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MODELING OF OPINION FORMATION UNDER INFLUENCE OF SOCIAL MEDIA FOR ANALYZING HISTORICAL EVENTS WITH BENGAL PARTITION AS CASE STUDY

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Topics in Intelligent Computing and Industry Design (ICID) 2(2) (2020) 138-141
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Cite The A rticle: Pr iyadar sini Sinha, Milan Mukh erjee, Souvi k Roy, Abhik Mukhe rjee( 2020) .Model ing Of Op inion Forma tion U nder Influe nce Of Soci al Medi a For
Ana lyzing Histo rical E vents With B engal Partitio n As C ase Study.
Top ics In Inte lligent Comp uting And I ndust ry De sign, 2(2): 138 -141
.
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DOI: http://doi.org/10.26480/etit.02.2020.138.141
MODELING OF OPINION FORMATION UNDER INFLUENCE OF SOCIAL MEDIA FOR
ANALYZING HISTORICAL EVENTS WITH BENGAL PARTITION AS CASE STUDY
Priyadarsini Sinhaa*, Milan Mukherjeeb, Souvik Royc, Abhik Mukherjeea
a CST Dept, IIEST Shibpur
b Hyland Software
c IT Dept, IIEST Shibpur
*Corresponding Author Email: georgenelson5006@gmail.com
This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, an d
reproduction in any medium, provided the original work is properly cited.
ARTICLE DETAILS
Article History:
Received 25 October 2020
Accepted 26 November 2020
Available online 03 December 2020
Error correcting codes are important for communication sys- tems to retrieve messages transmitted over
noisy channels. Recent ad- vancement of low density parity check (LDPC) codes has enabled reliable
communication in highly noisy environment of deep space or underwater. The LDPC decoder algorithm
employs localized neighbourhood based parity check equations to improve upon the error correcting
capability. It is shown in this work that such principle can be implemented on bi- partite graph to simulate
the connectivity among people of the society who form opinion through influence from their connected
neighbour- hood. With the advent of social media, this concept of neighbourhood has broken the localized
boundaries so that influencing opinions can be far spread. Historical event like Partition of Bengal in 1947,
when revis- ited in light of this model, provides alternate course of history.
KEYWORDS
online social media, graph algorithm, error correcting codes.
1. INTRODUCTION
Error correcting codes is a well studied subject in communication theory
(Lin and Costello, 1999). Low Density Parity Check (LDPC) codes are one
of the best error correcting codes (apart from Turbo codes) till now for
practical applications like wireless communications and deep space
missions. The decoders of LDPC codes are, by nature, some generic
iterative decoders which can be used to decode any block code for a given
channel. Iterative decoders are different from the standard algebraic
decoders that settle in one pass for the codeword situated at global
minimum distance from the received word. Rather, they care for the
connectivity established by the individual bits of the parity check
equations and initiate corrections so that all parity check equations are
satisfied. The process does not often terminate in one pass and may
require a good number of iterations before convergence of the parity
check equations. The process may terminate without being decisively able
to resolve the ambiguity even after running large number of iterations.
In the present work, individuals of the society are considered to be
represented by the bits who participate in parity check equations where
they try to settle to some convergent opinion by changing their own
opinion based on majority of opinions they receive.
The binary content of the bit is suitable to implement the two possible
states of being agitated (1) or at peace (0) with the issue in question. The
codeword has two parts, the message bits and check bits. Here the check
bits are considered to be the influencing members of society who matter
to the individuals while forming their opinion through the satisfying of
parity check equations. Analogy may be drawn with how individual
opinions can converge to some opinion about some societal issue.
The main contention of this paper is to show how more influencing fro m
remotely located individuals could dominate over local influences or
global trends resulting in convergence to different state. This arguably is
one of the main feature today with the exodus of social media in the life of
an individual. For this, we have chosen the historical event of Bengal
partition (Chatterjee, 1994) that was decided largely through localized
political interest groups. We have argued that an alternate course of
history could have been arrived at if social media was present in that era.
This is hypothetical reasoning but nevertheless useful for understanding
how opinions form in the present and what the future holds.
