comment from the same user in our dataset. This is an indication of
spamming especially in its broader definition that we adopt here. Such
phenomenon is more pronounced for higher word counts: 63% of comments have
verbatim copies for length over 1,000 words , and 83% of comments with length
2,000 words or longer. This suggests that comment length is a helpful feature
in detecting misbehavior.

##  4\. Feature-based Misbehavior Identification

Having identified interesting features, we develop a method to identify
misbehaving users and their effectiveness. For convenience, we outline the
features in Table 1, and we intend to define them in detail in an extended
version of this paper.

Figure 5. (a) Distribution of reported comments of a user. (b) Number of users
having $k$ reported comments.

A. Establishing the ground truth. To overcome the lack of absolute truth, we
rely on “proxy signals". Here, we use the community’s own opinion: any user
can report (a.k.a. flag) a comment as “inappropriate". Below, we explain how
we use this community feedback to construct the ground truth, as the process
hides several subtleties.

Ground-truth: Reportings per malicious comment. To increase our confidence, we
set a minimum threshold of reports, $\phi$, that a comment must have to
labeled malicious. The rationale is that a single reporting can be created
even accidentally (the authors have regrettably done this once). After
analysis and deliberation omitted here, we settled on $\phi=3$ reportings. We
use the term reported comment to refer to a comment with more than $\phi$
reports.

Ground-truth: Reported comments per malicious user. In the same vain, we want
to be careful in labeling a user as malicious based on the number of reported
comments. We use the reported comments threshold, $r$, to control tune the
definition of malicious user.

Roughly 86% of the users have no reported comments. We plot the distribution
of the total number of reported comments for each user in Figure 5. We find
that 86.2% of users have no reported comments, and only 1.6% of users have
more than 10 reported comments.

We consider users with zero reported comments as benign for the purpose of
establishing the ground truth.

Building the ground truth datasets: $D_{r}$. We create a set of labeled
datasets as follows. First, we distinguish reported users into groups,
$R_{r(i)}$, with $r(i)=2^{i},for\leavevmode\nobreak\ \leavevmode\nobreak\
i=0,1,...$ A user is in group $R_{r(i)}$, if the number of her reported
comments are greater or equal $r(i)$. It turns out that no user has more than
128 reported comments. The numbers of users in each group with threshold
$r(i)$ are shown in Figure 5. Second, we create datasets $D_{r(i)}$ by
randomly selecting 200 reported users from $R_{r(i)}$, and combining them with
200 benign users (zero reported comment).

Benign user selection: Minimizing the effect of the number of comments of a
user. When selecting the 200 benign users to build the datasets, we follow the
insightful approach of the earlier in this space (Cheng et al., 2015). Namely,
we find benign users that “match" the number of comments of reported users.
The goal is to minimize the dominant role that the number of comments of a
user can play. First, the number of comments and number of reported comments
of a user are strongly positively correlated with a Pearson Correlation
Coefficient of 0.73. Second, most users have few comments given the skewness
of the distribution. Thus, a purely random selection of benign users would
have probably created a low-activity benign set in terms of user comments, and
a highly-active reported users. The classification would have been very
accurate by relying heavily on the number posts.

Figure 6. (a) Classification results as a function of the number of reported
comments that “incriminate" a user. (b) AUC of our approach and the baseline.

B. The benign-malicious classification. For the classification, we use the
Random Forest classifier provided by Weka (Witten et al., 1999), which gave
the best results among many that we tried. We perform ten-fold cross
validation and report the precision, recall, and ROC curve (AUC) of each
dataset in Figure 6. The plot shows that our features can identify reported
users with more than 80% precision when the threshold $r$ is larger than 16.

Selecting reported comments threshold $r=32$. We manually examined reported
users in $D_{16}$, $D_{32}$ and $D_{64}$ by sampling 20 users from each group.
We find that users with more than 16 reported comments exhibit a persistent
misbehavior throughout their lifetime. The 40 reported users sampled from
$D_{32}$ and $D_{64}$ are 100% labeled as misbehaving users by our independent
human evaluators. This gives us confidence to claim that users with 32 or more
reported comments are misbehaving users. Thus, we use dataset $D_{32}$ as
reference below.

The baseline classifier. We adapt and use a previously proposed algorithm as a
reference in our study (Cheng et al., 2015). That work focuses on predicting
whether a user will get banned in the future, which is a somewhat different
goal from our work.

We faithfully reproduce the reference method (Cheng et al., 2015), which also
uses the Random Forest technique like we do. In their work, they use 35
features, however 6 are not publicly available, namely the website moderator
features, such as the number of up-votes given to others (similar to a
Facebook “Like”). Unfortunately, we were not able to access those features
through the public API, therefore we do not use them in our experiments.

The accuracy of our method exhibits 90% AUC. For clarity of presentation, we
only show the comparison of AUC of the two methods in Figure 6. Our method
performs better than the baseline classifier, with the caveat that both
approaches are restricted to the publicly available features. The most
interesting conclusion is that our features have good discriminatory power in
classifying misbehaving and benign users.

