# Neutrino mass observables and non-Hermitian version of Type-I seesaw model

Sasmita Mishra<EMAIL_ADDRESS>National Institute of Technology
Rourkela, Odisha, India, $769008$

###### Abstract

We study the non-Hermitian extension of the Lagrangian of the Standard Model
extended by singlet right-handed heavy neutrinos. The neutrino mass
eigenvalues are calculated for three generation case. Using experimental data
available for neutrino mass observables, the non-Hermitian parameters are
constrained. New contributions to leptogenesis are analyzed. While allowing
for a low scale seesaw it is identified that branching ratio close to the
experimental limit for lepton flavor violation is achievable in the context of
Type-I seesaw mechanism.

##  I Introduction

The experiments based on neutrino oscillation phenomenon have established the
fact that this abundant particle in the Universe has non-zero mass Fukuda et
al. (1998); Ahmad et al. (2002a, b); Bahcall and Pena-Garay (2004). This is in
contrast to the prediction of the standard model (SM), which otherwise is a
very successful theory of particle physics at low energy. Subsequently one
relies on theories beyond the SM in order to circumvent the problem. The
canonical or Type - I seesaw mechanism Minkowski (1977); Gell-Mann et al. ;
Yanagida (1979); Mohapatra and Senjanovic (1980) is one such leading candidate
which accounts for non-zero neutrino mass by adding the extra heavy right-
handed singlet neutrinos to the SM. In addition, the said mechanism can
contribute to the baryon asymmetry of the Universe (BAU) through the out of
equilibrium decays of right-handed neutrinos through leptogenesis mechanism
Fukugita and Yanagida (1986). Also, it induces source of lepton flavor
violation (LFV). The quantitative analysis of both the phenomena (Leptogenesis
and LFV) depend on $h_{\nu}$ where $h_{\nu}$ is the Yukawa coupling of right-
handed neutrinos with the SM lepton doublets and Higgs. It is observed that
$h_{\nu}$ must be complex in order to contribute positively to the mechanism
like leptogenesis. To be specific the CP asymmetry parameter, $\epsilon$
depends on imaginary part of $(h_{\nu}h_{\nu}^{\dagger})^{2}$.
$h_{\nu}^{\dagger}$ appears in the hermitian conjugate part of the extended SM
Lagrangian by demanding that Lagrangians are in general real. Here we study
one scenario which allows us to relax the condition of hermiticity of the
Yukawa interaction terms of the Lagrangian while keeping all the experimental
findings related to neutrinos intact.

The Lagrangian of the SM is constructed based on three principles; locality,
Lorentz invariance in vacuum and hermiticity. The hermiticity of the
Lagrangian/Hamiltonian ensures real energy eigenvalues and unitarity of time
evolution. In standard texts of Quantum Mechanics one often deals with
Hamiltonians which are hermitian because of the preceding reason. It has been
shown in Bender and Boettcher (1998); Bender et al. (1999); Bender (2005) that
hermiticity is a mathematical requirement to achieve real eigenvalues from the
Hamiltonian. Further, a rather non-Hermitian Hamiltonian which is symmetric
under the combined operation of space reflection operator, ${\mathcal{P}}$ and
the time inversion operator ${\mathcal{T}}$ has real eigenvalues provided
${\mathcal{PT}}$ symmetry is unbroken111Under ${\mathcal{P}}$ the two
fundamental operators, $\hat{x}$ and $\hat{p}$ transform like
$\hat{x}\longrightarrow-\hat{x}$ and $\hat{p}\longrightarrow-\hat{p}$. The
time inversion operator has the effect $\hat{x}\longrightarrow-\hat{x}$,
$\hat{p}\longrightarrow-\hat{p}$ and $i\longrightarrow-i$Bender (2005) .  .
Thus ${\mathcal{PT}}$ symmetry is an alternative requirement to hermiticity
for constructing many new Hamiltonians which would have been rejected in the
past on the basis of hermiticity. For example consider a complex Hamiltonian
which is not hermitian,

$\begin{pmatrix}re^{i\theta}&\sigma\\\ \sigma&re^{-i\theta}\end{pmatrix},$ (1)

where the $r,\sigma$ and $\theta$ are real parameters. The eigenvalues are
given by $r\cos\theta\pm\sqrt{\sigma^{2}-r^{2}\sin^{2}\theta}$. The
eigenvalues are real in one of the parametric region
$\sigma^{2}>r^{2}\sin^{2}\theta$ and are complex for
$\sigma^{2}<r^{2}\sin^{2}\theta$.

Taking a step ahead of Bender and Boettcher (1998); Bender et al. (1999);
Bender (2005) the non-Hermitian version of Quantum Field Theory has been
studied in Bender et al. (2004a, b). Also, a non-Hermitian version of a
Quantum Electrodynamics has been studied in Bender et al. (2005) which is CPT
invariant and consistent with unitarity. More specifically, the variant of the
Lagrangian has the Dirac mass term, $m\bar{\psi}\psi$ along with anti-
Hermitian mass term, $\mu\bar{\psi}\gamma_{5}\psi$. In the associated kinetic
term of the fermion, the covariant derivative $D_{\mu}$ has both vector and
axial vector coupling of the photon with the fermion. The authors have also
studied the gauge invariance in the model and shown the restoration of gauge
invariance in the limit $\mu^{2}=m^{2}$. Further, Alexandre et al. (2015)
studies a similar non-Hermitian Yukawa model with an aim to explore the
implications in neutrino sector of the SM. Similarly, Korchin and Kovalchuk
(2016) has given a model for non-Hermitian Yukawa interaction for one fermion
generation. More particularly they study the effects of the Yukawa interaction
in the Higgs boson decay to a pair of $\tau-$leptons. Also adding non-
Hermitian ${\mathcal{PT}}$-symmetric Hamiltonian and taking matter effect into
account, two flavor neutrino oscillation has been studied in Ohlsson (2016).
It has been shown that such consideration can give rise to sub-leading effects
in neutrino oscillation provided the additional parameters are small.

In this work, we study a special case of Type-I seesaw mechanism where the
condition of hermiticity on Yukawa coupling terms is relaxed. We calculate the
small neutrino masses for three generation case and extend the analysis to
gauge the implications for other phenomenological aspects related to
neutrinos. The Yukawa sector of the Lagrangian of the extended SM has both
Hermitian and non-Hermitian couplings. While allowing for generation of Dirac
mass term through Higgs mechanism, the couplings are constrained from
experimental data. Also, the analysis shows avenue for low scale seesaw
supporting enhanced branching ratio for LFV. In addition, it has the potential
for additional CP violation required for leptogenesis.

In section II we recapitulate the non-Hermitian extension of extended SM
Lagrangian Alexandre et al. (2015) in the context of Type-I seesaw mechanism.
While the neutrino masses has always been calculated Alexandre et al. (2015)
for two generation case we calculate the three mass eigenvalues for three
generation case and constraints form results arising from oscillation
experiments. In section III we discuss various direct searches of neutrino
mass observable to constrain the unknown coupling constants. In sections IV
and V we analyze optimistic contributions to leptogenesis and branching ratio
for lepton flavor violation process. In section VI we conclude with future
scope of extending the present work.

##  II Neutrino mass from non-Hermitian extension of fermionic Lagrangian

In this section, we summarize the important results of Alexandre et al. (2015)
related to neutrino masses coming from a non-Hermitian Yukawa model. And then
we generalize it for three generation case. In the SM the terms involving
Yukawa interactions of fermions with the Higgs field are gauge invariant and
Hermitian. Adding right-handed neutrinos, $N_{R}$’s one per generation to the
SM the Lagrangian for the lepton sector is given as

$\mathcal{L}=\bar{l}^{K}_{L}i\not{D}l_{L,k}+\bar{N}^{\alpha}_{R}i\not{\partial}N_{R,\alpha}-[y]_{k}^{\alpha}\bar{l}_{L}^{k}Hl_{R,\alpha}-[h]_{k}^{\alpha}\bar{l}_{L}^{k}\tilde{H}N_{R,\alpha}+{\rm
h.c.},$ (2)

where $l^{k}_{L}\equiv(\nu^{k}_{L}e^{k}_{L})^{T}$ are the left-handed lepton
doublets, $l_{R}$’s are the right-handed charged leptons and $\alpha,k$ are
generation indices. The Higgs doublet is represented as $H$ and
$\tilde{H}\equiv i\tau_{2}H^{*}$. $D_{\mu}$ is the covariant derivative of the
electroweak gauge group of the SM and $y$ and $h$ are the Yukawa coupling
matrices of Higgs with charged leptons and neutrinos respectively.