2. ERROR CORRECTING LDPC CODES
Early variant of LDPC code was discovered by Robert in early 1960s
(Gallager, 1962). Largely suppressed from further research due to
technical limitations. Tanner’s graph theoretic view (Tanner, 1981) on
block codes presented in 1981 was also ignored. Late 1990s came up with
the same idea of LDPC code when a researchers and other eminent
researchers fo und out these codes independently while investigating on
graph based iteratively decodable codes (Davey et al., 1998; MacKay,
1999).
An LDPC code is defined with respect to its parity check matrix. They are
a subclass of block codes in general. The term low density signifies a sparse
parity check matrix in terms of the number of 1s present in the matrix. Due
to this sparseness, LDPC codes possess great advantages in terms of
efficient decoder implementation and storage and can approach the
Shannon Limit very effectively. It has been implemented in various
practical standards such as IEEE 802.16, IEEE 802.20, IEEE 802.3, DVB-
Topics in Intelligent Computing and Industry Design (ICID) 2(2) (2020) 138-141
Cite The A rticle: Pr iyadar sini Sinha, Milan Mukh erjee, Souvi k Roy, Abhik Mukhe rjee( 2020) .Model ing Of Op inion Forma tion U nder Infl uence Of S ocial M edia F or
Ana lyzing Histo rical E vents With B engal Partitio n As C ase S tudy.
Top ics In Inte lligent Comp uting And I ndust ry De sign, 2(2): 138 -141
.
RS2 and many others. Such is the advantage that now researchers are even
investigating non-binary LDPC codes and their applicabilities.
An
(
N, w
c
, w
r)
LDPC code with a parity check matrix
H
of size (
M
×
N
),
where the Hamming weight of each column and each row are two fixed
integers
,
w
c
and
w
r
respectively with
w
r
> w
c
>
2. Since the matrix is
sparse in nature, so
w
c
M
and
w
r
N.
The total number of
1
s
=
w
c
×
N
=
w
r
×
M
.
Thus,
M
=
(
N
×
w
c
)
must be an integer. This also
implies that every code bit participates in
w
c
parity check sums and each
parity check sum involve
s
w
r
code bits. The density of this parity check
matrix is defined as
Ψ
= wr
= wc .
This helps to understand, both
intuitively and mathematically, how much sparse
H
really is.
R. M. Tanner in 1981 showed the existence of a bijection between the
parity check matrix of any block code and a bipartite graph (Tanner,
1981). This graph is now referred to as
a Tanner graph. Each row of a
(
n
k
) ×
n
parity check matrix
H
of a block code denotes a parity check
sum
f
i
for all
i
= 0
,
1
, . . . ,
(
n
k
).
Each column denotes a particular position
,
c
j
for all
j
=
0
,
1
, . . . , n
of the code word with block length
n
.
Whenever
H
[
i,
j
]
=
1,
it indicates that the
i
th
parity check sum affects the
j
th
code bit
position or the
j
th
code bit. From this Tanner constructed a bipartite
graph where the two sets of vertices/nodes consists of the parity check
sums and code bits as nodes respectively.
(
f
i
, c
j
)
is an edge in the graph
whenever
H
[
i, j
]
=
1.
Construction of the generator matrix can be initiated by forming a sub-
matrix
H
0
of size M ×
N
as follows : each row of
H
0
has
w
r 1
s
in
such a way that the
i
th row of
H
0
contains all its
w
r 1
s
in the
columns [(
i
1)
.w
r + 1] to
i.w
r.
After this, the entire parity check
matrix can be constructed by stacking any
(
w
c 1) column
permutations
of
H
0
. Here
Π
k
(
H
0
),
k
1,
denotes a sub-matrix obtained
by permuting the columns of
H
0
randomly while
Π
1(
H
0
) =
H
0
.
If each
permutation is chosen randomly, it can sometimes produce good code. The
average minimum distance of the code increases with
N
for
w
c 3.
Since
the so designed LDPC code is not necessarily linear code,
Rank
(
H
)
M
.
Therefore dimension of the code is
Dim
(
C
) (
N
M
) or
K
(
N
M
).
Hence rate of the code
R
=
K
N- M
= 1 wc .
Hence the actual rate of
the code is higher than the
H
matrix suggests as the designed rate. F or
practical LDPC codes
N
is taken to be quite large, like
N >
5000,
while
the column weight is held around 3 or 4, so the density of 1s in the matrix
is quite low.