C. The fine-grained malicious role classification. The novelty of the work
relies partly on going beyond the “malicious" label to the role of the
misbehaving user.

Ground truth for the roles of misbehaving users. Here, we resort to manual
labeling to create our reference data: we examine 200 misbehaving users in
$D_{32}$ and categorize them into three different roles: trolls, spammers and
fanatics. To the best of our knowledge, this is the first work that does such
a fine-grained classification of user behaviors, especially in commenting
platforms.

Table 2. Role classification result Role |  Precision |  Recall
---|---|---
Trolls |  86.4% |  73.1%
Spammers |  58.6% |  81%
Fanatics |  86.1% |  73.3%
Benign |  81% |  87.5%
Overall accuracy | 80.8%

Each user is labeled by three evaluators who were presented with the
definitions in Section 2. In absence of unanimity, we set their role by taking
the majority label. Out of 200 misbehaving users, 104 are labeled as trolls,
21 as spammers and 75 as fanatics.

Role classification: Our approach has 80.8% overall accuracy. Having ground
truth, we apply 10-fold cross validation with the same classifier and the same
73 features that we used to identify misbehaving users. Our result shows that
our model can effectively classify the role of misbehaving users with an
overall accuracy of 80.8% as shown in Table 2. For all the classes the recall
is above 73% and the precision above 81% except the Spammers.

The community shows tolerance to non-provocative spammers. Intrigued by the
low precision for spammers, we find that spam comments without provocative
language, swear words and sarcasm often do not get reported by the community.
Recalling Section 3.4, the unusually long comments are more likely to be spam,
due to verbatim repetitions. However, this behaviors seems to either escape
detection or be met with tolerance.

Our method identifies un-reported spammers. We examine the 12 false positive
in the spam category: our spam label is not corroborated by the community. We
actually find that at least one of these users exhibits clear spamming
behavior, as she repeats the exact same comment 3 times in one article and 5
times in another. This investigation suggests that our approach could be
catching parasitic behaviors that the community could miss. As a result, the
accuracy of our algorithm could be better than reported here, especially for
spammers.

D. Studying the misbehaving users in the wild.

We apply the classier to the whole dataset to understand how misbehaving users
distributed in the wild. For identifying misbehaving users, the classifier
labeled 1,738 (0.86%) users as misbehaving with confidence over 80%. The role
classification results are: 866 users are labeled as trolls, 165 users are
labeled as spammers and 597 users are labeled as fanatics. We also study how
misbehaving users distributed in each websites, the result is shown in Table
3. It shows that CNBC has the largest number of misbehaving users with 1,167
which is 1.48% of total users active on the website while the rest of websites
are at most 0.56% of users are misbehaving users. Again, we only label
misbehaving users with confidence over 80%.

Table 3. Misbehaving users in websites Website |  Total users |  Misbehaving users
---|---|---
ABC News |  129,053 |  717 (0.56%)
CNBC |  78,618 |  1167 (1.48%)
Bloomberg Views |  33,223 |  131 (0.39%)
Breaking-News (Disqus channel) |  11,607 |  48 (0.41%)

##  5\. Interpretable two-stage classification

In this section, we introduce a novel, two-stage approach in classifying
misbehaving users. In the first step we identify tightly-knit groups of users
who exhibit very similar behavior across a certain subset of the features we
discussed in the previous section. Each such group of users and their
associated features defines a latent user behavior. Note that we do not define
those latent user behaviors a-priori, they rather emerge from the data
automatically. Subsequently, we use these latent user behaviors as our new
features towards classifying misbehaving users. The advantage of this two-
stage approach is that the latent user behaviors offer interpret-ability of
the results and allow for in-depth analysis of different user (mis-)behaviors.

###  5.1. Identifying latent behaviors: Co-clustering

The first stage of our two-stage approach can be exactly mapped to an instance
of co-clustering. In a nutshell, co-clustering is the simultaneous clustering
of all data modalities. In our case, consider a representation of a user in
the vector space defined by the entire set of their features. Hence, the
modalities of our data are two: “user” and “feature”. Co-clustering of a users
$\times$ features data matrix essentially yields different groups (or co-
clusters), where each one contains a subset of the users and a subset of the
features. In other words, when grouping users and features together, co-
clustering allows for the flexibility of finding a set of users that are
highly similar only for a subset of their features. This subset of features is
key to our method. Essentially, the subset of features of a co-cluster defines
a latent user behavior.

Figure 7. Co-clustering discovers latent user behaviors and the assignment of
users and features to those behaviors.

