# Semi-analytical technique for the design of disordered coatings with
tailored optical properties

Bhrigu Rishi Mishra  1 Nithin Jo Varghese  1 and Karthik Sasihithlu1
1Department of Energy Science and Engineering, Indian Institute of Technology
Bombay
<EMAIL_ADDRESS>
###### Abstract

Disordered media coatings are finding increasing use in applications such as
day-time radiative cooling paints and solar thermal absorber plate coatings
which require tailored optical properties over a broad spectrum ranging from
visible to far-IR wavelengths. Both monodisperse and polydisperse
configurations with thickness of coatings up to 500 $\mu m$ are currently
being explored for use in these applications. In such cases it becomes
increasingly important to explore utility of analytical and semi-analytical
methods for design of such coatings to help reduce the computational cost and
time for design. While well-known analytical methods such as Kubelka-Munk and
four-flux theory have previously been used for analysis of disordered
coatings, analysis of their utility has so far in literature been restricted
to either solar spectrum or IR but not simultaneously over the combined
spectrum as required for the above applications. In this work, we have
analysed the applicability of these two analytical methods for such coatings
over the entire wavelength range from visible to IR, and based on observed
deviation from exact numerical simulation we propose a semi-analytical
technique to aid in the design of these coatings with significant
computational cost savings.

††journal: oe††articletype: Research Article

##  1 Introduction

Disordered coatings, which consist of dielectric/metal nanoparticles dispersed
randomly in a matrix, find their application in several fields such as solar
thermal absorber coatings [1], solar reflecting coatings [2], color paints
[3], translucent paints [4], tissue optics [5], daytime passive radiative
cooling coatings [6, 7, 8], and many more. The main advantages that such
disordered media offer that make them an attractive proposition for use in
these applications are their cost-effective means of fabrication, and
tunability of the desired optical properties of the coating - since the
spectral position of Mie (plasmon) resonance of the embedded dielectric
(metal) particles strongly depend on the size of the particles. The main
challenging task in the design of such disordered media is the modelling of
its optical properties. Techniques based on homogenization of the composite
structures that predict effective permittivity and permeability of the
disordered media, such as Maxwell-Garnett theory [9] and Bruggeman’s model
[10], are valid only when the particle sizes are much smaller than the
incident wavelength [11]. Doyle et al. [12] showed that the use of Mie
coefficients in this effective medium theory provides good accuracy to the
calculation of effective optical properties of metal spheres suspended in a
polymer. However, the theory predicts absorption for a nonabsorbing particle
[11] and thus cannot be used to predict the effective refractive index of
disordered media for solar reflecting paint/coatings where non absorbing
particles are utilized. In literature, other analytical techniques developed
for this objective include those which consider diffusion of photons [13], and
those which solve the radiative transfer equation under $N$-flux ($2\leq N\leq
4$) approximations [14, 15]. Of these methods Kubelka Munk (KM) theory [16]
(for which $N=2$) and the four-flux (FF) method [17] are commonly used. In
addition, simulation techniques such as the Monte Carlo method [18], and exact
electromagnetic solvers are employed to model the optical/radiative properties
of disordered coatings. However, these simulation techniques do not present a
clear picture linking the microscopic properties of the particles, such as the
scattering and absorption coefficients, to the macroscopic optical properties
of the coating. Moreover, exact electromagnetic solvers which solve Maxwell’s
equations numerically to obtain radiative properties of the coating, put a
premium on computational resources and the time for design when the thickness
of random media is in the order of tens/hundreds of microns - as is currently
being deployed in these applications. Particularly when several parameters of
the configuration are in play, such as that encountered in disordered media,
analytical techniques such as KM and FF theories provide important means to
arrive at an optimum combination of the parameters with minimal computational
resources while also explicitly linking the properties of the micro
constituents to the observed optical properties of the coating.

KM and FF theories have so far in literature been used in applications where
the spectrum of interest has been limited to either the visible spectrum or IR
separately. For example, KM theory has been used extensively in paints and
coatings [1, 3], paper industry [19], tissue optics [5] among others.
Similarly, the FF method has been used extensively by researchers to model,
predict and optimize the optical properties of light scattering coatings [2,
20, 21, 22]. However, the applicability of these theories over a broad
spectrum covering both visible and IR spectrum simultaneously has not been a
subject of attention. This becomes important when designing coatings for
applications such as day-time passive radiative cooling and solar thermal
absorber plate coatings where tailored optical properties over a broad
spectrum covering both the solar spectrum as well as far-infrared are crucial.
For example, coatings for day-time passive radiative cooling [23] require high
reflectivity in solar spectrum (0.3-3 $\mu$m wavelength range) and high
emissivity in the infra-red spectrum (5-15 $\mu$m wavelength range). It is not
obvious that the analytical techniques retain their accuracy over such a broad
spectrum since with increasing wavelength there is a possibility that the
nature of scattering transitions from the independent scattering regime (where
scattering cross-section of particles can be superposed) to dependent
scattering regime (where near-field effects, and interference between far-
field scattered radiation become important). Previously reported relation [24]
demarcating the two regimes has been obtained from experimental observations
carried out in the visible spectrum only. Thus there is a need to explore the
applicability of these analytical techniques over a broad spectrum in greater
depth. In regimes where the predictions from these analytical techniques are
not satisfactory, other possible methods of design which combine the accuracy
of exact electromagnetic solvers with the minimal computational requirements
of analytical methods are expected to be of pressing need to researchers
interested in designing such coatings.

With this in mind, the manuscript has been arranged as follows. In Section 2
we have compared the reflectivity and emissivity predictions of KM and FF
techniques with results from exact numerical solvers for different degrees of
absorption in the particles (imaginary index of particle = 0.0, $10^{-2}$, and
$10^{-1}$) and in the matrix (imaginary index of matrix = 0.0, $10^{-4}$, and
$10^{-2}$) for different thickness of the coating (10 $\mu$m and 50 $\mu$m) in
the wavelength range $0.3-15~{}\mu m$. We show that these techniques are
accurate over the entire spectrum when particles are in the limit of
independent scattering and under low absorption conditions but fail when
volume fraction of particles is high such that interaction among particles is
no longer negligible or when absorption in the matrix/particles is high. For
such conditions where analytical techniques fail to predict the optical
properties accurately we propose an alternative technique which combines the
use of exact numerical solver and KM theory which we show can predict optical
properties with accuracy as well as with minimal computational requirements.
This ‘semi-analytical’ technique is detailed in Section 3. In the end, as an
example to showcase the applicability of this semi-analytical technique, we
predict the properties of a disordered coating suitable for the application of
passive radiative cooling and compare these with experimental measurements
previously reported in literature.

##  2 Analytical techniques - Kubelka Munk (KM) and the Four-Flux (FF) methods

We start with the expressions for reflectivity and transmissivity of the
coating as obtained from KM and FF theories which we use in the work to
analyze the optical properties of the disordered coating. Detailed derivations
of these expressions can be found in several references [25, 17, 26]. The
optical coating considered in this work is a plane-parallel slab of
particulate composite on a substrate as shown in Fig. 1. The composite is
considered to be of finite thickness and infinite extension in the lateral
direction. The randomly distributed spherical particles embedded within the
host medium (also called the matrix) act as inhomogeneities to the propagating
EM wave, thereby causing its scattering (and absorption, in case the particle
is lossy). The objective is to predict the optical properties of this coating
including the total reflectance, transmittance and absorption.

Figure 1: Schematic of coating considered in this work with incident plane
wave source.

