Data Mining and Mathematical Modeling in Big Data: Partial-Rogue
Lump Ripple Model on Sina Weibo Public Opinion
Weiwei Wu, Xiqin Ao and Wanjun Yao
School of Big Data and Artificial Intelligence, AnHui XinHua University, 555 Wangjiang St., Hefei, Anhui, China
Keywords: Data Mining, Big Data, Online Public Opinion, Nonlocal Kadomtsev-Petviashvili Equation, Partial-Rogue
Lump Ripple.
Abstract: There has been a tremendous rise in the growth of Chinese Microblog --- Sina Weibo in the past few years.
Sina Weibo contains many interesting popular issues. The mining of these vast amounts of data and the
corresponding mathematical models is an interesting question. In particular, the trend of some popular
topics can be described by the soliton wave model based on some hypothesis and parameter settings. The
evolution trend of the sub-events belonging to a super popular topic is stated by employing the partial-rogue
lump ripple solution theory of the nonlocal Kadomtsev-Petviashvili equation.
1 INTRODUCTION
Sina Weibo is a major Chinese microblogging
platform. It was founded in 2009 and has since
become one of the most popular social media
platforms in China, with millions of active users.
Weibo allows users to share posts, images, videos,
and more in real-time, similar to Twitter. However,
the platform is more open and allows for longer
posts, making it more suitable for discussions and
in-depth content. Weibo hashtags are also very
popular, often trending topics that users can follow
or participate in discussions around. One unique
feature of Weibo is its integration with traditional
media. Many news outlets and celebrities have
official accounts on Weibo, using it as a platform to
share news, updates, and interact with their
followers. This has made Weibo a powerful tool for
both information dissemination and social
commentary. In addition to its popularity in China,
Weibo has also gained a significant user base among
overseas Chinese and Chinese speakers around the
world. The platform offers multiple language
options, allowing users to switch between Simplified
and Traditional Chinese, as well as English and
other languages. Overall, Weibo is a dynamic and
vibrant social media platform that offers a window
into Chinese culture, society, and current affairs. It
continues to evolve and adapt to the changing needs
of its users, making it a must-follow platform for
anyone interested in understanding the Chinese
perspective.
The public opinion events are often reflected on
Weibo. Weibo is the most important observation
window for online public opinion. The study of
public opinion on Weibo has attracted a lot of
attentions[1-6]. It is worth mentioning that the
evolution and the control for the popular issues on
Sina Weibo public opinion is the main problem in
the research field. There exists such a popular topic
in online public opinion, which encompasses
numerous sub-events, each with a high level of
popularity. We can refer to this as a popular topic
matrix. We have discovered this trend in the popular
topic of the film "Full River Red". Then we use the
partial-rogue lump ripple solution theory of the
nonlocal Kadomtsev-Petviashvili equation to
describe the system and state the appropriate
complete strategic classifications.
This paper is organized as follows. The next
section deals with the partial-rogue lump ripple
waves in the development process of the popular
spots on Sina Weibo public opinion. The nonlocal
Kadomtsev-Petviashvili equation is introduced in
section 3, which is 2+1 dimension model. The
partial-rogue lump ripple solutions of the nonlocal
Kadomtsev-Petviashvili equation are also presented
in this section. Section 4 is devoted to conclusions
and discussions.
64
Wu, W., Ao, X. and Yao, W.
Data Mining and Mathematical Modeling in Big Data: Partial-rogue Lump Ripple Model on Sina Weibo Public Opinion.
DOI: 10.5220/0012879500004536
Paper published under CC license (CC BY-NC-ND 4.0)
In Proceedings of the 1st International Conference on Data Mining, E-Learning, and Information Systems (DMEIS 2024), pages 64-68
ISBN: 978-989-758-715-3
Proceedings Copyright © 2024 by SCITEPRESS – Science and Technology Publications, Lda.
2 DATA MINING
The film Full River Red is a suspense comedy
directed by Zhang Yimou and starred by Shen Teng,
Yiyang Qianxi, Zhang Yi, Lei Jiayin and Yue
Yunpeng. Full River Red was released in Chinese
Mainland on January 22, 2023. It was released in
North America on March 17th. Full River Red tells
the story of Qin Hui leading his troops to talk with
the Jin State four years after Yue Fei died in
Shaoxing of the Southern Song Dynasty. On the eve
of the meeting, the envoy of the Jin Dynasty died at
the prime minister's residence, and the secret letter
he carried disappeared without a trace. The story of
a soldier and the deputy commander of the personal
battalion who coincidentally become entangled in
this huge conspiracy. Prime Minister Qin Hui orders
the two to search for the culprit and the truth. Man
Jianghong's box office revenue reached 4.544 billion
yuan. Full River Red won the 36th China Film
Golden Rooster Award Award, the 18th China
Changchun Film Festival, the 30th University
Student Film Festival and other honorary awards.