An illustrative example is shown in Figure 7, where we have four distinct
latent user behaviors: “Benign”, “Troll”, “Spammer”, and “Fanatic”. After
properly rearranging the users and the features, in this simple example we see
that each latent user behavior is forming a block within the matrix. Notice
that blocks can overlap since: (a) in some cases a user can be classified with
different types of behavior, and (b) some features may be associated with
multiple types of behavior. Mathematically, each block (formally co-cluster)
in the data can be seen as (approximately) a rank-one matrix. By definition, a
rank-one matrix can be written as the outer product of two vectors, i.e.,
$\mathbf{ab}^{T}$. We, thus, can use the following formulation for co-
clustering, which was originally proposed in (Papalexakis et al., 2013):

(1) $\displaystyle{\min_{\mathbf{A\geq 0,B\geq
0}}\|\mathbf{X}-\mathbf{AB}^{T}\|+\lambda\sum_{i,r}|\mathbf{A}(i,r)|+\lambda\sum_{j,r}|\mathbf{B}(j,r)|}$

The above equation decomposes the data matrix $\mathbf{X}$ into a sum of rank-
one matrices (each one being approximately a co-cluster) and the
regularization penalties on the $\ell_{1}$ norms of matrices $\mathbf{A,B}$
(whose columns hold the indicator vector for each co-cluster, as shown in Fig.
7) ensure that the solution is sparse, so that only the users and features
that belong to a particular co-cluster have a non-zero (and positive) value in
our indicator vectors. Using this type of overlapping co-clustering, a user
may be assigned to multiple latent behaviors at the same time, with varying
degrees of participation. This enhances interpretability because it can give
further insight on whether e.g., a user has more than one roles or their
account has been hijacked and some of their comments are benign but some are
malicious. Finally, the above co-clustering formulation is lossy, which means
that it does not require all users to belong to at least one co-cluster. In
other words, the above formulation focuses on identifying the most dominant
latent behaviors and the users that engage in them, and leaves out users who
do not clearly belong in one (or more) of those latent behaviors. We,
henceforth, refer to those users as “non-clustered”.

###  5.2. Methodology

We apply co-clustering to the same dataset we used for role classification.
This dataset contains 200 benign users and 200 misbehaving users, which
include 104 trolls, 21 spammers and 75 fanatics. After fine tuning the
parameters of co-clustering, we find that the best number of co-clusters in
the data is 8. An indication for this number is that the algorithm returned
empty clusters for larger numbers of clusters. We show the distribution of
users in each clusters in Figure 8.

The size of clusters varies from 29 to 268, indicating that co-clustering
could not only capture the common behaviors but also the obscure ones (small
clusters). In each cluster, the clustered users will exhibit a different level
of value on multiple features comparing to non-clustered users as we present
in Figure 8. The X-axis demonstrates the 27 features used to capture the
cluster and the Y-axis is the mean of features value. Clustered users have a
much higher value on feature 18 and 21 which are the percentage of capital
letters and number of sentences. This explains users in this cluster exhibits
a latent behavior of using more capital letters and more sentences in their
comments.

Figure 8. Co-clustering. (a) Distribution of users in each cluster. (b)
Example of latent behavior from cluster 1.

Using latent behaviors to identify misbehaving users: 0.77 AUC. In order to
show that the latent behaviors can be used to identify misbehaving users, we
take A matrix from the co-clustering result. Each row in the matrix is a user
and each column corresponds to a cluster, with the $(i,j)$ value being the
“membership” of user $i$ to the cluster $j$. We use these values as features
to train a classifier. Note that for each set of features we use the
classifier that yielded the highest performance. In the case of raw features
this was Random Forest, but for the case of the latent behavior features it
was Support Vector Machine (SVM) 111This behavior is expected since the latent
behavior features, contrary to the raw features, are embeddings of the users
in a vector space, thus SVM should work better than Random Forest.. We thus
report results using SVM. Our result shows that we can still accurately
identify misbehaving users with an AUC of 0.77 with 86.3% precision and 63.5%
recall. The role classification result is shown in Table 4.

Using latent behaviors to identify misbehaving roles: 73.3% overall accuracy.
Using 10-fold cross validation, we assess the ability of our method to
identify misbehaving roles, and we show the results in Table 4.

The overall classification accuracy when using the latent behaviors is lower
than using the raw features, albeit still very good. However, we argue that
the reduction in accuracy comes with an increase in the interpretability of
the classification using latent behaviors, as we present below.

Interpreting latent behaviors. Due to the space limitation, we are not able to
discuss all latent behaviors in the data. We will, thus, focus on the latent
behaviors that help us understand misbehaving users.

  1. (1)

Latent behavior 1: Users who exhibit such behavior are, on average, making
more comments to articles, are highly active between 7-13 UTC (midnight in
US), use more capital letters and also more characters and sentences on
average in their comments.

  2. (2)

Latent behavior 3: Users are highly active between 13-26 UTC, having ~60% more
comments and degrees of collaboration than the average.

  3. (3)

Latent behavior 4: Users are active between 3-8 UTC, making slightly more
(24%) comments than the average.

  4. (4)

Latent behavior 6: Users are active between 6-14 UTC, making comments which
have better readability.

Figure 8 shows that 87.9% of users who exhibit latent behavior 1 are
misbehaving users. This is in contrast to users of latent behavior 6, which
are active at similar periods of time but only 56% of them are misbehaving
users. This explains that using more capital letters and making longer
comments are the characteristic of misbehaving users.