The expression for the reflectivity ($R_{\text{KM}}$) and transmissivity
($T_{\text{KM}}$) from KM theory is given by [25, 3]:

$R_{\text{KM}}=\frac{(1-\gamma)(1+\gamma)(\exp(AL)-\exp(-AL))}{(1+\gamma)^{2}\exp(AL)-(1-\gamma)^{2}\exp(-AL)}$
(1)
$T_{\text{KM}}=\frac{4\gamma}{(1+\gamma)^{2}\exp(AL)-(1-\gamma)^{2}\exp(-AL)}$
(2)

where, $L$ is the thickness of the layer, the coefficients $\gamma$ and $A$
are given by [3, 27]:

$\gamma=\sqrt{k/(k+s^{\prime})};\,\,A=\sqrt{2k(2k+s^{\prime})}$ (3)

with

$s^{\prime}=\frac{3s(1-g)-k}{4};\,\,$ (4)

and the factors $s$ and $k$ got using Mie theory [1]

$s=\frac{3fQ_{\text{sca}}}{4r};\,\,\,\,\,\,k=\frac{3fQ_{\text{abs}}}{4r},$ (5)

where $f$ is the volume fraction, $r$ is the radius of the sphere,
$Q_{\text{sca}}$ $(Q_{\text{abs}})$ is the Mie scattering (absorption)
efficiency of a single particle embedded in a host medium of index $n_{h}$,
and $g$ is the asymmetry parameter. Expressions for $Q_{\text{sca}}$,
$Q_{\text{abs}}$, and $g$ in terms of standard Mie coefficients can be found
in Ref. [28]. It should be pointed out that the relations between the coating
properties $\gamma$ and $A$, and the particle properties $s$ and $k$ given in
Eq. 3 are not unique - several other relations [29, 30, 31, 32, 4, 5, 33] have
been proposed over the years. The expressions in Eq. 3 and Eq. 4, taken from
Ref. [3, 27], is representative and have been chosen for demonstrative
reasons. As we will see in Sec. 3 the semi-analytical method being proposed in
this work does not depend on such relations and hence do not affect the
central results of this work.

In the limit of low absorption, $kL\rightarrow 0$, the reflectivity in Eq. (1)
can be shown to reduce to [25]:

$R_{\text{KM}}=\dfrac{s^{\prime}L}{s^{\prime}L+1}.$ (6)

It must be noted that Eq. (1) and Eq. (2) do not take into account surface
reflection of incident radiation at interface (1). Modified reflectance
$R_{0}$ and transmittance $T_{0}$ which take into account surface reflection
correction are calculated using [34]:

$R_{\text{0}}=R_{\text{c}}+\frac{(1-R_{\text{c}})(1-R_{\text{i}})R_{\text{KM}}}{1-R_{\text{i}}R_{\text{KM}}};\,\,\,\,\,T_{\text{0}}=\frac{(1-R_{\text{c}})T_{\text{KM}}}{1-R_{\text{i}}R_{\text{KM}}}$
(7)

where, $R_{\text{c}}$ is the specular reflectance of incident light got from
Fresnel reflection which for normal incidence from a medium of index
$n_{\text{surr}}$ reads:

$R_{\text{c}}=\left(\frac{n-1}{n+1}\right)^{2}$ (8)

with $n=n_{\text{h}}/n_{\text{surr}}$ and $R_{\text{i}}$ is the diffuse
reflectance of internal radiation at interface (1), marked in Fig. 1, which is
calculated using:

$R_{i}=2\int_{0}^{\pi/2}\rho(\theta)\,\text{sin}\theta\,\text{cos}\theta\,\text{d}\theta.$
(9)

where, from Fresnel’s coefficients:

$\rho(\theta)=\frac{1}{2}\left[\left(\dfrac{\sqrt{n^{2}-\text{sin}\theta}-\text{cos}\theta}{\sqrt{n^{2}-\text{sin}\theta}+\text{cos}\theta}\right)^{2}+\left(\dfrac{n^{2}\text{cos}\theta-\sqrt{n^{2}-\text{sin}\theta}}{n^{2}\text{cos}\theta+\sqrt{n^{2}-\text{sin}\theta}}\right)^{2}\right].$
(10)

The expression for $R_{\text{i}}$ from Eq. 9 can be used even the limit of low
diffuse scattering since the contribution from the product
$R_{i}R_{\text{KM}}$ will be negligible in this regime.

Many configurations developed for radiative cooling application [7, 35, 36]
and solar absorber plates [37, 38] involve use of a substrate. In the presence
of a substrate, the net reflectance and transmittance from Eq. 7 will have to
be further modified as [39]:

$R=R_{\text{0}}+\frac{T_{\text{0}}^{2}R_{\text{g}}}{1-R_{\text{0}}R_{\text{g}}};\,\,\,T=\frac{(1-R_{\text{g}})T_{\text{0}}}{1-R_{\text{0}}R_{\text{g}}}$
(11)

Here $R_{\text{g}}$ is the diffuse reflectance at interface (2) obtained from
Eq. 9 with $n=n_{\text{h}}/n_{\text{g}}$. The substrate index $n_{g}$ is taken
to be 1.5 in this work.

The derivation of reflection and transmission coefficients from KM theory
assumes that the incident light is diffuse. When the incident radiation is
collimated, alternate methods such as the four-flux theory, which take into
account the propagation of both collimated and diffuse radiation across the
interfaces in two directions, are expected to be more accurate. This careful
consideration of both collimated and diffuse components leads to expressions
for the optical properties being far more complicated than in KM theory. The
net reflection and transmission coefficients when incident radiation is fully
collimated can be expressed in terms of a summation over collimated-collimated
reflectivity $(R_{\text{cc}})$, collimated-diffuse reflectivity
$(R_{\text{cd}})$, collimated-collimated transmissivity $(T_{\text{cc}})$, and
collimated-diffuse transmissivity $(T_{\text{cd}})$ as:

$R=R_{\text{cc}}+R_{\text{cd}}+R_{\text{dd}};\,\,\,\,T=T_{\text{cc}}+T_{\text{cd}}+T_{\text{dd}}$
(12)

Expressions for $R_{\text{cc}}$, $R_{\text{cd}}$, $T_{\text{cc}}$ and
$T_{\text{cd}}$ are quite elaborate and have been included in the
supplementary document (Section S1) for reference.

(a)

(b)

(c)

(d)

Figure 2: Reflectivity and transmissivity spectrum for $n_{\text{h}}=1.5,$
$r=0.25~{}\mu\text{m},$ $f=0.05,$ and (a) $n_{\text{p}}=2.5,$
$L=10~{}\mu\text{m}$; (b) $n_{\text{p}}=2.5,$ $L=50~{}\mu\text{m}$.
Reflectivity and absorptivity spectrum for $n_{\text{h}}=1.5,$
$r=0.25~{}\mu\text{m},$ $f=0.05,$ and (c) $n_{\text{p}}=2.5+i0.1,$
$L=10~{}\mu\text{m}$; (d) $n_{\text{p}}=2.5+i0.1,$ $L=50~{}\mu\text{m}$. Here,
FF stands for four flux, KM for Kubelka Munk, and LM for Lumerical.

In Sections 2.1, 2.2, and 2.3, we use the expressions for $R$ and $T$ given in
Eqs. 11 for KM theory and Eqs. 12 for FF to predict the optical properties of
disordered coatings and compare these with the results obtained from Lumerical
FDTD solver [40]. We analyze situations where both the particles and host
medium are absorbing as well as non-absorbing, and also consider the effect of
different thickness of the coating. The degree of absorption in particles
considered in this work are relevant for dielectric inclusions typically
included in coatings for use in radiative cooling and solar thermal
applications. In addition, to facilitate the parametric study we assume non-
dispersive form of refractive index for both the particles as well as the host
matrix. We first confine our analysis to the independent scattering regime in
Sections 2.1 and 2.2, and extend the analysis to dependent scattering regime
later in Sec. 2.3. The FDTD simulations were set up in ANSYS Lumerical.
Periodic boundary conditions were applied in the lateral $x$ and $y$
directions, and coating is illuminated with a plane wave source from $z$
direction. A mesh size of 30 nm was used which we find is sufficient for
convergence (mesh convergence study is shown in supplementary Fig. S3).