As discussed in the previous section we explore the relaxation of hermiticity
imposed on the Yukawa interactions. Since right-handed neutrinos are singlets
under the SM a Majorana mass term is also added in the Lagrangian. Focusing
only on the neutrino sector, in this case, the Lagrangian can be written as

$\mathcal{L}=\bar{N}^{\alpha}_{R}i\not{\partial}N_{R,\alpha}-[h_{-}]_{k}^{\alpha}\bar{l}_{L}^{k}\tilde{H}N_{R,\alpha}-[h_{+}]^{k}_{\alpha}\bar{N}_{R}^{\alpha}\tilde{H^{\dagger}}l_{L,k}-\left(\frac{1}{2}\bar{N}^{C}_{R,\alpha}M_{R}^{\alpha\beta}\bar{N}_{R\beta}+{\rm
h.c.}\right),$ (3)

where $C$ denotes the charge conjugation. The Yukawa couplings
$h_{\pm}=h\pm\eta$, assuming $h$ and $\eta$ are complex valued matrices and
$h^{\dagger}_{-}\neq h_{+}$. After spontaneous symmetry breaking due to the
Higgs field acquiring vacuum expectation value,

$\displaystyle H=\frac{1}{\sqrt{2}}\begin{pmatrix}0\\\
\upsilon+\xi\end{pmatrix},$
$\displaystyle\tilde{H}=\frac{1}{\sqrt{2}}\begin{pmatrix}\upsilon+\xi\\\
0\end{pmatrix},$ (4)

the Lagrangian can be written as,

$-\mathcal{L_{\nu}}\supset\frac{1}{2}(\bar{\nu}^{k}_{L}~{}~{}~{}~{}\bar{N}^{C}_{R,\alpha})\begin{pmatrix}0&[m_{-}]^{\beta}_{k}\\\
[m_{+}]^{\alpha}_{l}&M_{R}^{\alpha\beta}\end{pmatrix}\begin{pmatrix}\nu_{L}^{C,L}\\\
N_{R,\beta}\end{pmatrix}+\frac{1}{2}(\bar{\nu}^{C}_{L,k}~{}~{}~{}~{}\bar{N}^{\alpha}_{R})\begin{pmatrix}0&[m_{-}]_{\beta}^{k}\\\
[m_{+}]_{\alpha}^{l}&M_{R,\alpha\beta}\end{pmatrix}\begin{pmatrix}\nu_{L,l}\\\
N_{R}^{C,\beta}\end{pmatrix},$ (5)

where

$m_{\pm}=\frac{\upsilon}{\sqrt{2}}(h\pm\eta).$ (6)

From the above equation the mass matrix of the light and heavy neutrinos cane
written as,

$M=\begin{pmatrix}0&m_{-}\\\ m_{+}^{T}&M_{R}\end{pmatrix}.$ (7)

Further one can block diagonalize the mass matrix by a unitary transformation.
This would yield the mass matrix of the light neutrinos and is given by,

$m_{L}=-\frac{\upsilon^{2}}{2}(h_{+}^{T}M_{R}^{-1}h_{-}).$ (8)

It is interesting to note that this seesaw formula is a non-Hermitian one in
contrast to the usual cases. From eq.(8) the individual mass eigenvalues can
be found for physical neutrinos.

###  II.1 Case for two generation of neutrinos

For two generation $h$ and $\eta$ are $(2\times 2)$ complex matrices. Hence
there are total $16$ parameters which can be constrained from experimental
data. The individual neutrino mass eigenvalues for $N=2$ is given by

$m_{1(2)}=-\frac{\upsilon^{2}}{4}\left[{\rm
tr}h_{+}^{T}M_{R}^{-1}h_{-}-(+)\left(2{\rm
tr}\left(h_{+}^{T}M_{R}^{-1}h_{-}\right)^{2}-({\rm
tr}h_{+}^{T}M_{R}^{-1}h_{-})^{2}\right)^{1/2}\right],$ (9)

The non-Hermitian theory would account for a massless spectrum if

$h=\pm\eta.$ (10)

But one can obtain a non-zero mass for neutrinos when,

${\rm det}h_{+}^{T}M_{R}^{-1}h_{-}=0\quad\implies\quad{\rm
tr}\left(h_{+}^{T}M_{R}^{-1}h_{-}\right)^{2}=({\rm
tr}h_{+}^{T}M_{R}^{-1}h_{-})^{2}.$ (11)

With this condition we obtain the spectrum

$m_{1}=0,\quad\quad m_{2}=-\frac{\upsilon^{2}}{2}{\rm
tr}h_{+}^{T}M_{R}^{-1}h_{-}.$ (12)

The physical neutrino mass are real i.e. for $M_{2}$ to be real we require

${\rm Im~{}tr}~{}h_{+}^{T}M_{R}^{-1}h_{-}=0;\quad{\rm
Re\,tr}(h_{+}^{T}M_{R}^{-1}h_{-})\neq 0,$ (13)

and we can restore a massless spectrum again if the following condition is
met.

${\rm Re~{}tr}~{}h_{+}^{T}M_{R}^{-1}h_{-}=0.$ (14)

For two generation of neutrinos there are total $16$ parameters in the complex
valued $2\times 2$ Yukawa matrices. The constraints provided by eq.s.(13) and
(14) are much weaker than that given in eq.(10) in determining the Yukawa
matrices. However neutrino oscillation data will be useful in provided
observational constraints on $h$ and $\eta$.

###  II.2 Case for three generation of neutrinos

In order to verify the results of experiments related to neutrino
phenomenology, it is necessary to calculate neutrino masses for three
generations of neutrinos. In this case $h$ and $\eta$ are $(3\times 3)$
complex matrices having $18$ real parameters each. The characteristic equation
in diagonalizing the mass matrix given by eq.(8 ) for $N=3$ is given by,

$\displaystyle\left({\rm tr}(m_{+}^{T}M_{R}^{-1}m_{-}+\lambda
I)\right)^{3}-3{\rm tr}(m_{+}^{T}M_{R}^{-1}m_{-}+\lambda I){\rm
tr}\left(m_{+}^{T}M_{R}^{-1}m_{-}+\lambda I\right)^{2}$ $\displaystyle+2{\rm
tr}\left(m_{+}^{T}M_{R}^{-1}m_{-}+\lambda I\right)^{3}=0,$ (15)

where $m_{\pm}$ is given in eq.(6). After simplification the mass eigenvalues
are given by,

$\displaystyle m_{1}$ $\displaystyle=$
$\displaystyle-\frac{a}{3}-\frac{2^{1/3}(a^{2}/2-3b/2)}{3f}+\frac{f}{3\times
2^{1/3}},$ $\displaystyle m_{2}$ $\displaystyle=$
$\displaystyle-\frac{a}{3}+\frac{(1+i\sqrt{3})(a^{2}/2-3b/2)}{3\times
2^{2/3}f}-\frac{(1-i\sqrt{3})f}{6\times 2^{1/3}},$ $\displaystyle m_{3}$
$\displaystyle=$
$\displaystyle-\frac{a}{3}+\frac{(1-i\sqrt{3})(a^{2}/2-3b/2)}{3\times
2^{2/3}f}-\frac{(1+i\sqrt{3})f}{6\times 2^{1/3}},$ (16)

where

$\displaystyle f$ $\displaystyle=$
$\displaystyle\left[-2a^{3}+9ab+\sqrt{4(a^{2}/2-3b/2)^{3}+(-2a^{3}+9ab-9c)^{2}}-9c\right]^{1/3},$
$\displaystyle a$ $\displaystyle=$ $\displaystyle{\rm
tr}\left(m_{+}^{T}M_{R}^{-1}m_{-}\right),$ $\displaystyle b$ $\displaystyle=$
$\displaystyle{\rm tr}\left(m_{+}^{T}M_{R}^{-1}m_{-}\right)^{2},$
$\displaystyle c$ $\displaystyle=$ $\displaystyle{\rm
tr}\left(m_{+}^{T}M_{R}^{-1}m_{-}\right)^{3}.$ (17)

From eq.(16) the sum of three neutrino masses can be verified to be,

$\sum_{i}m_{i}=-a=-{\rm tr}\left(m_{+}^{T}M_{R}^{-1}m_{-}\right),$ (18)

which can be compared with case $N=2$ given in eq.(9). Also we can have a
massless spectrum of light neutrinos for $h=\pm\eta$ as discussed in the
previous subsection.

In eq.(16) the first term is equal for all three mass eigenvalues,
-$\frac{1}{3}{\rm tr}m_{+}^{T}M_{R}^{-1}m_{-}$. The mass eigenvalues arising
from the non-Hermitian theory can account for both degenerate and hierarchical
spectrum by adjusting the parameters in $h$ and $\eta$. The masses are
degenerate, $m_{1}=m_{2}=m_{3}$ for

$f=2^{1/3}\sqrt{a^{2}/2-3b/2},$ (19)

$f$ can not be zero, else masses will be undetermined. In order to comply with
neutrino oscillation data the tiny mass squared difference can be calculated
in the leading order to be ,

$\displaystyle\Delta m_{ij}^{2}$ $\displaystyle\sim$
$\displaystyle\mathcal{O}({\rm
tr}~{}m_{+}^{T}M_{R}^{-1}m_{-})^{2}\sim\mathcal{O}\left(\frac{\upsilon^{4}}{4}({\rm
tr}~{}h_{+}^{T}M_{R}^{-1}h_{-})^{2}\right)$ (20) $\displaystyle\sim$
$\displaystyle\mathcal{O}\left(\frac{\upsilon^{4}}{4}\left({\rm
tr}~{}\left(h^{T}M_{R}^{-1}h-\eta^{T}M_{R}^{-1}\eta+\eta^{T}M_{R}^{-1}h-h^{T}M_{R}^{-1}\eta\right)\right)^{2}\right)$

The neutrino oscillation data can be used to constrain the parameters of $h$
and $\eta$. For example using the order of magnitude of atmospheric neutrino
mass squared difference $\sim\mathcal{O}(10^{-3})~{}{\rm eV}^{2}$ and using
$\upsilon\simeq 246~{}$GeV we get,

$\mathcal{O}\left({\rm
tr}~{}\left(h^{T}M_{R}^{-1}h-\eta^{T}M_{R}^{-1}\eta+\eta^{T}M_{R}^{-1}h-h^{T}M_{R}^{-1}\eta\right)\right)^{2}\sim
10^{-3}\times\frac{4}{\upsilon^{4}}{\rm eV}^{-2}\sim\mathcal{O}(10^{-24}){\rm
eV}^{-2}$ (21)

This indicates that the parameters of $h$ and $\eta$ must accommodate mutual
cancellation among themselves in order to be consistent with above condition.
It is interesting to note that the parameters are independent of the choice of
the scale of $M_{R}$ as identified by Alexandre et al. (2015). This opens up a
new possibility for low energy seesaw scales. Also, it may have interesting
implications in lepton flavor violation scenario in the context of Type-I
seesaw.