Another interesting observation here is that, the active period could also
imply whether a user is misbehaving or not. We see that there is an active
time shift from latent behavior 3, latent behavior 4 to latent behavior 6, and
the percentage of misbehaving users are 20.7%, 31.3% and 56% respectively. If
we assume that most of the users are active in the timezone between ET and PT,
then we may further deduce that the later at night a user is active, the more
likely they are to be misbehaving.

Table 4. Role classification result (co-clustering) Role |  Precision |  Recall
---|---|---
Trolls |  78.7% |  71.2%
Spammers |  60.7% |  81%
Fanatics |  76.4% |  73.3%
Benign |  71.4% |  73.5%
Overall accuracy | 73.3%

##  6\. Related Work

We only have space to review indicative studies in five areas.

Detecting malicious behavior. Many studies detect anti-social behavior (Cheng
et al., 2015)(Cheng et al., 2017), bots(Chu et al., 2012)(Morstatter et al.,
2016) or cyber-bullying (Hosseinmardi et al., 2016) but they focus on OSNs. A
recent work (Cheng et al., 2015) analyzes the comments on three websites using
Disqus, but the focus is to predict if a user will be banned due to
misbehavior, which is somewhat different from ours: (a) some misbehaviors are
not necessarily reported, as we saw, and (b) we have a fine-grained definition
of misbehavior.

Detecting malicious behavior. Many studies detect anti-social behavior (Cheng
et al., 2015)(Cheng et al., 2017), bots(Chu et al., 2012)(Morstatter et al.,
2016) or cyber-bullying (Hosseinmardi et al., 2016) but they focus on OSNs. A
recent work (Cheng et al., 2015) analyzes the comments on three websites using
Disqus, but the focus is to predict if a user will be banned due to
misbehavior, which is somewhat different from ours: (a) some misbehaviors are
not necessarily reported, as we saw, and (b) we have a fine-grained definition
of misbehavior.

Analyzing text of online users. Many studies leverage textual analysis to
detect spammers on OSNs (Sculley and Wachman, 2007) and blogs (Mishne et al.,
2005) or how to achieve the same objective by analyzing the behavioral
patterns (Sureka, 2011).

Modeling and understanding online user behavior. Several works study temporal
and behavioral patterns of OSN users (Ferraz Costa et al., 2015) (Devineni et
al., 2015) (Gu et al., 2016). Some recent studies also use mobile phones and
OSNs to profile users’ psychological states (Wang et al., 2014)(De Choudhury
et al., 2014).

##  7\. Conclusion

We develop a systematic and comprehensive methodology to identify malicious
users on commenting platforms. The novelty of our work lies in its: (a) fine-
grained classification of malicious behavior, and (b) interpretable approach
to classification. From an algorithmic point of view our work uses a
comprehensive set of 73 features across four different types of information,
and a novel two-stage classification.

The overall classification accuracy of our approach is 80.8% for the fine-
grained 4-class problem. We also identify several unusual and surprising
behaviors, and we provide a broader understanding of the users of these
platforms.

Our work is a first step towards an efficient, easy-to-understand and easy-to-
manage approach to safeguarding commenting platforms from parasitic and
malicious users.

In the future, we aim at: (a) create a public larger labeled datasets to
facilitate further research, (b) consider more categories of malicious roles,
and (c) conduct large scale study of the evolution of malicious behavior on
commenting platforms.

## References

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11institutetext:  University of Aberdeen, UK 22institutetext: University
College London, UK 33institutetext: University of Liverpool, UK
44institutetext: University of Leeds, UK 55institutetext: NepAl Applied
Mathematics and Informatics Institute (NAAMII), Nepal
55email<EMAIL_ADDRESS>
# A Client-server Deep Federated Learning for Cross-domain Surgical Image
Segmentation

Ronast Subedi 55 Rebati Raman Gaire 55 Sharib Ali 44 Anh Nguyen 33 Danail
Stoyanov 22 Binod Bhattarai Corresponding author11

###### Abstract

This paper presents a solution to the cross-domain adaptation problem for 2D
surgical image segmentation, explicitly considering the privacy protection of
distributed datasets belonging to different centers. Deep learning
architectures in medical image analysis necessitate extensive training data
for better generalization. However, obtaining sufficient diagnostic and
surgical data is still challenging, mainly due to the inherent cost of data
curation and the need of experts for data annotation. Moreover, increased
privacy and legal compliance concerns can make data sharing across clinical
sites or regions difficult. Another ubiquitous challenge the medical datasets
face is inevitable domain shifts among the collected data at the different
centers. To this end, we propose a Client-server deep federated architecture
for cross-domain adaptation. A server hosts a set of immutable parameters
common to both the source and target domains. The clients consist of the
respective domain-specific parameters and make requests to the server while
learning their parameters and inferencing. We evaluate our framework in two
benchmark datasets, demonstrating applicability in computer-assisted
interventions for endoscopic polyp segmentation and diagnostic skin lesion
detection and analysis. Our extensive quantitative and qualitative experiments
demonstrate the superiority of the proposed method compared to competitive
baseline and state-of-the-art methods. Codes are available at:
https://github.com/thetna/distributed-da.