###  2.1 Comparison of predictions from KM, FF theories and FDTD solver in the
independent scattering regime for monodisperse inclusions with and without
absorption in particles and in host medium

Figure 2(a) and 2(b) show the comparison between KM, FF, and FDTD results for
the case when particles are non-absorbing and Fig. 2(c) and 2(d) show the
corresponding comparison when particles are absorbing with imaginary index of
particles $n_{p}^{\prime\prime}=10^{-1}$. We compare the predictions for
different coating thicknesses $10~{}\mu m$ and $50~{}\mu m$ keeping the other
parameters $r=0.25~{}\mu m$, $f=0.05$, $n_{h}=1.5$ non varying. It is observed
that particularly for smaller thickness of coating and in the absence of
absorption the predictions from FF method deviates significantly from the FDTD
simulations as compared to KM method in both the visible as well as IR
spectrum. However, for larger thicknesses of the coating and in the presence
of absorption in particles, FF is relatively more accurate than the KM method
across the spectrum, more so for higher wavelengths.

In the presence of absorbing host media, the expressions for $\gamma$ and $A$
in Eqs. 1 and 2 needs to be modified to account for absorption in the matrix
[20, 22] as: $\gamma=\sqrt{k^{\prime}/(k^{\prime}+s^{\prime})}$, and
$A=\sqrt{2k^{\prime}(2k^{\prime}+s^{\prime})}$ where,
$k^{\prime}=k+(1-f)\alpha.$ Here, $\alpha=4\pi
n^{\prime\prime}_{\text{h}}/\lambda$, with $n^{\prime\prime}_{\text{h}}$ being
the imaginary part of refractive index of the matrix, and $\lambda$ the
wavelength in vacuum. In addition, expressions for $Q_{\text{sca}}$ and
$Q_{\text{abs}}$ in Eq. 5 needs to be modified as shown by Mischenko et al.
[41]. Figure 3(a) and 3(b) show the comparison between KM, FF, and FDTD
results for the case when host medium is weakly absorbing with
$n_{h}^{\prime\prime}=10^{-4}$ and Fig. 3(c) and 3(d) show the corresponding
comparison when it is more strongly absorbing with
$n_{h}^{\prime\prime}=10^{-2}$. In the presence of weakly absorbing matrix and
for smaller thickness of the coating FF is again observed to deviate
significantly from the FDTD simulations. As absorption increases we observe
significant deviation from FDTD results in both FF and KM theories
particularly for the higher wavelengths.

(a)

(b)

(c)

(d)

Figure 3:  Reflectivity and absorptivity spectra for $n_{\text{p}}=2.5$,
$r=0.25~{}\mu\text{m}$, $f=0.05$, and (a) $n_{\text{h}}=1.5+i10^{-4},$
$L=10~{}\mu\text{m}$; (b) $n_{\text{h}}=1.5+i10^{-4},$ $L=50~{}\mu\text{m}$;
(c) $n_{\text{h}}=1.5+i10^{-2},$ $L=10~{}\mu\text{m}$; (d)
$n_{\text{h}}=1.5+i10^{-2},$ $L=50~{}\mu\text{m}$. Here, FF stands for four
flux, KM for Kubelka Munk, and LM for Lumerical.

###  2.2 Comparison of predictions from KM, FF theories and FDTD solver in the
independent scattering regime for polydisperse inclusions with and without
absorption in particles

(a)

(b)

(c)

(d)

Figure 4: Reflectivity and transmissivity for $n_{\text{h}}=1.5,$
$r=0.25~{}\mu\text{m},$ $\sigma=0.016,$ $f=0.05$ and (a) $n_{\text{p}}=2.5,$
$L=10~{}\mu\text{m}$; (b) $n_{\text{p}}=2.5,$ $L=50~{}\mu\text{m}$.
Reflectivity and absorptivity for $n_{\text{h}}=1.5,$ $r=0.25~{}\mu\text{m},$
$\sigma=0.016,$ $f=0.05$ and (c) $n_{\text{p}}=2.5+0.01i,$
$L=10~{}\mu\text{m}$; (d) $n_{\text{p}}=2.5+0.01i,$ $L=50~{}\mu\text{m}$.
Here, FF stands for four flux, KM for Kubelka Munk, and LM for Lumerical.

In this section we explore the predictive capability of KM and FF theories for
polydisperse medium which consists of randomly positioned particles with
different sized radius. The study is motivated from the observation that
synthesis of nanoparticles via various methods such as sol-gel [42],
microemulsion [43], hydrothermal [44], results in a polydisperse size
distribution of particles. Moreover, some recent studies [45, 46] have also
deliberately adopted coatings with different size distribution of particles to
make use of the property of size-dependent scattering of particles to obtain
wavelength-selective coatings. Such a particulate medium can be analyzed by
considering the particles to be distributed about a mean radius $r$ with
standard deviation $\sigma$, with the expressions for $s$ and $k$ to be used
in Eqs. 5 got by summing over the respective coefficients for individual
particle volume fractions $f_{i}$ [22] as:

$s=\sum_{i=1}^{N}s_{i};\,\,\,\,k=\sum_{i=1}^{N}k_{i}$ (13)

where $s_{i}$ and $k_{i}$ are the Mie scattering and absorption coefficients
respectively of the particle with fill fraction $f_{i}$. Equation (13) can
also be used to calculate $s$ and $k$ when there are two or more type of
particles present in the matrix (with different refractive index). For
demonstration we consider a Gaussian distribution of spherical particles about
mean radius $r=0.25~{}\mu m$ with standard deviation $\sigma=0.016~{}\mu m$
with and without absorption. The particle size distribution curve has been
shown in Fig. S2. Figure 4(a) and 4(b) show the comparison between KM, FF, and
FDTD results for the case when particles are non-absorbing and Fig. 4(c) and
4(d) show the corresponding comparison when particles are absorbing with
$n_{p}^{\prime\prime}=10^{-2}$. Other parameter values are retained as for the
case of monodisperse particulate coating. The observations follow the trend
seen for the case of monodisperse coating with significant deviations observed
in the predictions of FF method for lower values of thicknesses of coatings
and when particles are nonabsorbing. For larger thicknesses of the coating and
in the presence of absorption, both FF and KM are observed to predict the
optical properties with reasonable accuracy across the spectrum.

###  2.3 Comparison of predictions from KM, FF and FDTD solvers in the
dependent scattering regime

So far we have analyzed for the situations where the fill fraction $f$ of
particles in the composite is small enough so that the particles can be
assumed to independently scatter from one another. However, as the fill
fraction of particles increases, there will be a transition to dependent-
scattering regime where both the near-field interaction between the particles
as well as far-field interference between the scattered field of individual
particles have a significant impact on the overall properties of the coating.
Hotel [24] empirically determined this transition to occur when $f>0.27$ and
$\overline{d}/\lambda>0.3$ where $\overline{d}$ is the mean inter-particle
spacing and $\lambda$ is the wavelength. Several coatings reported in
literature [7, 47, 48, 49, 46] have fill fractions in the range 0.1-0.6 where
such effects cannot be neglected. We thus explore here the predictive
capability of FF and KM theories for such coatings by considering a
monodisperse distribution of particles with increased fill fraction $f=0.3$
while retaining other parameter values to be same as that included for Fig.
2(b). This comparison is shown in Fig. 5, where we observe that the
predictions from both FF and KM theories deviate significantly from FDTD
simulations across the spectra, and thus cannot be relied on for predicting
optical properties of such coatings.