##  III Constraints from neutrino mass observables

In this section, we discuss different experimental results related to neutrino
mass observables and their possible connection with non-Hermitian parameters
discussed in the previous section. The light neutrino mass matrix, $m_{\nu}$
is diagonalized by a unitary matrix $U$,

${\rm Diag}(m_{1},m_{2},m_{3})=U^{T}m_{\nu}U,$ (22)

where $m_{i}$’s are the three light absolute neutrino masses, $U$ is the
Pontecorvo-Maki-Nakagawa-Sakata (PMNS) unitary matrix given by,

$U=\begin{pmatrix}c_{12}c_{13}&s_{12}c_{13}&s_{13}e^{-i\delta}\\\
-s_{12}c_{23}-c_{12}s_{23}s_{13}e^{i\delta}&c_{12}c_{23}-s_{12}s_{23}s_{13}e^{i\delta}&s_{23}c_{13}\\\
s_{12}s_{23}-c_{12}c_{23}s_{13}e^{i\delta}&-c_{12}s_{23}-s_{12}c_{23}s_{13}e^{i\delta}&c_{23}c_{13}\end{pmatrix}P,$
(23)

where $c_{ij}=\cos\theta_{ij},s_{ij}=\sin\theta_{ij},\theta_{ij}$’s are flavor
mixing angles, $i,j=1,2,3$, and $P$ is the diagonal matrix that contains the
Majorana phases and is given by,

$P={\rm diag}(1,e^{i\alpha},e^{i\beta}).$ (24)

The neutrino oscillation experiments (solar and atmospheric) are sensitive to
the angles $\theta_{12},\theta_{23}$ and the angle $\theta_{13}$ is limited by
reactor experiments. The information on Dirac CP phase, $\delta$ comes from
long baseline experiments. The flavor oscillation experiments rather can
determine the mass squared differences; $\Delta m^{2}_{21}$ and $|\Delta
m^{2}_{13}|$, where $\Delta m^{2}_{ij}=m^{2}_{i}-m^{2}_{j}$. For neutrino
masses that follow normal ordering, the results suggest that $m_{1}\sim
0,m_{2}\sim\Delta m^{2}_{21},m_{3}\sim\Delta m^{2}_{31}$. And $m_{3}\sim
0,m_{2}\sim\Delta m^{2}_{13},m_{1}\sim\Delta m^{2}_{21}$ if inverted ordering
is followed. However for degenerate neutrino masses $m_{1}\sim m_{2}\sim
m_{3}$, the oscillation experiments can not determine the absolute mass
scales.

Other than the oscillation experiments there are three and complementary
different ways of measuring three mass eigenvalues $m_{1},m_{2}$ and $m_{3}$.

  * •

Kurie-plot experiments:
These are spectrometer experiments where the external source of beta emitters;
e.g. tritium are used. The energy distribution of electrons in a beta decay
process is sensitive to non-zero neutrino mass. The distribution is sensitive
to incoherent sum of neutrino masses (no cancellation due to phases),

$m_{\beta}=\sqrt{\sum|U_{ei}|^{2}m_{i}^{2}}.$ (25)

The upper bound on $m_{\beta}\leq 2.3$ eV at $95\%$ C.L. comes from Mainz
Kraus et al. (2005) in Tritium beta decay. The KATRIN experiment is expected
to modify the bound by an order of magnitude, $m_{\beta}=0.2$ eV at $90$⁒ C.L.
Bonn et al. (2011).

  * •

Cosmological Observations:
The interplay between cosmology and particle physics has opened up the
possibility to constrain neutrino mass from cosmological observations. But
these observations are only sensitive to sum of three neutrino masses,
$\sum_{i}m_{i}$. The combined constraints from cosmic microwave background
(CMB) experiments, large scale structure (LSS) surveys, Type-Ia supernovae and
other provide the current upper bound on the absolute neutrino mass is
approximately Hannestad (2010),

$\sum_{i}m_{i}\leq 0.5\,{\rm eV}.$ (26)

Further with the Planck satellite Ade et al. (2014) it would be possible to
limit the combined neutrino masses as low as $0.1\,{\rm eV}$ Hannestad (2006).
Further Planck 2015 results Ade et al. (2016) have analyzed the sum of
neutrino masses to be,

$\sum_{i}m_{i}\leq 0.23\,{\rm eV}.$ (27)

  * •

Neutrinoless double beta decay:
The Majorana nature of neutrinos can be probed through neutrinoless double
beta decay experiments because the decay process violates lepton number
conservation by two units. The measured half-life of neutrinoless double beta
decay in 76Ge has been reported to be $T_{1/2}^{0\nu}\sim 10^{25}$ years
Klapdor-Kleingrothaus et al. (2001, 2004); Klapdor-Kleingrothaus (2005).
Assuming light neutrino exchange being responsible for neutrinoless double
beta decay, lifetime of the decay is inversely proportional to the square of
the effective masses of the neutrinos given by a coherent sum,

$\langle m\rangle=|\sum U_{ei}^{2}m_{i}|.$ (28)

So the measured half life in neutrinoless mode of decay translates into the
bound on the effective masses of neutrinos. Depending on the uncertainty in
the nuclear matrix element the upper limit on $\langle m\rangle$ is deduced is
around $0.6$ eV signaling degenerate neutrino masses Klapdor-Kleingrothaus
(2005). This bound will improve considerably with help of future experiments.
From eq.(28) the maximum value of the effective mass can be expressed as,

$\langle m\rangle^{\rm max}=\sum|U_{ei}|^{2}m_{i}.$ (29)

In the above approximation we choose all Majorana phases to be zero Rodejohann
(2010).

We now work towards using the above three neutrino mass observables in getting
constraints on non-Hermitian Yukawa couplings as discussed in sec.(II). We
first consider the case which can lead to degenerate neutrino masses. For the
condition given in eq.(19) we have a common mass scale for neutrinos given by,

$m_{0}=-\frac{1}{3}{\rm
tr}~{}m_{+}^{T}M_{R}^{-1}m_{-}=-\frac{\upsilon^{2}}{6}{\rm
tr}~{}(h_{+}^{T}M_{R}^{-1}h_{-}).$ (30)

In the limit of degenerate neutrinos and assuming unitarity of $U$, different
observables in eqs.(25), (27) and eq.(29) can be related Rodejohann (2010)
with a common mass scale,

$m_{0}=m_{\beta}=\frac{\sum_{i}m_{i}}{3}=\langle m\rangle^{\rm max}.$ (31)

There will be corrections to the above relation relying on neutrino
oscillation experiments which give hint of non-zero mass splittingFarzan et
al. (2001); Farzan and Smirnov (2003); Rodejohann (2010). Taking $m_{0}$ as
the heaviest neutrino mass, so that $m_{3}=m_{0}$ for normal hierarchy and
$m_{2}=m_{0}$ for inverted hierarchy and by defining two quantities,

$\displaystyle r_{\odot}$ $\displaystyle=$ $\displaystyle\frac{\Delta
m^{2}_{\rm sol}}{2m_{0}},$ $\displaystyle r_{A}$ $\displaystyle=$
$\displaystyle\frac{\Delta m^{2}_{\rm atm}}{2m_{0}},$ (32)

the individual mass eigenvalues up to leading order would change say for
normal ordering as

$m_{3}=m_{0},\quad m_{2}\simeq m_{0}(1-r_{A}-\frac{1}{2}r_{A}^{2}),\quad
m_{1}\simeq m_{0}(1-r_{A}-\frac{1}{2}r_{A}^{2}-r_{\odot}).$ (33)

Using this parametrization, the three mass observables can be expressed as,

$\displaystyle m_{\beta}$ $\displaystyle\simeq$ $\displaystyle
m_{0}\left(1-c_{13}^{2}r_{A}-\frac{1}{2}c_{13}^{4}r_{A}^{2}-c_{12}^{2}c_{13}^{2}r_{\odot}\right),$
$\displaystyle\langle m\rangle^{\rm max}$ $\displaystyle\simeq$ $\displaystyle
m_{\beta},$ $\displaystyle\Sigma$ $\displaystyle\simeq$ $\displaystyle
3m_{0}\left(1-\frac{2}{3}r_{A}-\frac{1}{3}r_{A}^{2}-\frac{1}{3}r_{\odot}\right).$
(34)

Their difference is given by,

$\displaystyle m_{\beta}-\langle m\rangle^{\rm max}\simeq m_{0}A_{1},$
$\displaystyle\frac{1}{3}\Sigma-m_{\beta}\simeq\frac{1}{3}\Sigma-\langle
m\rangle^{\rm max}\simeq\frac{m_{0}}{6}A_{2},$ (35)

where

$\displaystyle A_{1}$ $\displaystyle=$
$\displaystyle\left(\frac{1}{4}\sin^{2}2\theta_{12}r_{\odot}^{2}+|U_{e3}|^{2}c_{12}^{2}r_{\odot}r_{A}+\frac{1}{2}|U_{e3}|^{2}r_{A}^{2}\right),$
$\displaystyle A_{2}$ $\displaystyle=$ $\displaystyle\left((3\cos
2\theta_{13}-1)r_{A}+r_{A}^{2}+(1+3\cos 2\theta_{12})r_{\odot}\right).$ (36)

Combining the results obtained in eq.s(30) and (35)