###### Keywords:

Domain Adaptation Federated Learning Decentralised Storage Privacy

##  1 Introduction

The deployment of artificial intelligence (AI) technology in medical image
analysis is rapidly growing, and training robust deep network architectures
demands millions of annotated examples. Despite significant progress in
establishing large-scale medical datasets, these are still limited in some
clinical indications, especially in surgical data science and computer-
assisted interventions [21]. Scaling training data needs multi-site
collaboration and data sharing [1], which can be complex due to regulatory
requirements (e.g. the EU General Data Protection Regulation [31], and China’s
cyber power [13]), privacy, and legal concerns. Additionally, even after
training, practical AI model deployment in the clinic will require fine-tuning
or optimization to local conditions and updates [11]. Therefore, architectures
trained in federated and distributed ways to tackle cross-domain adaptation
problems are critical. Yet, developing such architectures has challenges [25].

Figure 1: Sample training examples collected from various centres for polyp
segmentation (left); Sizes of training and test set at different centres for
polyp segmentation (middle) and skin lesion segmentation (right).

Several works [29, 7, 8] have been proposed to tackle the problem of cross-
domain adaptation in medical imaging. However, these methods require raw
source and target domain data and cannot address the ever-increasing privacy
concerns in sharing medical data. To circumvent the problem of privacy
protection, there is a lot of research interest growing in Federated Learning
(FL) in the medical domain [25, 18, 27, 30, 28, 15, 24].Some methods even rely
on synthetic data [10] to avoid sharing real data. For more details, we refer
readers to a survey [23] on federated learning for smart health care. The
common drawback of most existing methods [25, 18, 15, 24] is that these
methods are not designed for the domain shift problem. The most common
topology in the FL workflow is averaging the local gradients (FedAvg) at the
center and peer-to-peer gradient (FedP2P) sharing. These architectures are
effective when data are independent and identically distributed (IID) in every
client. In reality, domain shift is quite prevalent as data collected at
different centers tend to be center specific. In Fig. 1, we can see the
training examples for polyp segmentation collected at different centres. These
examples show the discrepancy in lighting, camera pose and modalities in
different centers. Some recent works, such as by Guo et al. [9] and FedDG by
Liu et al. [19], address cross-domain problems in FL. However, [9] limits to a
source-target pair at a time. Also, they employed adversarial loss to align
the parameters, which is difficult to optimize. Similarly, FedDG [19] shares
the information between the sources in the form of amplitudes of images. Their
evaluation is limited to fundus images and MRI.

To tackle the problems of cross-domain adaptation and privacy protection in
surgical image segmentation, we propose a simple yet effective Client-server
FL architecture consisting of a server and multiple clients, as shown in Fig.
2. A server hosts a set of _immutable_ task-specific parameters common to all
the clients. Whereas every client requests the server to learn their domain-
specific parameters locally and make the inference. In particular, every
client learns an encoder’s parameters to obtain an image’s latent
representation. These latent representations and ground truth masks are sent
to the server. The decoder deployed on the server makes the predictions and
computes the loss. The gradients are computed and updated only on the encoder
to align the client’s features with task-specific parameters hosted on the
server. Aligning domain-specific parameters to common parameters helps
diminish the gap between the source and target domains. We can draw an analogy
between our framework with public-key cryptography. A client’s network
parameter is equivalent to a private key, and the decoder’s parameters shared
on the server are equivalent to the public key. Thus a client only with access
to its private key can transfer its latent vector to the server containing the
public key to obtain the semantic mask. Distributed storage of the parameters
diminishes the risk of model parameter theft and adversarial attacks [20].
Moreover, each client communicates to the server only via a latent image
representation, which prevents exposing the information of the raw data
collected on the client side. It is possible to encrypt data transfer between
the server and clients to make it more secure. Finally, the server receives
only fixed latent dimension representations, making it agnostic to the
client’s architecture. This enables clients to communicate with the server
concurrently, improving efficiency. Likewise, none of the centres can modify
the parameters deployed on the server; this would prevent the memorisation of
client-specific information and parameter poisoning on the server [17].

To sum up, we propose a Client-server Federated Learning method for cross-
domain surgical image segmentation. We applied our method to two multi-centre
datasets for endoscopic polyp and skin lesion segmentation. We compared with
multiple baselines, including recent works on cross-domain FL [19, 9] and
obtained a superior performance.

##  2 Method

Background: We consider a scenario where we have $C_{1},C_{2},\dots C_{n}$
represent $n$ number of different institution’s centres located at various
geographical regions. Each centre collects its data in the form of tuple
$(\textbf{x},\textbf{y})$ where $\textbf{x}\in\mathbb{R}^{w\times h\times
c},\textbf{y}\in\mathbb{R}^{w\times h}$, where, $w,h,c$ represent the width,
height, and number of channels of an image. The annotated examples collected
at the different centers are not IID due to variations in the illumination,
the instruments used to acquire data, the ethnicity of the patients, the
expertise of the clinician who collects the data, etc. We denote the total
number of annotated pairs in each centre by $N_{n}$. In this paper, one of the
major goals is to address the problem of domain adaptation, avoiding the need
for the sharing of raw data to protect privacy.