3. ITERATIVE DECODER ALGORITHM
Iterative decoding principle is employed for decoding of LDPC codes.
Unlike one shot method used in algebraic decoding of linear block codes,
this uses multiple iterations capable of eliminating high noise. A study
introduced a simple Bit-Flipping algorithm that corrected a single bit in
every iteration (Gallager, 1962). If multiple bits are allowed to flip in one
iteration, then the algorithm is called a Multi-Bit-Flipping (MBF)
Algorithm.
In every iteration of this algorithm the code word bit(s) with the highest
number of a metric are flipped. Metric is characterized by the type of
algorithm: Hard-Decision and Soft-Decision. Hard decision metric is the
number of unsatisfied parity check equations. Soft decision metric consists
both the number of unsatisfied and satisfied parity check sums, since
reliability information is present. An algebraic decoding algorithm in this
context can only correct up to its random error correcting capability. But
due to the sparse nature of H, the MBF algorithm may correct error
patterns whose number of errors exceeds the error correcting capability
of the code. Since the present work relies on hard decision message
passing only, the details of soft decision algorithm that exploits reliability
information is not introduced.
Message Passing Algorithm (MPA) in context of LDPC codes can be
visualized more easily if we refer to the Tanner graph of t he associated
code. Messages are passed between message nodes and check nodes along
the edges of the Tanner graph. The information that is sent from a node vi
to vj in MPA should not get influenced by the node
v
j
i.e., in other words,
the data that is being sent to a node must depend only on the other nodes.
This type of message is called an “extrinsic message” or “extrinsic
information”.
The generic message passing structure is as follows :
1) Initialize the decoder by sending the received values of the message
nodes to check nodes.
2) In each check node, an extrinsic message for each neighbor variable
node is calculated and sent.
3) Each message node calculates a new value for itself depending on the
previous received values and the information from the check nodes. The
output is then checked by all the parity check equations and if all of them
agree, decoding stops. Otherwise, an extrinsic message for each neighbor
check node is calculated and sent.
4) Repeat steps 2 and 3 until a maximum number of iterations is reached.
4. ANALOGY WITH SOCIETAL OPINION FORMATION
4.1 Dynamics of opinion formation
One large binary string with a number of zeros and ones can be considered
as a received word. Each bit can be considered as an individual having a
binary state of mind w here one represents agitated state and zero
represents peaceful state. Some of these individuals may be considered to
be influential and thus considered as check bits. The bipartite graph can
then be constructed with edges drawn between individual nodes on one
side and the influencing nodes on the other side.
Analogy can be drawn between this construction and the MPA decoder of
LDPC code discussed in the previous section. Each individual node is
connected to a number of influencing nodes.
Thus they receive message of being in agitated or peaceful state from each
such check node. Then they arrive at the majority and accordingly retain
or flip the bit, implying that they may go from agitated to peaceful state or
vice versa based on collected majority opinion.
This process may continue over a number of iterations with the
terminating condition described as reaching all zero codeword or
exceeding a certain number of iterations. Check bits also appear as
individuals thereby allowing flexibility of opinion for all.
The main argument is that with localized influence it is not possible to get
back from a number of ones and zeros in the received word back to the all
zero codeword. Along similar lines, unless the individual nodes get
connected to some remote influencing nodes, it is not at all possible for the
MPA of the iterative decoding algorithm to get to the all zero state. One
important flavour about the success of MPA is that the parity check matrix
is sparse yet it provides a spread of the check nodes.
4.2 Simulation results for message passing
The 20, 3, 4 code has been tested by creating bit strings where the all zero
code word resembling peaceful state is contaminated with number of 1s
(Gallager, 1962). The message passing based iterative decoder algorithm
is run on these simulated received words.
Success and failure along with the number of 1s corrected to 0s is reported
in Table 1 along with number of iteration needed to achieve the success. It
can be seen that for some cases, even after 5000 iterations, the error does
not get corrected. It depends on the distribution of the error with respect
to the generator matrix used for the code. The corresponding bipartite
graph is shown in Figure 1.
Figure 1: Bipartite graph showing the interaction among the nodes
The generator matrix is such that for the first five rows the influence is
localized,
so that
f
i
influences
c
4i+1 to
c
4i+4. However, apart
from
f
1,
c
1 is also influenced by
f
8
and
f
14.