$\displaystyle{\rm tr}~{}(h_{+}^{T}M_{R}^{-1}h_{-})$ $\displaystyle=$
$\displaystyle\frac{6}{\upsilon^{2}A_{1}}\left(m_{\beta}-\langle m\rangle^{\rm
max}\right),$ (37) $\displaystyle{\rm tr}~{}(h_{+}^{T}M_{R}^{-1}h_{-})$
$\displaystyle=$
$\displaystyle\frac{1}{\upsilon^{2}A_{2}}\left(\frac{1}{3}\Sigma-
m_{\beta}\right).$ (38)

In eq.s (37) and (38), the terms in $A_{1}$ and $A_{2}$ depend on oscillation
parameters and the quantities in the parentheses depend of direct observables
of neutrino masses. So the non-Hermitian parameters $h$ and $\eta$ can be
constrained from the combination of observables. The mass and mixing angle
observables being real,

${\rm Im\,tr}~{}(h_{+}^{T}M_{R}^{-1}h_{-})=0.$ (39)

Using neutrino oscillation data Esteban et al. (2017), taking $m_{0}=0.3$ eV
in the ratios defined in eq.(32) and using experimental data available for
$m_{\beta},\langle m\rangle^{\rm max}$ and $\sum m_{i}$, we find,

$\displaystyle{\rm Re\,tr}~{}(h_{+}^{T}M_{R}^{-1}h_{-})$ $\displaystyle\sim$
$\displaystyle{\rm
Re\,tr}~{}\left(h^{T}M_{R}^{-1}h-\eta^{T}M_{R}^{-1}\eta+\eta^{T}M_{R}^{-1}h-h^{T}M_{R}^{-1}\eta\right)$
(40) $\displaystyle\sim$ $\displaystyle\mathcal{O}(10^{-14}){\rm eV}^{-1},$

where we have used following oscillation data Esteban et al. (2017),

$\displaystyle\sin^{2}\theta_{12}=0.306,\,\,\,\sin^{2}\theta_{23}=0.441,\,\,\,\sin^{2}\theta_{13}=0.02166,$
$\displaystyle\Delta m^{2}_{21}=7.50\times 10^{-5}{\rm eV}^{2},\,\,\,\Delta
m^{2}_{31}=2.524\times 10^{-3}{\rm eV}^{2}.$ (41)

The constraint obtained in eq.(40) agrees well with eq.s(14) and (21). It
would be interesting to explore the parameter space available for the
parameters of $h$ and $\eta$ using the constraints obtained above. But for
three generation of leptons the number of complex parameters are way larger
than the number of constraints. So it will be useful to impose some symmetry
like $A_{4}$, $\mu-\tau$ or cyclic symmetry Adhikary et al. (2013) to explore
the parameter space.

##  IV Leptogenesis

Leptogenesis Fukugita and Yanagida (1986) is an attractive scenario which can
generate baryon asymmetry of the Universe (BAU) through out of equilibrium
decay of heavy right-handed Majorana neutrinos. Thus it creates a bridge
between seesaw mechanism and BAU. The baryon asymmetry from leptogenesis can
be approximated by Buchmuller et al. (2003),

$\eta_{B}(=6.11\pm 0.19)\times 10^{-10}\simeq 0.96\times
10^{-2}\epsilon_{1}\kappa,$ (42)

where $k$ is the efficiency factor calculated by solving the Boltzman
equation. $\epsilon_{1}$ is the CP violating decay asymmetry stemming from the
interference between tree level and one loop contributions in the decay of
$N_{1}$, the lightest of the three heavy Majorana neutrinos. In the generic
realizations of Type-I seesaw scenarios the decay asymmetry is given by,

$\epsilon_{1}\simeq\frac{1}{8\pi}\frac{1}{\left(h_{\nu}^{\dagger}h_{\nu}\right)_{11}}\sum_{j=2,3}{\rm
Im}(h_{\nu}^{\dagger}h_{\nu})^{2}_{1j}\left(f\left(\frac{M_{j}^{2}}{M_{1}^{2}}\right)+g\left(\frac{M_{j}^{2}}{M_{1}^{2}}\right)\right),$
(43)

where $h_{\nu}$ and $h_{\nu}^{\dagger}$ are associated with
$N_{1R}\longrightarrow l\,H$ and $N_{1R}\longrightarrow l^{c}\,H^{c}$ vertices
respectively. $f$ comes from vertex Fukugita and Yanagida (1986); Luty (1992);
Plumacher (1997), $g$ comes from self-energy Flanz et al. (1995); Covi et al.
(1996); Pilaftsis (1997); Buchmuller and Plumacher (1998) contributions. The
fraction $M_{j}^{2}/M_{1}^{2}$ is the ratio of the mass squared of right
handed heavy Majorana neutrinos. For a strong hierarchy among the Majorana
mass scales $M_{1}$ and $M_{2},M_{3}$, the ratios $M_{j}^{2}/M_{1}^{2}\gg 1$
and the functions $f$ and $g$ can be approximated to be Pascoli et al. (2003)

$f\left(\frac{M_{j}^{2}}{M_{1}^{2}}\right)+g\left(\frac{M_{j}^{2}}{M_{1}^{2}}\right)\simeq-3/2\left(\frac{M_{j}}{M_{1}}\right).$
(44)

The decay asymmetry, $\epsilon_{1}$ depends on the Majorana masses and
imaginary part of combination of Yukawa coupling matrix,
$(h_{\nu}^{\dagger}h_{\nu})^{2}$. So the Dirac Yukawa coupling, $h_{\nu}$ must
be complex for $\epsilon_{1}\neq 0$. In generic realizations of seesaw models
$h_{\nu}$ contains most of the unknown parameters. So, one generally adopts
different kind of parametrization schemes for $h_{\nu}$ like Casas-Ibarra
parametrization Casas and Ibarra (2001), biunitary parametrization Pascoli et
al. (2003) to generate leptonic phases in $\epsilon_{1}$ which can lead to
generation of adequate baryon asymmetry through leptogenesis. Coming to the
non-Hermitian version of Type-I seesaw mechanism the asymmetry produced
because of the decay of the lightest of the three right handed Majorana
neutrinos would be,

$\displaystyle\epsilon_{1}$ $\displaystyle\propto$
$\displaystyle\sum_{j=2,3}{\rm
Im}(h^{\dagger}_{+}h_{-})_{1j}^{2}\,\,\left(\frac{M_{j}}{M_{1}}\right)\approx\sum_{j=2,3}{\rm
Im}(|h|^{2}+|\eta|^{2}-2i{\rm
Im}(h^{\dagger}\eta))^{2}_{1j}\,\left(\frac{M_{j}}{M_{1}}\right)$ (45)
$\displaystyle\approx$ $\displaystyle{\rm Im}(|h|^{2}+|\eta|^{2}-2i{\rm
Im}(h^{\dagger}\eta))^{2}_{12}\,\left(\frac{M_{2}}{M_{1}}\right)+{\rm
Im}(|h|^{2}+|\eta|^{2}-2i{\rm
Im}(h^{\dagger}\eta))^{2}_{13}\,\left(\frac{M_{3}}{M_{1}}\right)$ (46)

Since the parameters of $h$ and $\eta$ are in general complex, more phases
enter into the elements of $(h^{\dagger}_{+}h_{-})^{2}$. So, the above terms
can provide an additional source of CP asymmetry for required leptogenesis. A
proper parametrization of $h$ and $\eta$ would establish the given argument
which is a work under progress.

##  V Lepton flavor Violation

The experimental evidence of flavor oscillation among neutrinos not only
suggest the massive nature of neutrinos but also mixing among lepton families
which can lead to lepton flavor violation. The MEG experiment has reported the
upper bound on the branching ratio of $\mu\longrightarrow e\gamma$, ${\rm
BR}(\mu\longrightarrow e\gamma)<4.2\times 10^{-13}$ at $90\%$ C.L. and a
future sensitivity of $4\times 10^{-14}$ Mori (2017). The minimal extension of
the SM by adding right-handed neutrinos induces LFV, but it is well known that
due to GIM cancellation Glashow et al. (1970) the branching ratio is about
$40$ orders of magnitude less than present-day predicted value Petcov (1977).
But considering the Majorana nature of right handed singlet neutrinos tiny
neutrino mass is generated via Type-I seesaw mechanism and also it induces
mixing between left handed and right handed neutrinos. As a consequence of
which the the unitary matrix which diagonalizes the neutrino mass matrix
$m_{\nu}$ does not coincide with PMNS unitary matrix and is no longer unitary
and is given byBroncano et al. (2003),

${\mathcal{U}}=\left(1-\frac{\upsilon^{2}}{2}h_{\nu}^{\dagger}m_{R}^{-2}h_{\nu}\right)U,$
(47)

The branching ratio is now given by Calibbi and Signorelli (2018).

${\rm BR}(\mu\longrightarrow
e\gamma)=\frac{3\alpha}{32\pi}\frac{\left|\sum_{i}{\mathcal{U}}_{\mu
i}{\mathcal{U}}^{*}_{ei}F(x_{k})\right|^{2}}{({\mathcal{U}}{\mathcal{U}}^{\dagger})_{\mu\mu}({\mathcal{U}}{\mathcal{U}}^{\dagger})_{ee}},$
(48)

where

$F(x_{i})=\frac{10}{3}-x_{i}+{\mathcal{O}}(x_{k}^{2});\,\,x_{i}=\frac{m_{i}^{2}}{M_{W}^{2}},$
(49)

where $m_{i}$’s are the light neutrino masses and $M_{W}$ is weak W-boson
mass.