Figure 2: The schematic diagram of the proposed framework. There are three
major components: Source domain, Target domains, and Server infrastructure to
share common parameters.

Learning Source Domain Parameters: First, we train a semantic segmentation
network on the source data. In Figure 2, the Source domain block shows the
training of source domain/centre parameters. For us, data collected on Centre
1, $C_{1}$ is source data. We employ fully-convolutional encoder-decoder
architecture. Such architectures are quite popular for semantic segmentation
[2, 26]. With the randomly initialised parameters, we minimise the objective
of the Equation 1. In Equation 1, $\theta_{C_{1}}^{e}$ and
$\theta_{C_{1}}^{d}$ represent the learnable parameters of the encoder and
decoder, respectively.

$\begin{split}L([\theta_{C_{1}}^{e};\theta_{C_{1}}^{d}])=-\frac{1}{N_{1}}\sum_{i=1}^{N_{1}}\sum_{i=j}^{W}\sum_{k=1}^{H}\textbf{y}_{ijk}\log\hat{\textbf{y}}_{ijk}\\\
+(1-\textbf{y}_{ijk})\log(1-\hat{\textbf{y}}_{ijk})\end{split}$ (1)

Setting-up Server Infra-structure: Figure 2 Server infra-structure block shows
the setting up of the server infrastructure. Once we learn the parameters of
the network from the source ($C_{1}$) data set, we upload the decoder
($\theta_{C_{1}}^{d}$) parameters on the server to share with every target
client. The decoder module specializes to segment anatomies, given the encoder
module’s latent vector representation of the input image. As this segmentation
task is common to all the centres, we propose to use a single decoder for all
the centres. The previous works on cross-modal [4] and cross-feature [3]
representations learning for cross-domain classification in computer vision
employed the idea of sharing Convolutional Neural Networks’ top layers
parameters. However, none of these methods were employed in Federated
Learning. The idea of sharing top layers parameters is in contrast to the
conventional transfer learning [12] where the parameters are initialised with
a model pre-trained on Imagenet and fine-tuned only the task-specific fully
connected layers. We freeze the shared decoder parameters of the source. This
arrangement brings advantages for privacy protection by preventing weight
poisoning attacks [17]. Weight poisoning attacks alter the pre-trained model’s
parameters to create a backdoor. The parameters of the encoders can be shipped
to the target client as per demand. Sometimes, the clients may demand these
parameters to initialize their local networks when the training data is very
small.

Federated Cross-domain Adaptation: Target centres other than the source centre
deploy only the encoder network of their choice. In Figure 2, the target
domain block depicts it. Every centre feeds its images to its encoder network
during training, generating the respective latent representations. The latent
representation and the ground truth ($\textbf{y}_{i}$) mask from each target
centre are pushed to the server where the pre-trained source decoder,
$\theta_{C1}^{d}$, is placed. The decoder feeds the latent representation,
which predicts the output segmentation labels ($\hat{\textbf{y}_{i}}$). We
learn the parameters of the target encoders ($\theta^{e}_{Ci}$) to minimize
the objective given in Equation 2. Since the decoder parameters are frozen and
shared with every client, only the target encoder’s parameters are updated on
the client side. This helps to align the latent representations to that of the
source decoder’s parameters and maximises the benefit from the task-specific
discriminative representations learned from the large volume of source data.

$\begin{split}\\\
L([\theta_{C_{i}}^{e};\theta_{C_{1}}^{d}])=-\frac{1}{N_{i}}\sum_{i=2}^{N_{i}}\sum_{i=j}^{W}\sum_{k=1}^{H}\textbf{y}_{ijk}\log\hat{\textbf{y}}_{ijk}\\\
+(1-\textbf{y}_{ijk})\log(1-\hat{\textbf{y}}_{ijk})\\\ \forall i\in{2,\dots
n}\end{split}$ (2)

The only thing that matters for target centres to communicate to the server is
the fixed dimension of latent representations of an image. Thus, our
architecture gives the flexibility of deploying the various sizes of networks
on the client side based on available computing resources. And it is also
entirely up to the target centres whether they want to initialize the
parameters of the encoder using the parameters of the source domain. If the
number of training examples is extremely few, then initialization using the
pre-trained model’s weight can prevent over-fitting.

##  3 Experiments

Data sets and Evaluation Protocol: We applied our method in two benchmark
datasets: endoscopic polyp segmentation and skin lesion segmentation. The
polyp segmentation dataset contains images collected at four different
centres. Kvasir-SEG [14] data set makes the source centre ($C_{1}$) in our
experiment. It has 800 images in the train set and 200 in the test set. These
high-resolution images acquired by electromagnetic imaging systems are made
available to the public by Simula Lab in Norway. Similarly, the EndoUDA-target
data set makes the first target domain ($C_{2}$) in our experiment, consisting
of 21 images in both the training and testing sets [5]. Our experiment’s
second target domain centre ($C_{3}$) consists of images from the CVC-ClinicDB
dataset made available to the research community by a research team in Spain.
There are 520 images in the train set and 92 in the test set. Finally, the
ETIS-Larib dataset released by a laboratory in France makes our third target
domain data set ($C_{4}$). This data set consists of 166 in the train set and
30 images in the test set. These data sets were curated at different time
frames in different geographical locations.