Figure 5: Reflectivity and transmissivity for $n_{\text{p}}=2.5,$ $n_{\text{h}}=1.5,$ $r=0.25~{}\mu\text{m},$ $f=0.3,$ and $L=50~{}\mu\text{m}$. Here, FF stands for four flux, KM for Kubelka Munk, and LM for Lumerical.  Table 1: Weighted-average reflectivity in solar spectrum $R_{\text{solar,KM}}$ ($R_{\text{solar,FF}}$) and emissivity in IR spectrum $\epsilon_{\text{IR,KM}}$ ($\epsilon_{\text{IR,FF}}$) calculated using KM (FF) theory. Values in brackets denote deviation of prediction from FDTD results. Sr. no. | Fig. no. | $R_{\text{solar,KM}}$ | $\epsilon_{\text{IR,KM}}$ | $R_{\text{solar,FF}}$ | $\epsilon_{\text{IR,FF}}$
---|---|---|---|---|---
1 | 2(a) | 0.391 (21.4%) | - | 0.509 (58.1%) | -
| 2
---
2(b) | 0.745 (0.67%) | - | 0.747 (0.4%) | -
| 3
---
2(c) | 0.076 (13.4%) | 0.08 (95%) | 0.081 (20.9%) | 0.043 (4.87%)
| 4
---
2(d) | 0.078 (18.2%) | 0.331 (70.6%) | 0.079 (19.7%) | 0.197 (1.55%)
| 5
---
3(a) | 0.376 (18.6%) | - | 0.483 (52.4%) | -
| 6
---
3(b) | 0.619 (8.22%) | 0.012 (100%) | 0.612 (6.99%) | 0.005 (16.67%)
| 7
---
3(c) | 0.112 (30.2%) | 0.205 (83.0%) | 0.110 (27.9%) | 0.086 (23.2%)
| 8
---
3(d) | 0.112 (36.6%) | 0.661 (51.3%) | 0.108 (31.7%) | 0.357 (18.3%)
| 9
---
4(a) | 0.392 (19.1%) | - | 0.510 (55.0%) | -
| 10
---
4(b) | 0.746 (4.63%) | - | 0.755 (5.89%) | -
| 11
---
4(c) | 0.260 (25.0%) | 0.008 (60%) | 0.279 (34.1%) | 0.004 (20%)
| 12
---
4(d) | 0.304 (16.5%) | 0.041 (78.3%) | 0.268 (2.68%) | 0.023 (0.01%)
| 13
---
5 | 0.944 (8.13%) | - | 0.935 (6.98%) | -

A comparison between the weighted average of the optical properties across the
spectra as predicted by KM and FF theories for the different cases considered
so far has been tabulated in Table 1. The weighted averages are calculated as:
$R_{\text{solar}}=\int I_{\text{AM1.5}}(\lambda)R(\lambda)d\lambda/\int
I_{\text{AM1.5}}(\lambda)\,d\lambda$, where $I_{\text{AM1.5}}(\lambda)$ is the
spectral solar irradiance [50] and $\epsilon_{\text{IR}}=\int
I_{\text{BB}}(\lambda)\epsilon(\lambda)d\lambda/\int
I_{\text{BB}}(\lambda)\,d\lambda$, where $I_{\text{BB}}(\lambda)$ is the black
body irradiance. For the relevant applications in consideration for this study
i.e. coatings suitable for radiative cooling application and for use in solar
thermal absorber plates, the reflection over the solar spectrum i.e. over
wavelength range $0.3-3\,\mu m$ and emissivity over the infra-red spectrum
i.e. over wavelength range $5-15\,\mu m$ is of primary importance, and the
weighted average over this spectral range is reported in Table 1 along with
the deviation from FDTD simulations expressed in % error in brackets.

##  3 Semi-analytical method

The comparison with FDTD simulations shown in Section 2 demonstrate the
failure of KM and FF analytical methods in configurations where dependent
scattering is not negligible and when matrix/particles are absorbing. This
failure can be attributed to the actual scattering and absorption coefficients
of these coatings diverging from the values calculated using Mie scattering
coefficients of the individual particles. At present no single analytical
technique exists that can correctly predict the optical properties of
particulate media in the presence of dependent scattering effects as well as
correctly account for the absorption in matrix/particles. One can then resort
to using exact numerical solvers to accurately estimate the optical properties
of the coating in such cases. However, as Fig. 6 shows, the computational time
required to simulate such structures increases exponentially with thickness of
the coating. For coatings of thickness in the range 100-500 microns which are
currently being adopted in literature for the radiative cooling application
[6, 49, 46, 36, 8] the design time is clearly prohibitive.

Figure 6: Comparison of computational time as a function of thickness of the
disordered media coating. Simulations are carried out in ANSYS Lumerical using
an eight-core Intel Xeon workstation for the configuration: $n_{p}=2.5$,
$n_{h}=1.5$, $r=0.25~{}\mu$m, $f=0.05$, with mesh size 30 nm. Auto shutoff
level (simulation termination criteria) is set at 10-3.

In such cases it becomes imperative to develop alternate techniques which can
combine the accuracy power of exact FDTD solvers with the simplicity and
minimal computational requirements of the analytical techniques. Particularly
when multiple parameters are involved in design - such as that observed for
disordered media - such a method will prove to be useful in reducing the
design time to find the optimum combination of parameters necessary to obtain
the required optical properties of the coating. In order to obtain a better
estimate for the absorption and scattering coefficients of such media where
dependent scattering effects are non-negligible, researchers have previously
[27, 51, 52, 53] relied on experimental measurements of the optical properties
of a fabricated coating and then using the KM theory results from Section 2 to
extract the required coefficients. Instead of relying on experimental
measurements which is not always feasible especially at the initial state of
design, we modify this technique and instead propose the following two-step
semi-analytical method to estimate the optical properties of random media of
thickness $L$ when usage of exact numerical solvers to simulate the properties
of such a thick coating is prohibitive.

  * •

Step 1: Use a numerical solver to obtain the optical properties $R$ and $T$ of
a similar coating but with much smaller thickness $t_{s}\ll L$ and extract the
$\gamma$ and $A$ parameters by inverting Eq. 1 and 2. Care must be taken at
this step to ensure that the configuration set up in the solver considers
incident light to be in the same medium as the index of matrix i.e.,
$n_{\text{surr}}=n_{\text{h}}$ in order to ensure that reflection from
surfaces and substrates are not included in this step. In case the host matrix
is absorbing then only the real part is considered i.e.,
$n_{\text{surr}}=\text{Re}(n_{\text{h}})$. Care must also be taken to ensure
that when scattering efficiency of the particles is high, the value of $t_{s}$
should be chosen such that $t_{s}\gg l_{s}$ where $l_{s}\approx
1/(N\sigma_{s})$ is the scattering mean-free path with $N$ being the particle
number density and $\sigma_{s}$ the scattering cross section. At the other
limit when scattering efficiency is low the optical properties of the coating
are primarily determined from surface reflection and transmission which are
accounted for in step 2. Thus the choice of $t_{s}$ is determined from the
scattering mean-free path calculated in the high-scattering regime.

  * •

Step 2: From the $\gamma$ and $A$ parameters extracted from step 1 use the
analytical expressions from KM theory i.e. Eqs. 1, 2, 7 and 11 to predict the
optical properties of the coating of the required thickness $L\gg t_{s}$.
Specular reflection at the surfaces as well as at the substrate are accounted
for here.

A more elaborate procedure, along with details of a supporting convergence
test which may need to be incorporated in some cases to arrive at the value of
thickness $t_{s}$ is included in Section S4 of supplementary.

(a)

(b)

Figure 7: (a) Reflectivity and transmissivity for $n_{\text{p}}=2.5$,
$n_{\text{h}}=1.5,$ $r=0.25~{}\mu\text{m},$ $f=0.3,$ and $L=50~{}\mu\text{m}$;
(b) Reflectivity and absorptivity for $n_{\text{p}}=2.5+0.1i$,
$n_{\text{h}}=1.5,$ $r=0.25~{}\mu\text{m},$ $f=0.3,$ and $L=50~{}\mu\text{m}$.
Here, SM stands for semi-analytical method and LM for Lumerical.