Likewise,
c
2 is influenced by
f
1,
f
9
and
f
12.
In this manner, the
localized
influence is perturbed and the maximum likelihood or
minimum distance decoding philosophy gets altered.
Results are tabulated in Table 1, clearly showing large number of
additional errors or agitated opinions getting corrected. Some of these
results are
Topics in Intelligent Computing and Industry Design (ICID) 2(2) (2020) 138-141
Cite The A rticle: Pr iyadar sini Sinha, Milan Mukh erjee, Souvi k Roy, Abhik Mukhe rjee( 2020) .Model ing Of Op inion Forma tion U nder Infl uence Of S ocial M edia F or
Ana lyzing Histo rical E vents With B engal Partitio n As C ase S tudy.
Top ics In Inte lligent Comp uting And I ndust ry De sign, 2(2): 138 -141
.
Table 1: Iterative decoding success for 20,3,4 LDPC code
Iteration count
Bits corrected
Remarks
102
12
Success
18
9
Success
9
8
Success
73
12
Success
5000
3
Failure
5000
4
Failure
5000
5
Failure
5000
9
Failure
indeed encouraging from our present perspective. Large number of
individuals in riotous state (1) can be brought to pacified state (0) through
the message passing algorithm that relies upon flipping of node bit based
on majority of its influencing bits.
It can be seen that often large number of iterations are needed, sometimes
the process fails in the long term as well. But this brings out the
importance of geographical spread of influencing bits beyond localised
boundaries. We found that the system inevitably terminates with failure if
influence is localized, c heck bits are less in number and the 1’s are
concentrated in some locality, it is never possible to get to the all zero
codeword at all.
5. CASE STUDY OF BENGAL PARTITION
5.1 Historical perspective
The first attempt towards partition of Bengal by the British in 1905 was
thwarted through peoples’ struggle and forced to be nullified in 1911. But
the second one by the same British rulers was rather invited - by the same
people in a gap of only 40 years. A spate of communal riots spread across
the entire territory of undivided Bengal; with Kolkata, Dhaka,
Mymensingh, Chittagong all throwing in their bit; gradually became
uncontrollable.
During the initial years, the communal riots of undivided Bengal largely
originated due to economic oppression. The feudal economic structure of
Bengal was such that the oppressing Zamindars or landlords of Eastern
Bengal were mostly Hindus and their Ryots r epresenting the peasantry
were mainly Muslims. The signature of this class character dominated till
1926 as claimed by the historians (Das, 2010). Such crowd leader
dichotomy however shifted during the 1930’s when the British
government were clearly instigating the riots, for example the Chittagong
riots of 1930. Finally, in the 1940’s the political parties came to the
forefront of the riotous population.
With two nation theory and its inevitable logic of Bengal partition
suddenly becoming the agenda of all the political outfits, this obviously
dominated the discussion forums. Under such circumstances, opinion poll
of the legislature representatives were held regarding the partition in a
state where the democratic institution was also cut across communal lines
as part of British policy of representation (Chatterjee, 1994). As expected,
the opinion was biased, driven by narrow interests of the representatives
and ignorant of public opinion altogether. Even, the decision of Eastern
Bengal legislature was not binding on the West. Hence the voting pattern
was highly communal and localized.
The localization can be understood from the distribution of minority
population on either side of the border as shown in Figure 2(L)
(Chatterjee, 1947). However, organized working class existed in the
Railways and to an extent in the trade unions of Jute industry and in these
spheres, there was a small spread cutting across the local barriers as
depicted in Figure 2(R).
But this was too weak compared to the geographical spread enjoyed by the
online social media of today. Recent Brexit debate has seen huge number
of such cross votings mainly from Conservative party bac kbenchers and
few Labour Party MPs as well in the British parliament, mainly because of
various extraneous influences (Aidt et al., 2019).
Figure 2: Map showing minority population on either side of the border,
indicator of local influence (Left) Map showing manufacturing industry
on either side of the border, indicator of remote influence (Right)
5.2 Presence of social media
To revisit the Bengal partition, the influence and spread of social media in
Bangla speaking regions is considered. Whatsapp or Facebook
connectivity depends more on acquaintance like school or office, such
friendship is sparse across the border. Friendship groups do exist but their
presence is formal. For example, the information shared by Bangladesh
India Friendship Association, a community in Facebook, are either visa
related or about health care services.