Data | Centres | mIOU
---|---|---
INDP | COMB |  [16] | [19] | FtDe | [9] | RandEn | FtEn
Endo. |  Kvasir-SEG ($C_{1}$, source) | 80.3 | 81.0 | 82.3 | 73.5 | N/A | 80.5 | 80.3 | 80.3
EndoUDA ($C_{2}$) | 52.0 | 57.5 | 53.1 | 29.7 | 59.9 | 61.7 | 50.6 | 62.0
CVC-ClinicDB ($C_{3}$) | 88.3 | 87.8 | 86.8 | 74.5 | 85.8 | 83.0 | 89.1 | 88.4
ETIS-Larib ($C_{4}$) | 62.1 | 66.9 | 61.4 | 70.8 | 65.1 | 71.7 | 64.3 | 69.9
Skin |  ISIC ($C_{1}$, source) | 81.3 | 75.7 | 84.9 | N/A | N/A | NA | 81.3 | N/A
PH2 ($C_{2}$) | 88.4 | 88.3 | 88.4 | N/A | 88.0 | NA | 89.6 | 89.4
Table 1: mIoU scores on Endoscopic Polyp Segmentation Data sets (upper block)
and Skin Lesion Segmentation (lower block).

For skin lesion segmentation, we took data set collected at two different
centres: ISIC(International Skin Imaging Collaboration) [6] and PH2 [22]. In
ISIC, there are 2596 training examples and 102 test examples. The PH2 database
is curated through a joint research collaboration between the Universidade do
Porto, Tecnico Lisboa, and the Dermatology Service of Hospital Pedro Hispano
in Matosinhos, Portugal. In this data set, there are only 180 training
examples and 20 testing examples. We consider ISIC and PH2 source and target
domain, respectively. We use the mean Intersection of Union (mIoU) and dice
score for both datasets for quantitative evaluations. Qualitative comparisons
also validate our idea.

Baselines: We have compared the performance of our method with several
competitive baselines, including both non-federated and federated frameworks.
One of the naive baselines is to train a model for each target centre
independently (_INDP_). The models of the centres with less training data
overfit. Another configuration is creating a data pool by combining the
training data (_COMB_) from all the centres and training a single model.
However, this method does not address any of the issues regarding privacy and
compliance. Another viable option is to adapt a pre-trained model to a new
domain by fine-tuning the parameters of the latter layers (_FtDe_). We also
compared our method with competitive federated learning algorithms. FedAvg
[16] averages the gradients computed in every center and shares the average
gradients with the clients. This method ignores the non-IID nature of data
from different centres. FedDG [19] is another Federated Learning method for
domain adaption published at CVPR 2021. Finally, we also compared with another
recent work by Guo et al. [9] for federated learning for multi-institutional
data published at CVPR 2021. Our methods have two variants: initialising
clients’ parameters randomly(RandEn) and with the source’s parameters (FtEn)

Figure 3: Curves show the learning behaviour of different methods on PH2 data
set.

Implementation Details and Learning Behaviour: We implement our algorithms on
PyTorch framework. All the images were resized to the dimension of $418\times
418$. For optimization, we employ Adam optimizer with values of $\beta 1$ and
$\beta 2$ set to 0.9 and 0.999 respectively. We initialize learning rate to
2e-4 and set the decaying of the learning rate every 25k iterations. Taking
UNet as a base architecture, we train the networks for 100k iterations and
save the best-performing checkpoints on the validation set and report the
performance on the test set. Figure 3 summarises the learning behaviour of the
different methods for the first 100k iterations on PH2 data set, a target
domain for skin lesion segmentation. The solid lines are our methods, and the
dashed lines are the compared methods. The smooth curves demonstrate that our
methods are easy to optimise the parameters.

Quantitative Evaluations: Table 1 shows the quantitative performance
comparison. In the table, the last two grey-shaded columns show the
performance of our methods. Our method outperforms _INDP_ in every target
centre. This signifies the importance of domain adaptation by our method.
Compared to the other Federated Learning methods, our methods obtain the
highest performance on 2/3 of target centres and are competitive on the third
one for endoscopic polyp segmentation. On skin lesion segmentation, our method
surpassed all the compared baselines and the recent competitive Federated
Learning methods. We have compared the performance on the dice score, too and
obtained a similar performance (See Supplementary). We have also evaluated the
performance with varying sizes of the target domain/centre encoders. Please
see the appendix for the details.