Similarly in the non-Hermitian extension as can be seen in eq.s (5) and (7)
due to mixing among left-handed and right-handed neutrino fields the matrix
that diagonalizes the neutrino mass matrix is no more unitary. Following
Broncano et al. (2003) we find the diagonalizing matrix is given by,

${\mathcal{U}}=\left(1-\frac{\upsilon^{2}}{2}h_{-}M_{R}^{-2}h_{+}\right)U.$
(50)

In eq.(49) the first term of $F(x_{i})$ is not suppressed by small neutrino
mass and hence dominates for finite deviation of ${\mathcal{U}}$ from
unitarity. In order to enhance the LFV rates close to experimentally
observable limit, it requires $M_{R}$ to be low and neutrino Yukawa coupling
$h_{+}$ and $h_{-}$ to be large. In general implementation of seesaw
mechanisms these two requirements are not compatible with smallness of the
neutrino masses. In the non-Hermitian extension of the SM, there is a
possibility to have low $M_{R}$ and set conditions for Yukawas to be of
magnitude ${\mathcal{O}}(1)$ as can be seen from constraints obtained in eq.s
(21) and (40).

##  VI Conclusion

Non-hermitian extension of Quantum Mechanics has gathered considerable
attention in the recent past. It allows for a wide class of Lagrangians or
Hamiltonians for study which might have been rejected on the basis of
hermiticity. In this context, the non-hermitian version of QED has been
pursued Bender et al. (2005), in particular, its application in neutrino
physics Alexandre et al. (2015). In the usual hermitian version of the SM and
in the neutrino sector the Yukawa coupling of neutrinos with the SM leptons
appears as $h_{\nu}$ and it hermitian conjugate $h_{\nu}^{\dagger}$ which
ensures the mass eigenvalues are real. In the non-hermitian context, this
requirement is relaxed while keeping the mass eigenvalues to be real. The
Yukawa couplings in this case are $h_{\pm}=h\pm\eta$, where $h$ and $\eta$ are
complex matrices whose entries are unknown just like $h_{\nu}$ and
$h_{\nu}^{\dagger}$ and $h_{+}^{\dagger}\neq h_{-}$. For $N$ generation of
neutrinos, $h_{\pm}$ have $2N^{2}$ parameters which can be constrained from
experimental observations related to neutrinos. Here we have calculated the
non-Hermitian mass matrix for neutrinos for $3$ generation case and have
identified certain constraints which can be helpful in parameterizing $h$ and
$\eta$. Also, the fine-tuning between the parameters of $h$ and $\eta$ can
account for both hierarchical as well as degenerate neutrinos. The requirement
of the smallness of neutrino mass also supports a low scale of $M_{R}$ which
has potential application for low scale seesaw. And hence it is suitable for
producing sizable branching ratio for charged lepton flavor violation
processes. The Yukawa matrices $h$ and $\eta$ being complex can provide an
additional source of CP violation for Leptogenesis. But the number of unknown
parameters being more than the experimental constraints, it will be helpful
parametrize the matrices by imposing certain symmetry like $A_{4}$, cyclic
symmetry and see the parameter space available for the non-Hermitian version
of the neutrino sector Adhikary et al. (2013). The new couplings can also be
constrained from nonunitarity restriction of lepton mixing matrix Antusch et
al. (2006). A detailed study with proper parametrization would soon be
following this work.

The massive nature of neutrinos and flavor mixing among leptons is established
by the experiments which rely on the phenomenon of neutrino oscillation.
Although the latter phenomenon is considered to be the leading mechanism,
there may exist sub-leading effects and are known as non-standard interactions
(NSI) Ohlsson (2013). There may be effects from new physics beyond the SM in
the form of new couplings involving neutrinos such as supersymmetry, left-
right symmetry, models of extra dimensions etc., which give rise to NSIs. In
summary, the non-Hermitian version of the SM opens up a new area of study as a
physics of non-standard interactions in the neutrino sector.

##  VII Acknowledgement

This work is supported by Science and Engineering Research Board (SERB),
Department of Spence and Technology (DST), India grant no. YSS/$2015/000811$.
SM acknowledges the useful discussions with Amit Rai.

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# KazSAnDRA:
Kazakh Sentiment Analysis Dataset of Reviews and Attitudes

###### Abstract

This paper presents KazSAnDRA, a dataset developed for Kazakh sentiment
analysis that is the first and largest publicly available dataset of its kind.
KazSAnDRA comprises an extensive collection of 180,064 reviews obtained from
various sources and includes numerical ratings ranging from 1 to 5, providing
a quantitative representation of customer attitudes. The study also pursued
the automation of Kazakh sentiment classification through the development and
evaluation of four machine learning models trained for both polarity
classification and score classification. Experimental analysis included
evaluation of the results considering both balanced and imbalanced scenarios.
The most successful model attained an F1-score of 0.81 for polarity
classification and 0.39 for score classification on the test sets. The dataset
and fine-tuned models are open access and available for download under the
Creative Commons Attribution 4.0 International License (CC BY 4.0) through our
GitHub repository.

Keywords: BERT, dataset, Kazakh, KazSAnDRA, polarity, review, sentiment
analysis, text classification

languageresource

KazSAnDRA:
Kazakh Sentiment Analysis Dataset of Reviews and Attitudes

Rustem Yeshpanov, Huseyin Atakan Varol
---
Institute of Smart Systems and Artificial Intelligence
Nazarbayev University, Astana, Kazakhstan
{rustem.yeshpanov<EMAIL_ADDRESS>

Abstract content

## 1\. Introduction

In natural language processing, sentiment analysis is a widely employed text
classification task that involves extracting the sentiment expressed by
individuals towards a variety of entities that include products, services,
organisations, individuals, issues, events, and topics together with their
respective attributes (Liu, 2012). In this context, sentiment represents the
positive, negative, or neutral attitude of individuals conveyed through the
extracted textual content (Jurafsky and Martin, 2009). Sentiment analysis
demonstrates broad applicability across various domains, including marketing
(Fang and Zhan, 2015), social media (Go et al., 2009), healthcare (Greaves et
al., 2013), finance (Abraham et al., 2018), and politics (Abercrombie and
Batista-Navarro, 2020), among others.

Although research efforts in sentiment analysis for lower-resourced languages
are gradually gaining momentum (Mamta et al., 2022; Le et al., 2016; Gangula
and Mamidi, 2018), the English language continues to dominate as the primary
focus of current research in this area (Zhang et al., 2018). This preference
can be attributed to the abundant availability of linguistic resources, such
as lexica, corpora, and dictionaries specifically tailored to English (Medhat
et al., 2014).

With respect to Kazakh, an agglutinative Turkic language generally considered
lower-resourced, research in the field of sentiment analysis has only recently
come to the fore (Narynov and Zharmagambetov, 2016). Despite its importance,
the literature dealing with sentiment analysis in Kazakh remains limited and
includes only a few academic papers published within eight years. Furthermore,
there is a complete absence of publicly accessible Kazakh sentiment analysis
datasets, whether small or large, further underscoring the challenges in this
field.

Our study aims to address the existing gaps in this field and contribute to
its further advancement. Specifically, we present a dataset consisting of
customer reviews in Kazakh, accompanied by corresponding attitude scores. The
dataset comprises a total of 180,064 reviews collected from four domains.

In the context of Kazakhstan, it is crucial to acknowledge the prevalent
practice of code-switching between the Kazakh and Russian languages, as well
as the ongoing shift from the Cyrillic to the Latin script. Consequently,
Kazakh reviews may exhibit a combination of Cyrillic and Latin characters,
incorporate a mixture of Russian and Kazakh vocabulary, or be solely recorded
in the Cyrillic script with Russian characters substituting Kazakh ones. The
dataset we present includes reviews containing both exclusive Kazakh
vocabulary and words from other languages (Russian, English, and Arabic),
making it the largest dataset available for Kazakh sentiment analysis.

We also developed and evaluated four machine learning models to automate the
classification of Kazakh sentiments. The highest F1-score on the test sets was
0.81 for polarity classification and 0.39 for score classification.

The subsequent sections of this paper are structured as follows: Section 2
presents a review of existing research in Kazakh sentiment analysis. Section 3
is devoted to the detailing the process of developing the dataset. Section 4
delves into the aspects of data pre-processing and partitioning, the score
resampling techniques, the sentiment classification tasks, the models
employed, the experimental design, and the metrics used for evaluation, and
the corresponding results. Section 5 focuses on a thorough discussion of the
results. Section 6 provides a conclusive summary and final remarks for the
paper.

## 2\. Related Work

In recent years, remarkable progress has been made in addressing the limited
resources available for the Kazakh language. Mussakhojayeva et al. have made
significant contributions to this endeavour by presenting a text-to-speech
synthesis corpus comprising a substantial 271 hours of speech data
(Mussakhojayeva et al., 2022b), as well as introducing the first industrial-
scale open-source Kazakh speech corpus for automatic speech recognition
(Mussakhojayeva et al., 2022a). The latter corpus consists of 1,128 hours of
transcribed audio data, comprising over 520 thousand utterances. In a separate
study, Yeshpanov et al. (2022) made a noteworthy contribution to the field of
Kazakh natural language processing by introducing the largest dataset for
Kazakh named entity recognition. This dataset comprises 112,702 sentences and
136,333 annotations for 25 distinct entity classes. In addition, Toiganbayeva
et al. (2022) proposed an extensive dataset specifically tailored for
handwritten text recognition in Kazakh. This dataset includes 3,000
handwritten exam papers, with 140,335 segmented images and 922,010 symbols.

While the collective contributions to various speech and language processing
tasks for Kazakh have undeniably enriched the available resources, thus
creating new opportunities for research and development, progress in Kazakh
sentiment analysis research has been comparatively slower. This discrepancy
can be attributed to the limited availability of dedicated resources in this
area.