We now apply this technique for the cases considered in Section 2 where the
predictions from analytical methods deviated significantly from those of FDTD
solver, such as for the dependent scattering regime, as well as when the
absorption in the particles/host matrix is significant. Fig. 7 (Fig. 8) shows
the comparison between the predictions from the semi-analytical technique and
from FDTD simulations when absorption in particles (host matrix) is varied. In
both these cases the semi-analytical technique uses the results of exact FDTD
simulations of a $10~{}\mu$m thick coating to predict the optical properties
of a larger $50~{}\mu$m thick coating. A volume fill fraction $f=0.3$ is
maintained in both these cases where dependent scattering effects are known to
be dominant, while keeping other parameter values same as that analysed for
the monodisperse case of Sec. 2.1.

(a)

(b)

Figure 8: Reflectivity and absorptivity for $n_{\text{p}}=2.5,$
$r=0.25~{}\mu\text{m},$ $f=0.3,$ $L=50~{}\mu\text{m},$ and (a)
$n_{\text{h}}=1.5+i10^{-2}$; (b) $n_{\text{h}}=1.5+i10^{-1}$. Here, SM stands
for semi-analytical method and LM for Lumerical.

For these cases we observe a close match in the predictions of the semi-
analytical method with the FDTD results over the entire spectrum, with only a
slight deviation observed for the higher wavelengths when absorption is high.
The weighted-average reflectivity of the coating for solar spectrum, and
emissivity over the infra-red spectrum for the cases considered in Figs. 7 and
8 are listed in Table 2 along with the deviation from FDTD simulations
expressed in % error in brackets. Particularly illustrative of the
effectiveness of the semi-analytical technique is the reduction in error (1.03
% in Sr. no. 1) as compared to those obtained from analytical techniques and
reported in Table 1 ( 8.13 % using KM theory and 6.98 % using FF theory in Sr.
no. 13) for the configuration: $n_{\text{p}}=2.5$, $n_{\text{h}}=1.5,$
$r=0.25~{}\mu\text{m},$ $f=0.3,$ and $L=50~{}\mu\text{m}$ where dependent
scattering is expected to be dominant.

Table 2: Weighted-average reflectivity in solar spectrum $R_{\text{solar,SM}}$, and emissivity in IR spectrum $\epsilon_{\text{IR,SM}}$ calculated using the semi-analytical technique. Values in brackets denote deviation of prediction from FDTD results. Sr. no. | Fig. no. | $R_{\text{solar,SM}}$ | $\epsilon_{\text{IR,SM}}$
---|---|---|---
1 | 7(a) | 0.864 (1.03%) | -
| 2
---
7(b) | 0.059 (0.01%) | 0.710 (8.73%)
| 3
---
8(a) | 0.178 (2.73%) | 0.391 (6.25%)
| 4
---
8(b) | 0.062 (19.2%) | 0.935 (5.17%)

##  4 Comparison with experimental data

We now apply the semi-analytical technique described in Section 3 to predict
the optical properties of fabricated coatings reported in literature which
have been designed for radiative cooling application. We choose two such
disordered coatings where dependent scattering is expected to be dominant so
that analytical techniques are not applicable, and the thickness of the
coating prohibits the use of exact electromagnetic solvers to predict the
optical properties to good accuracy.

In Ref. [48], a hierarchically porous polymer (P(VdF-HFP)) coating of
thickness 300 $\mu$m containing air voids with sizes ranging from 0.05-5
$\mu$m in P(VdF-HFP) matrix has been fabricated, and experimentally
characterized to have solar reflectivity value of 0.96 and emissivity in the
8-13 $\mu$m wavelength range to be 0.97. In order to apply semi-analytical
technique to predict the properties of this coating, we set up a simulation in
FDTD solver with a smaller coating thickness $t_{s}=50~{}\mu$m (determined
using the convergence test explained in Section S4 of supplementary). This
thickness is chosen to ensure sufficient number of larger sized air voids
($r\approx 2.5~{}\mu$m) in this P(VdF-HFP) matrix. The size distribution of
nano-micro air voids used in the simulation is given in supplementary (Fig.
S4). Refractive index data of P(VDF-HFP) is extracted from Ref. [48]. The
reflectivity data in the wavelength range $0.3-16~{}\mu$ m, predicted using
the semi-analytical method for $L=300~{}\mu$m thickness, is compared with that
reported in Ref. [48] in Fig. 9(a). While an appreciable match is noticed in
the predicted values across the spectrum, small deviation observed in the
reflectivity values can be attributed to our inability to incorporate exact
size distribution of both micro and nano voids as present in the fabricated
structure, in ANSYS Lumerical.

In Ref. [46] an ultrawhite BaSO4 film of thickness 400 $\mu$m has been
developed with 60 % volume fraction of BaSO4 nanoparticles, and has been
characterized to have reflectivity of 0.976 in the solar spectrum and
emissivity of 0.96 in 8-13 $\mu$m wavelength range. In order to apply the
semi-analytical technique to predict the properties of this coating, we set up
a simulation in FDTD solver with structure thickness $t_{s}=15~{}\mu$m and
BaSO4 spherical particles randomly distributed with volume fraction 60 %. The
particles are taken to be of uniform size distribution with diameters spread
over the range $398\pm 130$ nm to match that reported in Ref. [46]. Matrix is
considered to be air for BaSO4 film. Refractive index data of BaSO4 is
extracted from Ref. [54]. The emissivity data in the wavelength range
$0.3-16~{}\mu$m, predicted using the semi-analytical method for $L=400~{}\mu$m
thickness, is compared with that reported in Ref. [46] in Fig. 9(b). While we
again observe an appreciable match across the spectrum, some deviation
observed particularly around wavelength of $2~{}\mu$m is suspected to be due
to difference in the refractive index of the fabricated film and that
calculated from first-principles in Ref. [54].

(a)

(b)

Figure 9: (a) Reflectivity of hierarchically porous P(VDF-HFP) coating
calculated using semi-analytical technique is compared with experimental
result given by Mandal et al. [48]; (b) Absorptivity/emissivity of BaSO4 film
calculated using semi-analytical technique is compared with experimental
result given by Li et al. [46].

##  5 Conclusion

In this study we have analyzed the applicability of well-known analytical
techniques of KM and FF theories to predict optical properties of a disordered
metamaterial coating over a broad spectrum ranging from 300 nm to
$15~{}\mu\text{m}$ wavelength. Recent advancements in the use of disordered
coatings in applications such as radiative cooling and solar thermal absorber
plates which require tailored optical properties over this wavelength range
necessitates such a study. Based on deviations observed between the
predictions of these analytical techniques and exact FDTD solver in the
dependent scattering regime, a two-step semi-analytical technique has been
proposed which can be used to predict optical properties of such coatings with
good accuracy and minimal computational resources. Such a method is expected
to be resourceful for designing coatings with specific optical properties
where several parameter combinations need to be investigated to arrive at an
optimal combination. Small deviations observed when absorption in host matrix
is high warrants further research to improve this technique.

## Acknowledgments

B.R.M. acknowledges support from Prime Minister’s Research Fellowship (PMRF).
K.S. acknowledges support from La Fondation Dassault Systèmes and SERB Grant
No. SRG/2020/001 511.

## Disclosures

The authors declare no conflicts of interest.

## Supplementary information

See Supplement 1 for supporting content.