We therefore looked for some social media that binds on language and
discusses on convergent issues. Quora is one such platform and analysis of
Quora discussion forums can be fo und in literature as well (Wang et al.,
2013; Maity et al., 2018). So for the present work, Quora Bangla dataset
has been taken and the spread of interactions on Quora Bangla posts
amongst the Bangla speaking community across the border is explored.
Quora Bangla data was collected for 10 questions raised in the platform
with 3006 responding users along with the users profile location. Figure 3
shows the binding of both sides of the partition. The nodes depict the user
profile (blue for users from Bangladesh and red for users from West
Bengal) and two nodes are connected via edges depending on upvote and
comments response. The group attribute layout of the graph is shown
depending on country attribute which shows how engrossed both sides of
the partition are in this respect.
Typical location specific results are shown in Figure 3(R) which depicts
response from Bangladesh users (A: Dhaka & Southwards; B: Mymensingh
& Northwards; C: Chittagong & Eastwards; and D: Bangladesh other area)
for the posts from West Bengal users and response from West Bengal (A:
Kolkata & Southwards; B: Siliguri & Northwards; C: North East India) for
the posts from Bangladesh users.
Figure 3: Left: Quora response graph with Attribute view; Right: Response
statistics
5.3 Simulation perspective
We look back at the excitors and inhibitors of communal tension in terms
of the propaganda on either side of the divide (Chatterjee, 1994). The
bipartite graph based model can be useful with edge being drawn between
groups of the population based on their roles as excitors and inhibitors.
The graph would be sparse but with strong possibility of cycles. We
consider binary opinion for the legislative representatives. As political
groups, they employ local connectivity. Their initial state is highly biased
as most Congress and Hindu Mahasabha legislators with majority located
in West Bengal were in favour of partition (state 1) and tho Muslim League
Topics in Intelligent Computing and Industry Design (ICID) 2(2) (2020) 138-141
Cite The A rticle: Pr iyadar sini Sinha, Milan Mukh erjee, Souvi k Roy, Abhik Mukhe rjee( 2020) .Model ing Of Op inion Forma tion U nder Infl uence Of S ocial M edia F or
Ana lyzing Histo rical E vents With B engal Partitio n As C ase S tudy.
Top ics In Inte lligent Comp uting And I ndust ry De sign, 2(2): 138 -141
.
and Praja Krishak Party legislators with majority in East Bengal wanting
to avoid partition (state=0). Purely local connectivity can never result in
convergence to the all zero state.
Now, the LDPC code example discussed in previous section allows remote
influence of check bits on code bits. In some form, social media was
present, like the newspaper or leaflet to circulate opinions. But that is not
adequate enough to guarantee the sort of remote connectivity needed to
make the mark. Updating of the state at each node is based on the majority
rule applied by considering all opinions that reach it. Now, some of the
representatives are allowed remote connectivity outside their party
opinion to an extent as per the permutation based construction of the
parity check matrix described in previous section (see Figure 1). Iterative
decoding can be employed and the system is able to reach sometimes the
stable all zero state which implies thwarting of partition. Hence with the
kind of influencing Quora Bangla provides, the chances of alternate
courses of history might have been realized.
6. CONCLUSION
There is no way to go back in time and change the course of historical
events. However, it is worthwhile to learn lessons from history and
deconstruct the events in light of modernity to explore new possibilities.
This work looks back at the Bengal partition in light of the advent of online
social media,
This leads us to the conclusion that there was lack of enough
communication amongst the people of undivided Bengal to the detriment
of different options reaching them and influencing their decision. The
probability of alternative discourse would have been higher in today’s
connected world. However, here only some random simulation
perspective is given. To present more realistic picture of history, we have
plans to incorporate the traits of legislators who actually participated in
the process.
ACKNOWLEDGEMENT
This work received support of MHRD/ICSSR IMPRESS project.
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Bengal divided Hindu communalism and partition 1932-1947
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Chatterjee J, 1994, Bengal divided Hindu communalism and partition 1932-1947, Cam-bridge University Press.
Error Correcting Codes
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