In the earliest work found on Kazakh sentiment analysis (Narynov and
Zharmagambetov, 2016), the researchers curated a dataset of 30,000 Russian
news articles that were manually labelled. In addition, they labelled 10,000
Kazakh news articles, of which 3,021 were positive, 2,548 negative, and 4,431
neutral, to train a sentiment classifier. While the performance of the
classifier for Russian was 86.3%, it yielded relatively lower results for
Kazakh, with an accuracy of 72.8%. This result could possibly be attributed to
the limited size of the training dataset and the absence of lemmatisation,
which may have affected the overall performance.

In Abdullin and Ivanov (2017), the research aimed to analyse opinions in short
texts written in several languages, with a specific focus on English, Russian,
and Kazakh (Go et al., 2009; Rubtsova and Zagorulko, 2014). The authors
presented an approach that utilised a deep recurrent neural network and
bilingual word embeddings to effectively capture semantic features between
words across these languages. By conducting sentiment analysis experiments on
language pairs such as English-Russian and Russian-Kazakh, the authors
achieved noteworthy performance, with a competitive accuracy rate of 72% for
Russian and a comparatively lower accuracy of 58% for Kazakh. While the
authors made the development codes available on their GitHub page for result
reproducibility, it is worth noting that the repository does not include the
Kazakh training data that were utilised.

In Yergesh et al. (2017), reviews of three hotels were collected from online
travel platforms. The authors employed fuzzy logic (Zadeh, 1996) for sentiment
analysis. However, it is important to acknowledge that the study does not
provide precise information about the number of reviews collected and the
accessibility of the data collected. In their later study (Yergesh et al.,
2019), the researchers presented an overview of the rule-based methods
employed in sentiment analysis and the approaches utilised to determine the
sentiment of Kazakh sentences by formalising morphological rules. To
facilitate the determination of text polarity, a dictionary of approximately
11,000 emotional Kazakh words and phrases was manually compiled and annotated
on a five-point scale [-2, 2]. In addition, semantic hypergraphs were used to
describe ontological models of the morphological rules of the Kazakh language.
As a result of this research, a morphological analyser was developed, enabling
the extraction of morphological information from texts. The authors reported
that they achieved a result of 83% using their rule-based method, which they
describe as “good”, although it is interesting to note that this result was
peculiarly compared to studies dedicated to sentiment analysis in Russian.

Bekmanova et al. (2019) developed a method for analysing Kazakh texts related
to terrorist threats. The research involved selecting social networks along
with specific foreign Internet resources that disseminate terrorist content.
Through this selection, a database was developed that comprised 1,200 entries.
This database facilitated the detection of more than 50 similar sites. It is
important to note, however, that access to the database is not possible.

In Mutanov et al. (2021), a dataset of news posts from the Kazakhstani media
space was collected, comprising texts labelled across three sentiment classes:
positive, negative, and neutral. The dataset includes 80,873 sentiment-
labelled texts in Russian and 15,933 in Kazakh, revised by graduate students
specialising in political science. While the paper describes in detail the
steps of data pre-processing and the classification methods employed, it does
not delve into the approach taken for news posts exhibiting multiple
polarities (e.g., “Controversial Policy Sparks Outrage and Support Among
Citizens”), nor does it shed light on the provision of classification
guidelines or the inter-annotator agreement. Additionally, while detailed
classification metrics and confusion matrices are presented for Russian texts,
analysis for Kazakh texts is notably absent.

In Gimadi (2021), the aim of the study was to collect a dataset of 3,000
Kazakh reviews from the Google Play Store. However, the rationale behind the
researcher’s decision to manually label each of the collected reviews and
subsequently compare the assigned scores with the original scores remains
unclear.

More recently, Rakhymzhanov (2022) attempted to develop a Kazakh slang
dictionary using a website111https://janasozdik.kz and its associated
Instagram page. The researcher utilised
BeautifulSoup222https://www.crummy.com/software/BeautifulSoup to collect slang
word information, but due to the recent creation of the website, data
availability was limited. This study breaks new ground in Kazakh sentiment
analysis, and while the referenced slang dictionary provides amusing
expressions, its practical usefulness as a reliable reference source can be
questioned due to their infrequent use among native Kazakh speakers.

Nurlybayeva et al. (2022) presented the construction of a bag-of-words model
(Zhang et al., 2010) for sentiment classification of restaurant reviews into
positive or negative categories. The researchers collected a dataset of 2,000
restaurant reviews from the 2GIS application website333https://www.2gis.kz for
analysis and model development. However, it should be noted that the dataset
used in this study is not publicly accessible.

The last study on Kazakh sentiment analysis that we discuss in this paper is
by Nugumanova et al. (2022), who applied pre-trained BERT (Devlin et al.,
2019) models, originally developed for multilingual and Turkish sentiment
analysis, to Kazakh due to the lack of large labelled datasets in this
language. The Kazakh dataset was collected from Facebook groups, a consumer
complaints website444https://zhalobikz.com, and the 2GIS website, with the
reviews manually labelled and transliterated. The training dataset was very
small (only 30 samples), but the experimental results showed that the
multilingual BERT model outperformed the Turkish BERT model.

From the literature reviewed, it follows that while substantial efforts have
been made in the fields of automatic speech recognition, text-to-speech
synthesis, image-to-text conversion, and named entity recognition for Kazakh,
resulting in extensive, high-quality and publicly available datasets, the same
level of generosity seems to be lacking when it comes to research specifically
focused on Kazakh sentiment analysis. In other words, the availability of
sentiment analysis datasets for Kazakh is currently non-existent or
significantly limited.

## 3\. Dataset Development

### 3.1. Domains

The source data for our dataset came from four domains: (1) digital mapping
and navigation services (hereafter Mapping), (2) online marketplaces
(hereafter Market), (3) an online library that serves as a source of books and
audiobooks in Kazakh (hereafter Bookstore), and (4) an online store for
Android devices that offers a diverse range of applications (hereafter
Appstore).

### 3.2. Data Collection

The dataset was collected over a one-year period, from September 2022 to
September 2023. Reviews from Mapping and Market were collected through manual
means, while a BeautifulSoup script was employed for the acquisition of
reviews from Bookstore. The use of the Python package google-play-
scraper555https://pypi.org/project/google-play-scraper facilitated the
collection of reviews from Appstore.

All reviews were manually checked by a group of native Kazakh speakers. During
the review process, it came to light that reviews contained recurrent
instances of inappropriate content. However, in order to preserve the
authenticity and integrity of the reviews, no alterations or removals were
made to this content.

As a result, 8,897 reviews were obtained from Mapping, covering 407
institutions. Market provided a considerable portion of 30,289 reviews,
encompassing 8,418 unique items. Bookstore provided 5,805 reviews, comprising
3,792 audiobook reviews and 2,013 book reviews, resulting in a total of 1,026
unique audiobooks and books. Finally, Appstore provided 135,073 unique reviews
of 1,759 Android applications and games. Of the users contributing to these
reviews, 47,887 had a unique username, while the remaining 31,490 users
remained anonymous.

Each review was accompanied by a numerical rating from 1 to 5, providing a
measurable representation of individuals’ attitudes. Consequently, we named
the dataset KazSAnDRA /kәsændrә/, an acronym for the Kazakh Sentiment Analysis
Dataset of Reviews and Attitudes, reflecting its purpose and content. The
total number of reviews collected was 180,064. Table 1 provides information
about the distribution of reviews across different scores and domains.

Domain | Score | Total
---|---|---
1 | 2 | 3 | 4 | 5
Appstore | 22,547 | 4,202 | 5,758 | 7,949 | 94,617 | 135,073
Bookstore | 686 | 107 | 222 | 368 | 4,422 | 5,805
Mapping | 959 | 270 | 369 | 525 | 6,774 | 8,897
Market | 1,043 | 350 | 913 | 2,775 | 25,208 | 30,289
Total | 25,235 | 4,929 | 7,262 | 11,617 | 131,021 | 180,064
Table 1: Domain and score statistics

### 3.3. Variations of Kazakh Reviews

In Kazakhstan, code-switching between the Kazakh and Russian languages has
been observed (Pavlenko, 2008), alongside an ongoing shift from the Cyrillic
to the Latin script. Consequently, reviews regarded as Kazakh can take
different forms: (a) solely Kazakh words written in the Kazakh Cyrillic
script, (b) Kazakh words written in Latin script, (c) a combination of
Cyrillic and Latin characters, (d) a mixture of Russian and Kazakh words, or
(e) a text entirely in the Cyrillic script with Russian characters replacing
Kazakh characters, among other possible variants. Table 3 provides examples of
actual reviews, demonstrating their appropriate representation in accordance
with Kazakh spelling rules and the use of the Kazakh Cyrillic script,
accompanied by their correct form in English. Table 2 shows the number of
reviews with percentage of Cyrillic and Latin characters per review.

Character | 0–25% | 26–50% | 51–75% | 76–100%
---|---|---|---|---
Cyrillic | 67 | 399 | 1,694 | 170,233
Latin | 5,374 | 1,114 | 246 | 2,617
Table 2: Review counts by Cyrillic and Latin character percentages | Actual review | Correct form (Kazakh) | Correct form (English)
---|---|---|---
a | керемет кітап | керемет кітап | a wonderful book
b | keremet | керемет | wonderful
c | jok кітап | кітап жоқ | no books
d | Осы приложениеге көп рахмет! | Осы қолданбаға көп рақмет! | Many thanks to this app!
e | Кушти! | Күшті! | Great!
Table 3: Kazakh review variations

### 3.4. Sentiment Classification Tasks

To evaluate the effectiveness of KazSAnDRA, we utilised the dataset for two
tasks: (a) polarity classification (PC), which involves predicting whether a
review is positive or negative, and (b) score classification (SC), which
involves predicting the score of a review on a scale of 1 to 5. In the PC task
only, reviews with an original score of 1 or 2 were designated as negative and
subsequently assigned a new score of 0. In contrast, reviews with an original
score of 4 and 5 were classified as positive and assigned a new score of 1.
Reviews with an original score of 3 were categorised as neutral and excluded
from the task.