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Ayush Gupta, Rohan Sukumaran, Kevin John, Sundeep Teki 11institutetext:
PathCheck Foundation, Cambridge 22institutetext: Indian Institute of
Information Technology, Sri City, India
22email<EMAIL_ADDRESS>22email: {rohan.s16<EMAIL_ADDRESS>
22email<EMAIL_ADDRESS>
# Hostility Detection and Covid-19 Fake News Detection in Social Media

Ayush Gupta ** Rohan Sukumaran 11** Kevin John 22** Sundeep Teki

###### Abstract

With the advent of social media, there has been an extremely rapid increase in
the content shared online. Consequently, the propagation of fake news and
hostile messages on social media platforms has also skyrocketed. In this
paper, we address the problem of detecting hostile and fake content in the
Devanagari (Hindi) script as a multi-class, multi-label problem. Using NLP
techniques, we build a model that makes use of an abusive language detector
coupled with features extracted via Hindi BERT and Hindi FastText models and
metadata. Our model achieves a 0.97 F1 score on coarse grain evaluation on
Hostility detection task. Additionally, we built models to identify fake news
related to Covid-19 in English tweets. We leverage entity information
extracted from the tweets along with textual representations learned from word
embeddings and achieve a 0.93 F1 score on the English fake news detection
task.

###### keywords:

Hostility Detection, Hate Speech, Fake News, Misinformation, COVID-19,
Infodemic, Social Media, Devanagari

11footnotetext: *Denotes equal contribution.

##  1 Introduction

With the proliferation of social media platforms, information dissemination
knows no bounds. The public discourse that occurs on social media platforms
leads to a lot of information being shared and consumed, that more often than
not, cannot be verified as hostile free content or fact-checked for
authenticity. Usually, such harmful content is used to defame and hurt people,
especially from minority groups, specific countries, the LGBTQ community, and
several other organizations. Recently, as the COVID-19 pandemic is devastating
humanity, hostile content and misinformation on social media have transformed
into an “Infodemic”, further expediting the need for control of such content.
This being said, fake news and hostility detection are daunting tasks owing to
the context, domain knowledge, and the inherent complexity of the natural
language constructs, like different forms of hatred, target groups, ambiguous
word representations, and more, are required to understand it.

In this paper, as part of the Shared Task organized in CONSTRAINT 2020 [1, 18,
19], we look at fake news detection for English and Hindi (Devanagari) tweets,
as well as hostility detection for Hindi tweets. We evaluated machine learning
and deep learning models and propose an ensemble model that combines language
representations with the features (linguistic and otherwise) extracted from
the data. Furthermore, we measure the differential impact of each feature and
also notice that our model was able to provide the correct annotation for a
few of the miss-annotated samples in the English fake news dataset, opening up
to possibilities of weak supervision for labeling.

Our contributions in this paper are primarily the identification of entities
pertinent to fake news detection and data analysis steps that can be taken to
understand such micro-blogging data. We show that a lightweight ensemble of
Word2Vec [15] coupled with entity information gives better performance in
English fake news detection than larger BERT [6] based models. Our ensemble
model achieved 0.93 F1 score (above the baseline scores). Furthermore, we
perform Hostility detection by ensembling models based on Hindi BERT and Hindi
FastText. Further, we create various simple but effective text features
extracted from the tweets to be fed in the model and also compile a list of
abusive words that are used in an abusive words detector, which further boosts
the accuracy. Our methods obtained a weighted F1 score of 0.97 in coarse-grain
classification for Hostility task and ranked 5th out of 45 teams. For the
fine-grain classification, our model obtained a weighted F1 of 0.62 and ranked
7th out of 45 teams.

##  2 Related Works

Riedel et al., (2017) [20] used TF-IDF similarity scores between the title of
the news and the content concatenated with the corresponding TF-IDF vectors.
This was further fed into a fully connected neural network. Albeit impressive
results, this approach is not useful for identifying fake news that is
spreading via micro-blogging sites. Further, work from Khatter et al. (2019)
[9] looks at solving the problem using a multimodal approach. The authors make
use of a Variational Autoencoder to learn the representation of a social media
post, combining the textual and image representations. More recent work from
Lee et al. (2020) [12] utilizes a language model as a zero-shot fact-checker.
A masked language model (MLM) training followed by entailment check is
adapted. The model is tested in a closed-book setting. The results look
promising but require the presence of large scale fact-based data to enable
such training. Vijjali et al. (2020) [22] looked at the problem of claim
verification by following a two-stage pipeline. The paper uses a combination
of BERT [6] and ALBERT [11] models - for identifying explanations based on the
claims from a large dataset and checking if the claims are entailment of the
explanations.

Bohra et al. (2018)[3] uses various linguistic features such as character,
word, and lexicon-based features on Hindi-English code-mixed tweets into Hate
speech or Normal speech and attain 71.7% accuracy with an SVM model. In [24]
the authors use sentiment analysis to detect bullying in tweets and Latent
Dirichlet Allocation (LDA) topic models [2]. Also, hate speech detection is a
widely studied topic [7, 10] with most of the work focused on developing
binary classification models for English.

Research in Hostility detection is more focused on learning the discriminatory
features via Deep Learning models instead of relying on hand-crafted features.
Bhardwaj et al. (2020) [1] computes input embedding with help of a pre-trained
multilingual BERT(m-BERT) model[6],and is then fed into several machine
learning models like Random Forest (RF), SVM, and Linear Regression (LR).
Hostility detection on Devanagari is scant, and we apply Hindi FastText and
mBERT embeddings for hostility detection in Hindi; the classes for fine-grain
classification: Hate, offensive, Defamation, Fake, and non-hostile, and
coarse-grain classification: Hostile or non-hostile.

##  3 Method

###  3.1 English Fake News

####  3.1.1 Preprocessing

As the data in Patwa et al. (2020) [19] are based on tweets scraped from the
internet - abbreviations, social media lingo, URLs amongst other tokens are
present in the dataset. The dataset contained an almost 50-50 split of real
and fake tweets in train, validation and test. In order to create embeddings
from the data using Word2Vec[15], FastText[4], BERT[6] and many more, we used
multiple preprocessing steps. The data was initially rid of contractions, for
instance - y’all → you all, how’re → how are,and so on.

Figure 1: Data and modeling pipeline for English Fake News detection

These contractions were identified through a combination of regex pattern
matches and simple rules. Further, occurrences of URLs, mentions, emojis,
numbers and so on were cleaned and removed with the help of tweet-
preprocessor111https://pypi.org/project/tweet-preprocessor/ library, the
punctuation and special characters were stripped and the remaining text was
tokenized with the help of NLTK libraries.

####  3.1.2 Rule-based models

Based on data analysis we observed that length of tweets, number of hashtags,
number of mentions, etc. had a statistically significant impact in the class
labels. All such similar patterns specific to the dataset were analysed and
added as features to the model.

####  3.1.3 Distributional embeddings

Using distributional word embeddings like Word2Vec [15], FastText [4] etc. has
seen huge success in text classification. Word2Vec being a word level
embedding suffers from the issue of Out Of Vocabulary (OOV) distributions. To
mitigate this, an often adapted strategy is making use of sub-word level
embeddings like FastText, BERT and more. All these models were used to convert
raw text into a fixed-length embedding vectors.

####  3.1.4 Adding entity-based information using Bag of Words (BoW)

The data has significant presence of entities like names of government bodies,
scientific journals, places, organizations, etc and the distribution varies
per class. Using TF-IDF based rankings, we built a Bag of Words (BoW) feature
vector. This would indicate the presence or absence of each of the
corresponding terms in a given sentence.

####  3.1.5 Contextual embeddings - BERT based models

Transformer models [21] like BERT [6], RoBERTa [14], ALBERT [11], ELECTRA [5],
have shown success on NLP tasks like text classification, question answering
sequence labeling and more. We make use of these models to find meaningful
representations of the input sentences.

####  3.1.6 Ensemble model

The idea behind the ensemble technique is to leverage the performance and
robustness captured by the different models. Ensembling can be done using a
range of methods from using a logical OR/logical AND operation over the “n”
models’ predictions, to using fully connected neural network layers to learn
the representations of the models. Here, we also combine the metadata (length
of tweet, number of mentions, etc.) and Bag of Words along with the
predictions from different models, into a single vector representation and fed
into a fully connected neural network for ensembling. The overview of the data
pipeline is mentioned in Figure 1.