Qualitative Evaluations: Figure 4 shows the qualitative performance
comparisons between the baselines and the proposed methods on the target
domains. Rows 2-4 (inclusive) are from endoscopy benchmarks, and the last row
is from skin benchmarks. FedAvg, our closest work, fails to generalise well on
target domains (see ETIS-Larib and CVC-ClinicDB). Whereas our method is
consistent in every target domain. These results further validate that our
method is superior to the others. You can find more examples in the appendix
section.

Figure 4: Qualitative Comparisons

Computational Complexity: For INDP and FedAvg, the parameters of both the
encoders and decoders grow in O(n) with the number of centres. Similarly, for
FtDe and our method, the parameters of the encoder grow in O(n), while the
parameters of the decoder are constant, i.e., O(1). Although the growth of the
parameters for both the encoder and decoder for COMB is O(1), it does not
address any privacy concerns. From these, our method is computationally less
expensive and has high privacy protection.

##  4 Conclusions

In this paper, we presented a client-server Federated Learning architecture
for cross-domain surgical image segmentation. Our architecture addresses the
cross-domain adaptation problem without sharing the raw images. Moreover,
sharing only a part of the parameters from the source domain enhances privacy
protection. Extensive experiments on two benchmarks from various data centres
demonstrated improved cross-domain generalisation and privacy protection over
the baselines and the competitive contemporary method.

##  5 Acknowledgements

This work is partly supported by the Wellcome/EPSRC Centre for Interventional
and Surgical Sciences (WEISS) [203145Z/16/Z]; Engineering and Physical
Sciences Research Council (EPSRC) [EP/P027938/1, EP/R004080/1, EP/P012841/1];
The Royal Academy of Engineering Chair in Emerging Technologies scheme; and
the EndoMapper project by Horizon 2020 FET (GA 863146).

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##  Appendix 0.A Appendix

Varying Encoder Size: To further validate the robustness of our proposed
framework, we trained the networks with different numbers of learnable
parameters in the encoder module as shown in table 2. We vary the parameters
by adding or removing the constituting layers in the encoding blocks of the
network. We designate the conventional encoder of the UNet architecture as an
encoder with medium size. The learnable parameters in the medium encoder are
approximately 17 million. Table 3 depicts the architecture of a general
encoder. It consists of three down-sampling layers, represented as Down Block.
We vary the number of layers in the Down Blocks of the general encoder as per
the availability of labeled data and computing resources in the particular
centre.

Data |  Centres |  Size |  Trainable Parameters |  mIoU
---|---|---|---|---
|  |  |  INDP |  RandEnc(Ours)
Polyp | ETIS-Larib | Small | 6,311,616 | 61.6 | 62.9
Medium | 17,080,896 | 62.1 | 64.3
Large | 27,850,176 | 62.5 | 64.7
Skin | PH2 | Small | 6,311,616 | 88.4 | 88.4
Medium | 17,080,896 | 88.5 | 89.6
Large | 27,850,176 | 89.4 | 89.8
Table 2: Result on Endoscopic Polyp Segmentation Data sets (upper block) and Skin Lesion Segmentation (lower block) with different sizes of encoder networks. Operations | Output Size
---|---
Input Image | $c\times h\times h$
Down Block | $c\times\frac{h}{2}\times\frac{h}{2}$
Down Block | $c\times\frac{h}{4}\times\frac{h}{4}$
Down Block | $c\times\frac{h}{8}\times\frac{h}{8}$
Table 3: Architecture of the general encoder.

The proposed federated distributed framework for domain adaptation provides
flexibility to choose different network architectures to learn a common latent
representation of images. These architectures can be designed based on the
data size and available resources at a particular center. The performance
evaluation results of various encoder sizes on polyp segmentation and skin
lesion segmentation are shown in table 2. From the table, we can observe that
segmentation performance for various sizes of the encoder is higher when
trained using our framework than training independently for a specific center.

Equations for Gradient Update: Equations 3 and 4 show mathematical formulation
to update gradients of decoder and encoder modules in the proposed framework.
Equation 3 updates the gradient of the decoder in the source center. Equation
4 represents the mechanism of updating gradients of each encoder module in
every center. Here, $\alpha$ is the center-specific learning rate. Please note
the parameters of the decoder remain the same for every target centre. $L$
denotes the loss function.

$\theta_{C_{1}}^{d}=\theta_{C_{1}}^{d}-\alpha_{1}\times\frac{\partial
L([\theta_{C_{1}}^{e};\theta_{C_{1}}^{d}])}{\partial\theta_{C_{1}}^{d}};$ (3)

$\theta_{C_{i}}^{e}=\theta_{C_{i}}^{e}-\alpha_{i}\times\frac{\partial
L([\theta_{C_{i}}^{e};\theta_{C_{1}}^{d}])}{\partial\theta_{C_{i}}^{e}};\forall
i\in{1,\dots n}$ (4)

Additional Qualitative Results: Figure 5 depicts the segmentation results on
Endoscopic polyp data from the target domain centres. The first four rows are
from the ETIS-Larib dataset, the next three are from the CVC-ClinicDB data
set, and the last two are from EndoUDA. Columns RandEn and FtEn show the
results of our method.

Figure 5: Additional Qualitative Comparison