### 3.5. Data Pre-Processing

Irrespective of the task for which the dataset was intended, the data pre-
processing stage involved several essential steps aimed at preserving the
integrity and uniformity of the dataset. First, all emojis were systematically
removed from the text to eliminate potential noise. Subsequently, to ensure
consistency and ease of analysis, all reviews were lowercased. The elimination
of punctuation helped to streamline the text for further processing. In
addition, the characters for line break (\n), tab (\t), and carriage return
(\r) were removed to avoid interference with subsequent computations. To
enhance readability and minimise unnecessary mismatches, multiple spaces were
uniformly replaced with a single space. Furthermore, it is important to note
that in the Kazakh language, consecutive characters are allowed to occur in
pairs (e.g., айттым “I said”, құжаттар “documents”, қосса “if s/he adds”) but
not in larger clusters. Hence, to conform to this linguistic feature, any
consecutive characters that appeared repeatedly were reduced to two instances
(e.g., кееррреемееетт to кеерреемеетт). Lastly, all duplicate entries, defined
as reviews sharing identical text and scores, were removed. The total numbers
of reviews following pre-processing were 167,961 for PC and 175,158 for SC.

### 3.6. Data Partitioning

To ensure consistency and reproducibility of our experimental results across
different research groups, KaZSAnDRA was divided into training (Train),
validation (Valid), and test (Test) sets, maintaining a ratio of 80/10/10. The
division ensured a balanced and proportional distribution of review scores and
domains across the sets.

Tables 4 and 5 present the distribution of reviews across the three sets based
on the domains for the PC and SC tasks, respectively, after pre-processing,
including the total number of reviews as well as the respective counts for
each set pertaining to both tasks. Tables 6 and 7 present the distribution of
reviews across the three sets in terms of their scores for the PC and SC
tasks, in turn.

Furthermore, an analysis of the KazSAnDRA dataset was conducted to extract
unique reviews (i.e., reviews with distinct textual content) per
classification task. The numbers of unique reviews in the training,
validation, and test sets for PC were 132,152, 16,739, and 16,757,
respectively. For SC, the corresponding counts were 137,365, 17,464, and
17,445. The intersection between the training, validation, and test sets was
then computed, as depicted in Figure 1. Significantly, over 96% of the unique
reviews present in the test sets for both PC and SC tasks did not occur in
either the training or validation sets. This substantial discrepancy
corroborated the appropriateness of utilising the test sets to effectively
evaluate the generalisation capabilities of sentiment classification models.

Domain | Train | Valid | Test
---|---|---|---
# | % | # | % | # | %
Appstore | 101,477 | 75.52 | 12,685 | 75.52 | 12,685 | 75.52
Market | 22,561 | 16.79 | 2,820 | 16.79 | 2,820 | 16.79
Mapping | 6,509 | 4.84 | 813 | 4.84 | 814 | 4.85
Bookstore | 3,821 | 2.84 | 478 | 2.85 | 478 | 2.85
Total | 134,368 | 100 | 16,796 | 100 | 16,797 | 100
Table 4: Domains across the sets for PC  Domain | Train | Valid | Test
---|---|---|---
# | % | # | % | # | %
Appstore | 106,058 | 75.69 | 13,258 | 75.69 | 13,257 | 75.69
Market | 23,278 | 16.61 | 2,909 | 16.61 | 2,910 | 16.61
Mapping | 6,794 | 4.85 | 849 | 4.85 | 849 | 4.85
Bookstore | 3,996 | 2.85 | 500 | 2.85 | 500 | 2.85
Total | 140,126 | 100 | 17,516 | 100 | 17,516 | 100
Table 5: Domains across the sets for SC  Score | Train | Valid | Test
---|---|---|---
# | % | # | % | # | %
1 | 110,417 | 82.18 | 13,801 | 82.17 | 13,804 | 82.18
0 | 23,951 | 17.82 | 2,995 | 17.83 | 2,993 | 17.82
Total | 134,368 | 100 | 16,796 | 100 | 16,797 | 100
Table 6: Scores across the sets for PC Score | Train | Valid | Test
---|---|---|---
# | % | # | % | # | %
5 | 101,302 | 72.29 | 12,663 | 72.29 | 12,663 | 72.29
1 | 20,031 | 14.29 | 2,504 | 14.30 | 2,504 | 14.30
4 | 9,115 | 6.50 | 1,140 | 6.51 | 1,139 | 6.50
3 | 5,758 | 4.11 | 719 | 4.10 | 720 | 4.11
2 | 3,920 | 2.80 | 490 | 2.80 | 490 | 2.80
Total | 140,126 | 100 | 17,516 | 100 | 17,516 | 100
Table 7: Scores across the sets for SC Figure 1: Unique reviews across the
sets for PC (top) and SC (bottom)

### 3.7. Score Resampling

Table 1 shows the score distribution in KazSAnDRA, indicating a significant
imbalance. This raises concerns about biassed model performance, favouring the
majority scores and neglecting underrepresented scores. Therefore, our study
included analysis of results obtained from both balanced and imbalanced data,
which had previously been employed with varying degrees of success (see Burns
et al., 2011; Mutanov et al., 2021).

In response to the data imbalance in our training data, we employed random
oversampling (ROS) and random undersampling (RUS) to balance the
representation of classes by creating new samples for the smaller class to
align with the majority class count and eliminating samples from the larger
class to match the minority class count, respectively (Ramentol et al., 2012).
In this study, we deferred the investigation of alternative approaches (e.g.,
data augmentation through back-translation) for future research. The resulting
training sets for both tasks are detailed in Tables 8 and 9.

Score | Balanced | Imbalanced
---|---|---
ROS | RUS
0 | 110,417 | 23,951 | 23,951
1 | 110,417 | 23,951 | 110,417
Table 8: Training sets for PC Score | Balanced | Imbalanced
---|---|---
ROS | RUS
1 | 101,302 | 3,920 | 20,031
2 | 101,302 | 3,920 | 3,920
3 | 101,302 | 3,920 | 5,758
4 | 101,302 | 3,920 | 9,115
5 | 101,302 | 3,920 | 101,302
Table 9: Training sets for SC

### 3.8. Dataset Organisation

The dataset comprises ten CSV files. Files “01” to “05” are associated with
PC, while files “06” to “10” are related to SC. Different training set
variations are indicated by the suffixes “ib” for imbalanced data, “ros” for
random oversampling, and “rus” for random undersampling. Each file includes
records containing a custom review identifier (custom_id), the original review
text (text), the pre-processed review text (text_cleaned), the corresponding
review score (label), and the domain information (domain). The dataset can be
conveniently downloaded from our GitHub
repository.666https://github.com/IS2AI/KazSAnDRA

Model | Polarity Classification |  | Score Classification
---|---|---|---
Balanced (ROS) |  | Balanced (RUS) |  | Imbalanced |  | Balanced (ROS) |  | Balanced (RUS) |  | Imbalanced
A | P | R | F1 |  | A | P | R | F1 |  | A | P | R | F1 |  | A | P | R | F1 |  | A | P | R | F1 |  | A | P | R | F1
mBERT | 0.84 | 0.74 | 0.83 | 0.77 |  | 0.85 | 0.76 | 0.82 | 0.78 |  | 0.89 | 0.82 | 0.79 | 0.80 |  | 0.67 | 0.34 | 0.36 | 0.35 |  | 0.63 | 0.35 | 0.39 | 0.36 |  | 0.77 | 0.44 | 0.36 | 0.37
XLM-R | 0.86 | 0.76 | 0.83 | 0.79 |  | 0.85 | 0.75 | 0.83 | 0.78 |  | 0.89 | 0.81 | 0.81 | 0.81 |  | 0.58 | 0.36 | 0.42 | 0.36 |  | 0.66 | 0.36 | 0.41 | 0.37 |  | 0.77 | 0.42 | 0.37 | 0.39
RemBERT | 0.88 | 0.79 | 0.82 | 0.81 |  | 0.87 | 0.78 | 0.82 | 0.80 |  | 0.89 | 0.81 | 0.82 | 0.81 |  | 0.73 | 0.37 | 0.36 | 0.36 |  | 0.62 | 0.35 | 0.40 | 0.35 |  | 0.76 | 0.41 | 0.38 | 0.39
mBART-50 | 0.87 | 0.77 | 0.79 | 0.78 |  | 0.81 | 0.72 | 0.81 | 0.74 |  | 0.89 | 0.82 | 0.78 | 0.80 |  | 0.74 | 0.36 | 0.34 | 0.35 |  | 0.55 | 0.36 | 0.41 | 0.34 |  | 0.77 | 0.42 | 0.37 | 0.38
Table 10: PC and SC results on the test sets

## 4\. Experiment

### 4.1. Sentiment Classification Models

For the evaluation of KazSAnDRA, we utilised four multilingual machine
learning models, all incorporating the Kazakh language and accessible through
the Hugging Face Transformers framework (Wolf et al., 2020). The framework was
chosen for its state-of-the-art pre-trained models, user-friendly interface,
and collaborative ecosystem. Details on the implementation of the sentiment
classification model are available on our GitHub repository.6

mBERT is a case-insensitive variant of the multilingual BERT (Devlin et al.,
2019) model. This model comprises about 168 million parameters and has been
pre-trained on a corpus of 102 languages.