###  3.2 Hostility and Fake News Detection Hindi

####  3.2.1 Problem Formulation

The Devanagari dataset demanded a coarse grained evaluation (Hostile or not)
as well as a fine grained one(Non-Hostile, Hate, offensive, Fake and
Defamation).

####  3.2.2 Data and Preprocessing

Data distribution can be seen from Table 1. Prior to training the models, we
perform a few preprocessing steps as follows:

| Hostile posts | Non-Hostile
---|---|---
| Fake | Hate | Offensive | Defame | Total |
Train | 1144 | 792 | 742 | 564 | 2678 | 3050
validation | 160 | 103 | 110 | 77 | 376 | 435
Test | 334 | 237 | 219 | 169 | 780 | 873
Overall | 1638 | 1132 | 1071 | 810 | 3834 | 4358
Table 1: The data distribution for Hindi Hostility Dataset.

  * •

Tokenization and removal: We designed a tweet-tokenizer to parse and remove
every username-mention, hashtags, and URLs present.

  * •

Stopword Removal: Tokenized tweets were passed through a customized stop word
removal for the Hindi language.

  * •

Emoji Removal: Demoji library222https://pypi.org/project/demoji/ was used to
identify and remove emojis.

  * •

Tweet cleaning: Removes all punctuation, new line, Unicode characters (u200B,
u200C, u200D) which are zero-length white spaces.

####  3.2.3 Baseline Classifier

As baselines, we experiment with three broad representations. (1)TF-IDF
(2)mBERT Embedding (3)FastText Embedding

####  3.2.4 TF-IDF feature

TF-IDF as the basic approach for text representation is widely used to score
words thus helping in applications like text classification, topic modeling,
etc. We clean the tweets by passing them through the above four preprocessing
steps. The feature vector created from the clean tweets is passed into the
machine learning models.

####  3.2.5 mBERT Embedding

The initial baseline was defined by using the multilingual BERT (m-bert) model
[13] to handle the Hindi data. We use the approach defined by the authors[1]
to replicate the results for baseline. The preprocessing was a four-step
process, defined in the previous subsection. We calculate the word embedding
for each sentence in a tweet by tokenizing it and passing through the
embedding matrix defined using the mBERT model. We use sentence embeddings as
a feature for machine learning models.

####  3.2.6 FastText Embedding

FastText333https://fasttext.cc/ is an open-source, lightweight library trained
on 157 different languages, that allows users to learn text representations
and text classifiers. FastText treats each word as a composition of character
n-grams thereby the word representation is created by the sum of the character
n-gram representations. The method of calculating sentence embedding is the
same as described in the previous section.

####  3.2.7 Feature Identification and Extraction

The feature Extractor module is used to identify and extract linguistic
features from a given natural unstructured tweet. The feature Extraction
module leverages several natural language processing (NLP) and regex
techniques to extract these features. We have categorized them broadly into
the following 3 modules: a) Abusive Language Detector b) Username Mention,
URL, and Hashtag count c) Emoji Detector.

####  3.2.8 Abusive Language Detector

We hypothesize that giving a count of abusive words as a feature to the
classification model boosts the accuracy in detecting offensive tweets. To
validate our hypothesis, we manually curated a list of commonly used 84
profane words in Hindi. We measure the presence of these profane words per
tweet and use this count as a feature for the classification model.

####  3.2.9 Username Mention, URL, and Hashtag counter

On analyzing the dataset, we found that on an average there were more hashtags
and URLs in the non-hostile tweets as compared to the hostile ones, whereas
there are more user mentions in the Hate tweets. Informed by this, we
hypothesize that the user mention, presence of URL or Hashtag can have
differential impact on the fine-grain classes (Hate, Offensive, Fake, and
Defamation). Therefore we design a rule-based method to parse each tweet to
extract the count of the occurrence of these entities and use the count as an
input feature.

####  3.2.10 Emoji Detector

The inherent nature of micro-blogging(short messages) has made people use
acronyms, emoticons, and various other special characters to express their
message. We hypothesize that the use of emoji as a feature for hostility
detection could increase the accuracy, as similar results were observed in
sentiment analysis[23]. To validate this hypothesis, we use the demoji library
to extract all the emojis present in the tweet and pass the count
corresponding to each tweet as a feature to the classification model along
with other features.

Figure 2: Data and modeling pipeline for Hindi Hostility Classification

####  3.2.11 FastText based LSTM + FastText Classifier

FastText represents a text by average of word vector and it also allows the
word vector to be updated through back-propagation while training. FastText
classifier uses (multinomial) logistic regression for training on the vector
average and leverages Hierarchical Softmax to reduce computational complexity.
We pass the cleaned training data to the FastText, and use grid search to find
the optimal hyperparameter for the model. For the multi-label classification
we use one-vs-all strategy.

####  3.2.12 FastText based LSTM + Features

In this paper, we built the hostility classiﬁcation model using the LSTM[8]
model with FastText embedding and metadata. We use the LSTM model owing to its
internal memory to process long-range dependencies in sequential inputs like
tweets. This model takes two inputs, the first being V = {v1, v2, …, vn} the
FastText Embedding, where each vi represents a cleaned tweet in vector space
and the second MD = {A, E, H, M, U} the 5-tuplet metadata representation where
A, E, H, M, U are the count of abusive words, emoji, hashtag, mention, and URL
per clean tweet respectively. We use keras444https://keras.io/ to define and
train our model.

####  3.2.13 BERT-Hindi Embedding with BERT model

Recent papers using BERT based contextual embedding models have shown SOTA
performance in Hostile language identification[16, 17]. We use Hindi-BERT pre-
trained model555https://huggingface.co/models and fine-tune it on our dataset.
The Hindi BERT model has 12 hidden layers, with an encoding layer of 256
dimensions instead of 786, the model has 4 attention heads for each attention
layer. The dimension of the feed-forward layer is kept as 1024 instead of 3072
which is the default in BERT models. We find the best learning rate (i.e.,
1.2e-4 here) for the model by simulating the training data briefly with
different learning rates and choose the one with minimum loss. For training,
we pass the preprocessed tweets into the BERT model and train the model for 12
epochs with a batch size of 8.

####  3.2.14 Ensemble Model

In this approach, we ensemble three base classifier, which are FastText
Embedding with FastText classifier, FastText Embedding with LSTM model, and
Hindi BERT Embedding with BERT model. The whole framework of ensemble setting
is illustrated in Fig. 2. Each of the base classifier is explained in the
above subsection. The final classification is made by fusing the outputs of
all three base classifiers through majority voting.

##  4 Experiments

###  4.1 English Fake News

####  4.1.1 Models

We experimented by using the word embeddings extracted from FastText and
Word2Vec and we used the mean of these word embeddings of the tweet as input
to the machine learning models, as shown in Figure 1. By examining the
predictions of our best models, we noticed a pattern of misclassification. In
order to mitigate this, we include entity level information extracted from the
data.

####  4.1.2 TF-IDF scoring for entities

We used a scoring factor to determine useful words to be included in the BoW
method by first calculating the tf-idf of misclassified tweets in the
validation data separated by the class(real/fake), and then comparing those
scores with the TF-IDF scores in the train data separated by class(real/fake).
For a real Tweet misclassified in validation data, let Vr be the TF-IDF score
of a word among the real misclassified tweets. Let Tr and Tf be the TF-IDF
score of a word from the real and fake tweets in train respectively. Further,
we find words which have high scores for Vr and Tr while simultaneously have
low scores of Tf to included these words to the BoW feature vector.

####  4.1.3 Contextual Embedding

Owing to the success of BERT based models in a suite of NLP tasks, we
calculated the contextual embeddings constructed from BERT. This embeddings,
concatenated with the meta features as shown in Fig 1, was further fed as
input to the machine learning or deep learning models.

###  4.2 Hindi Hostility Detection and Fake News

We set up our experiment in three parts. Firstly, for baseline accuracy,
embeddings - TF-IDF, mBERT, and Hindi FastText \- and models - RF, LR, SVM,
Gradient Boosting(GB), MLP \- are set up. We use grid search for
hyperparameter tuning. The results of the baseline classifiers are shown in
Table 3 in the TF-IDF, mBERT, FastText sections.

Secondly, we do an ablation study to determine the effectiveness of the
linguistic features extracted from tweets. For this, we chose FastText
Embedding as the base classifier and conducted a combination of experiments
utilizing m1, m2, m3 metadata. The results are shown in Table 3.

Finally, we test our proposed models that are FastText Classifier(FC), BERT-
Hindi Embedding with the BERT model, FastText Embedding with LSTM plus all
metadata. Further, conducted experiments with the combination of the an
ensemble model, due to limited space we only show the best ensemble model in
the Table 3 in the Proposed Model section All the experiments for coarse-grain
and fine-grain are conducted in two parts, one on the validation dataset, and
the other on the testing dataset and weighted F1 score is used as evaluation
metrics.

##  5 Results and Discussions

###  5.1 English Fake News Result

As seen from Table 2, the model which makes use of the metadata and BoW
features along with embeddings and pseudo labeling gives the best performance.
We hypothesize and validate the presence of entities involved in hostility and
fake news detection. Adding such entities via a BoW feature vector increases
the performance of the model. We also notice that contextual embeddings based
on BERT architecture didn’t provide huge improvements and in fact performed
worse than our best model. This could possibly due to the nature of the
dataset and the annotation strategy adapted. Furthermore, it is also important
to note that there were a few samples in the English fake news dataset which
were mis-annotated, but were correctly labeled by our model.

Model | Val Score (%) | Test Score (%)
---|---|---
Meta with SVM | 93.59 | 93.45
Meta + BoW with SVM | 93.74 | 93.41
Meta + BoW Ensemble OR | 91.86 | 91.66
Meta + BoW Ensemble Majority Vote | 93.55 | 93.10
Meta + BoW with SVM Pseudo-labelling | 93.64 | 93.41
Table 2: The weighted F1 scores on the English Fake news dataset. We notice that simple distributed embedding based models coupled with meta-data and entity information (via BoW features) exhibit the best performance. The pseudo-labelling was done on the test data Method | Models |  | Coarse Grain
---
w.F-1
| Fine Grain
---
w.F-1
Validation | Test | Validation | Test
TF-IDF | TF-IDF + RF | 0.78 | 0.77 | 0.35 | 0.34
TF-IDF + SVM | 0.79 | 0.80 | 0.34 | 0.36
TF-IDF + LR | 0.76 | 0.75 | 0.33 | 0.32
TF-IDF + GB | 0.79 | 0.79 | 0.34 | 0.35
TF-IDF + MLP | 0.71 | 0.69 | 0.29 | 0.29
mBERT based | mE +RF | 0.79 | 0.80 | 0.53 | 0.51
mE + SVM | 0.84 | 0.84 | 0.54 | 0.54
mE + LR | 0.83 | 0.84 | 0.51 | 0.51
mE + GB | 0.81 | 0.81 | 0.52 | 0.52
mE + LSTM | 0.83 | 0.83 | 0.54 | 0.53
FastText based | FE+ RF | 0.83 | 0.82 | 0.51 | 0.50
FE+ SVM | 0.87 | 0.87 | 0.55 | 0.55
FE+ LR | 0.85 | 0.86 | 0.52 | 0.52
FE+ GB | 0.85 | 0.84 | 0.52 | 0.53
FE+ LSTM | 0.91 | 0.91 | 0.56 | 0.56
Meta Data Ablation | FE + LSTM + m1 | 0.92 | 0.92 | 0.58 | 0.58
FE + LSTM + m2 | 0.92 | 0.92 | 0.57 | 0.58
FE + LSTM + m3 | 0.93 | 0.93 | 0.58 | 0.58
FE + LSTM + m1 +m2 | 0.92 | 0.92 | 0.58 | 0.58
FE + LSTM + m1 +m3 | 0.94 | 0.93 | 0.59 | 0.60
| FE + LSTM + m2 +m3 | 0.93 | 0.93 | 0.58 | 0.58
Proposed Model | FE+ LSTM + m1 + m2 + m3 | 0.94 | 0.95 | 0.59 | 0.63
FE + FC | 0.92 | 0.92 | 0.58 | 0.58
HBE + Bert | 0.96 | 0.96 | 0.60 | 0.61
Ensemble Model | 0.97 | 0.97 | 0.61 | 0.62
Table 3: The results on the Hindi Hostility dataset. Here m1, m2, m3 are
abusive language count, URL, mention, Hashtag count, and emoji count,
respectively. FE, mE, HBE, are FastText, mBERT, and Hindi-BERT Embedding.

Figure 3: Confusion Matrix of Hindi Hostility coarse-grain classification
(left) & English Fake News classification (right)

Class Name | Precision | Recall | F1
---|---|---|---
Non-Hostile | 0.98 | 0.96 | 0.97
Hostile | 0.96 | 0.97 | 0.97
W.avg/Total | 0.97 | 0.97 | 0.97

Class name | precision | Recall | F1 | Support
---|---|---|---|---
Defamation | 0.30 | 0.72 | 0.42 | 169
Fake | 0.67 | 0.84 | 0.77 | 334
Hate | 0.44 | 0.80 | 0.57 | 237
Offensive | 0.46 | 0.79 | 0.59 | 219
W.avg/Total | 0.50 | 0.80 | 0.62 | 959

Table 4: The Coarse-grain performance (left) & the Fine-grain performance of
the best Ensemble Model (right).

###  5.2 Hindi Hostility Detection Results

Baseline Classifiers: We see that the FastText based feature combined with
LSTM yields the best result, equally matched by the mBERT based embeddings.
TF-IDF based models perform poorly, due to the lack of contextual
understanding of the text. (Table 3)
Ablation Study: In Table 3, the addition of metadata (m1,m2,m3) increases the
F1 score by 1% in coarse-grain and 2% in fine-grain respectively. But when m1
and m3 are given together F1 increases by 4%, suggesting a better combination.
When all are provided together to the model, an increase of 7% F1 can be
observed in test data yielding to best F1 in fine-grain. Based on Table 3 we
observe that the fake tweet are easier to detect as compared to other classes.
We also see that, due to the abusive language detector(m1) as a feature, we
are able to detect the offensive tweets better.
Proposed Model: As an individual model, Hindi BERT Embedding with BERT model
yields the best result for coarse-grain classification and FastText-LSTM with
metadata yields best result on fine-grain classification on test data. Our
best score is achieved on the Hindi-Hostility task, where we secured 5th rank
out of 45 teams using an ensemble model. From Figure 3 we can see our Ensemble
model predicts only 20 out of 1653 tweets as False Negative and 35 out of 1653
detected as a false negative, yielding 0.97 F1.

##  6 Conclusion

In this paper, we address hostility and fake news detection on the Devanagari
(Hindi language) script using an ensemble model, coupled with abusive language
detector and metadata to attain an F1 score of 0.97. Furthermore, we also
attained an F1 score of 0.93 on the English fake news detection task using a
model based on Word2Vec embeddings, metadata, and entity features. Our results
highlight that representation learning models augmented with data specific
rules and features outperform the vanilla deep learning models.

Both the tasks attempted in our paper are far from solved and bringing in
modalities like, images or videos, social network structures, user-based
embeddings, event-based embeddings and more could help improve the current
model. Furthermore, as the manual curation of such datasets is laborious and
prone to errors, methods from semi-supervised learning and weak supervision
could be leveraged.

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