XLM-R We leveraged the XLM-RoBERTa model (Conneau et al., 2020), a
multilingual variant of RoBERTa (Liu et al., 2019). The rationale for
selecting this model stems from its substantial parameter count, exceeding
that of BERT by over fivefold (561M), and its pre-training on the CommonCrawl
corpus encompassing 100 languages.

RemBERT The rebalanced multilingual BERT model (Chung et al., 2021) is a
multilingual encoder pre-trained on Wikipedia over 104 languages. RemBERT
exhibits superior performance compared to the similarly sized XLM-R, despite
being trained on 3.5 times fewer tokens.

mBART-50 (Tang et al., 2020) is a multilingual sequence-to-sequence model
built on the foundation of the original mBART model (Liu et al., 2020). This
extended version was thoughtfully augmented with an additional 25 languages,
bringing the total number of languages supported to 50.

### 4.2. Experimental Setup

All four models were fine-tuned using both the balanced and imbalanced
training sets, while the hyperparameters were refined using the validation
set. The final and most optimal models were evaluated on the test sets. The
fine-tuning of the models was executed on a single A100 GPU hosted on an
NVIDIA DGX A100 machine. The initial learning rate was set at $10^{-5}$; the
weight decay rate was set at $10^{-3}$. Early stopping was employed, executed
when the F1-score exhibited no improvement for three consecutive epochs. We
set the batch size to 32 (mBERT, XLM-R, RemBERT) or 16 (mBART-50) and applied
800 warm-up steps.

### 4.3. Performance Metrics

Several conventional metrics were used to evaluate the performance of the
models, including accuracy (A), precision (P), recall (R), and F1-score (F1).
Given the imbalanced nature of the dataset, where all classes carry equal
importance, we opted for macro-averaging, calculated from the arithmetic
(i.e., unweighted) mean of all F1-scores per class, and thus ensuring equal
treatment of all classes during the evaluation, resulting in a stronger
penalty if the model performs worse on minority classes (Jurafsky and Martin,
2009; Yang, 2001).

### 4.4. Experiment Results

Table 10 presents the performance of the four models on KazSAnDRA test sets
for the PC and SC tasks. XLM-R and RemBERT consistently outperformed mBERT and
mBART-50 across various training scenarios. The highest F1-scores of 0.81 (PC)
and 0.39 (SC) were achieved by both XLM-R and RemBERT in the imbalanced
training scenario. In five out of six training scenarios, RemBERT achieved the
highest F1-scores, while XLM-R led in four. Table 11 presents data on the
number of epochs required to train models for the PC and SC tasks, considering
both balanced (ROS, RUS) and imbalanced (IB) training data scenarios. Tables
12–14 summarise the performance of RemBERT in the imbalanced training context,
with a detailed analysis following in the subsequent section.

Model | PC |  | SC
---|---|---|---
ROS | RUS | IB |  | ROS | RUS | IB
mBERT | 4 | 7 | 6 |  | 8 | 10 | 11
XLM-R | 5 | 7 | 5 |  | 4 | 9 | 16
RemBERT | 4 | 5 | 5 |  | 6 | 6 | 9
mBART-50 | 5 | 7 | 5 |  | 8 | 7 | 5
Table 11: Number of training epochs for models

## 5\. Discussion

Scores in the SC task were lower than in the PC task for all models, possibly
due to its increased complexity involving five-way classification. Table 12
shows that, in the PC task, the RemBERT model had stronger performance in
identifying positive reviews, but had a notable drawback misclassifying 1,036
positive reviews as negative, indicating a relatively high number of false
negatives.

Polarity Classification
---
|  predicted $\mathbf{\rightarrow}$
---
actual $\mathbf{\downarrow}$
0 | 1 | Total
0 | 2,155 | 838 | 2,993
1 | 1,036 | 12,768 | 13,804
Table 12: RemBERT PC results

In the SC task (Table 13), it appears that the model had higher accuracy in
identifying reviews with scores at the extremes (1 and 5) compared to the
middle scores (2, 3, and 4). The model had particularly low accuracy in
identifying reviews with a score of 2, with only 55 true positives. The reason
for this is most likely that the training data contained many more reviews
with scores of 1 and 5 than the middle scores (see Table 1).

Score Classification
---
|  predicted $\mathbf{\rightarrow}$
---
actual $\mathbf{\downarrow}$
1 | 2 | 3 | 4 | 5 | Total
1 | 1,379 | 145 | 132 | 64 | 784 | 2,504
2 | 182 | 55 | 56 | 25 | 172 | 490
3 | 173 | 54 | 118 | 65 | 310 | 720
4 | 110 | 39 | 90 | 169 | 731 | 1,139
5 | 564 | 59 | 165 | 297 | 11,578 | 12,663
Table 13: RemBERT SC results

In addition, the model exhibited a tendency for misclassifying reviews with
scores other than 5 as if they had a rating of 5. This also seems to be
related to the preponderance of reviews with a score of 5, causing the model
to have a bias towards this score. The substantial disparity between the
number of positive and negative reviews can be attributed to the fact that the
reviewed items predominantly represent highly popular or top-rated selections.
It is therefore to be expected that such items naturally receive a
significantly higher number of reviews than less popular or lower-rated items
(Aly and Atiya, 2013).

Domain | PC |  | SC
---|---|---|---
A | P | R | F1 |  | A | P | R | F1
Appstore | 0.87 | 0.80 | 0.81 | 0.80 |  | 0.74 | 0.41 | 0.37 | 0.38
Bookstore | 0.86 | 0.75 | 0.80 | 0.77 |  | 0.73 | 0.34 | 0.32 | 0.32
Mapping | 0.92 | 0.84 | 0.88 | 0.86 |  | 0.80 | 0.42 | 0.41 | 0.41
Market | 0.97 | 0.84 | 0.91 | 0.87 |  | 0.82 | 0.43 | 0.41 | 0.42
Table 14: RemBERT results by domain

In Table 14, an interesting observation is that the model exhibited more
accurate classification in both tasks for reviews from the Mapping and Market
domains, which were manually collected, as opposed to reviews from the other
two domains acquired through automated means. This observation suggests that
the moderators may have selectively collected reviews with higher readability,
fewer spelling and grammar errors, and reduced instances of code-switching and
inappropriate content during the review collection process. The availability
of cleaner, less noisy data could have positively influenced the performance
of the model in classifying Kazakh reviews.

It is also important to recognise that the poorer performance on the SC task
may not have solely stemmed from the increased complexity and challenges
inherent in multi-class classification tasks. It could also be an indicator of
the quality of the reviews present within the dataset. Recall that the main
objective of this study was to develop a dataset that includes a diverse array
of Kazakh reviews of different products and services, which, in turn, would
hopefully facilitate in-depth research in Kazakh sentiment analysis.
Nevertheless, we frankly admit that certain aspects, such as the correction of
spelling errors, the effective handling of frequent code-switching between
Kazakh and Russian, and the application of lemmatisation techniques, were not
explicitly addressed and may have resulted in the lower performance of the
models. These specific challenges offer promising opportunities for future
investigations to improve the quality and linguistic processing capabilities
of the dataset.

Upon addressing the aforementioned aspects, data augmentation techniques, such
as back-translation, could be considered as possible alternatives to ROS and
RUS, which were used in our study to address the data imbalance issue. The
experimental findings suggest that of the four models trained on data balanced
using the mentioned techniques only RemBERT exhibited improvement, albeit
solely in the PC task (Burns et al., 2011).

Another challenge that may have caused the low performance on the SC task lies
in the pronounced dependence of classification on the discretion of the author
of a review (Smetanin and Komarov, 2021). The potential introduction of
inaccuracies during the process of assigning ratings by the author could
engender misclassification of the final labels within the dataset. For
instance, an ostensibly positive review may paradoxically carry a score of 1;
conversely, a review strongly critical of a product may be concomitantly
associated with a high rating of 5. The absence of standardised criteria for
sentiment labelling leads to a subjective, intuitive approach by individual
authors and thus to considerable variability in the assignment of ratings
between authors. This underscores the exigency of formulating sentiment
annotation guidelines in and, more importantly, for the Kazakh language, which
can serve as a framework for future research in this area.

## 6\. Conclusion

The aim of this study was to create an extensive dataset for Kazakh sentiment
analysis. The result is KazSAnDRA, the first and largest publicly available
dataset for Kazakh. Comprising 180,064 reviews from four domains, KazSAnDRA
includes numerical ratings from 1 to 5 that quantitatively represent
customers’ attitudes. To automate Kazakh sentiment classification, we
developed and evaluated four machine learning models for both polarity and
score classification. The experimental analysis involved examining the results
obtained with both balanced and imbalanced training data. The most successful
model achieved an F1-score of 0.81 for the polarity classification task and
0.39 for the score classification task on the test sets. In the future, we
plan to improve KazSAnDRA by addressing spelling errors and effectively
handling code-switching phenomena. These improvements will facilitate the use
of advanced data augmentation techniques to cope with data imbalance
challenges.

The dataset and fine-tuned models are available for unrestricted access and
can be freely downloaded under the Creative Commons Attribution 4.0
International License (CC BY 4.0) from our GitHub repository.6

## 7\. Acknowledgements

We sincerely thank Alma Murzagulova, Aizhan Seipanova, Meiramgul Akanova,
Almas Aitzhan, Aigerim Boranbayeva, and Assel Kospabayeva, who acted as
moderators during the review collection process. Their tireless efforts,
diligence, and remarkable patience contributed significantly to the successful
completion of this endeavour.

## 8\. Bibliographical References

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