This is a film that has achieved great success, but
also has a lot of controversy. After its official
release, Full River Red quickly became a popular
topic in online public opinion, with a lot of
controversial discussions related to it. Since its
release on January 22, 2023, with the box office of
the film Full River Red rising all the way, there have
also been public opinion disputes about it, including
the landmark events, namely, box office fraud,
plagiarism, prosecuting the social media influencers,
publicizing errors, cultural and creative peripheral
products disputes and so on. We will introduce the
landmark events of the Full River Red, which is a
popular topic of online public opinion.
Event 1. Box office fraud (BOF). On the evening
of January 24, 2024, a netizen reported that his
movie ticket for The Wandering Earth II was
returned by the cinema on the grounds of
"equipment failure", but the netizen found that Full
River Red was shown in the same screening hall at
the same time of the day. After the incident broke
out, some netizens questioned that Full River Red
might have bad competition behaviors such as
"stealing box office".
Event 2. Plagiarism (PLA). During the film's
popular release, some netizens questioned that the
film Full River Red copied the TV series Longmen
Escort Agency released in 2013. In addition to this
plagiarism controversy, there is also the issue of
plagiarism in the ending theme song. Han Hong, a
famous singer, is suspected of plagiarizing the song
"Look" at the end of the movie Full River Red.
Event 3. Prosecuting the social media influencers
(PSI). In the evening of January 28, 2024, the
official blog of Full River Red posted five blog posts
in succession, intended to respond to and clarify the
negative accusations of "box office fraud", "ghost
field", "plagiarism", "black screen" and other
negative accusations that continued to surround it.
Subsequently, the film company issued another
article announcing the lawsuit against the relevant
rumormongers. From the attached screenspopular, it
can be seen that the defendants are four internet
influencers.
Event 4. Publicizing errors (PCE). Because in the
prosecution, the official Weibo of the film Full River
Red used the "false" argument from Qin Hui to
refute the negative accusations, which attracted
netizens' ridicule, and other mistakes in its publicity
were also fermented. Some netizens have found that
the official blog post previously released, which
stated "Do not forget the shame of Jingkang" and
"loyalty and righteousness are yet to be exhausted,"
mistakenly disconnected the fixed term "Jingkang".
We found that the Full River Red poster produced
by Wanda Movie also had typos, in which simple
and complex characters were mixed, and the "hair
with rage" was written as rich, not "hair". In
addition, when the official Weibo celebrates the box
office breaking through 2.5 billion yuan, the use of
copywriting such as "Step through the Mountains
and Rivers, Celebrate the New Year" and the use of
Song Huizong's thin gold font to write the names of
the main actors are quite inappropriate.
Event 5. Cultural and creative peripheral
products disputes (CPD). On February 13, 2023, the
film Full River Red cultural and creative
surrounding crowdfunding project was launched.
Soon, netizens around the shelves complained about
"hell", like "around Qin Hui". For example, two
"Prime Minister's Tongling" incense expanding
stones based on the "Qin Hui Token" were named
"Yaoqin" and "Qingmei", which were the names of
the two female singers who died tragically in Qin
Hui's hands. In addition, a creative hourglass that
turns cherry red easily reminds people of the "Storm
Pavilion" where Yue Fei was wrongly killed. In
addition, unlocking Qin Hui's Q bookmarks in Fulili
has become a point of roast. On February 14, with
the relevant queries on the popular search, the film
Full River Red officially released a statement of off
shelf: "The crowdfunding activities of derivatives
around the film Full River Red have a deviation
from some netizens' understanding of the original
Data Mining and Mathematical Modeling in Big Data: Partial-rogue Lump Ripple Model on Sina Weibo Public Opinion
65
intention of product design and creativity, which has
had a bad impact on online public opinion. We
apologize for this and decide to off shelf the
crowdfunding activities.
We collected the newly added messages per 2 days
on Sina Weibo from January 22, 2023 to February
20, 2023. The followed table shows the data of the
three cases.
Table 1 (a): The data of the new messages per 2 days
(Unit: Thousand).
24 26 28 02 04 06 08
Event 1 9 35 130 326 371 763 962
Event 2 5 27 145 289 332 651 828
Event 3 0 0 22 87 259 354 787
Event 4 0 0 8 34 121 208 369
Event 5 0 0 0 9 25 89 126
Whole 14 62 305 745 1108 2065 3072
Table 1 (b): The data of the new messages per 2 days
(Unit: Thousand).
10 12 14 16 18 20
Event 1 868 687 471 352 324 219
Event 2 734 814 627 583 347 201
Event 3 587 231 152 149 67 25
Event 4 501 324 217 173 88 63
Event 5 342 405 268 231 97 65
Whole 3032 2461 1735 1488 923 573
Denote time by t. The following figure is used to
describe the variation of the six indexes as Whole
(general description of the film Full River Red) and
Event 1-5.
Figure 1: The trend of six indexes.
The Figure 1 illustrates that Full River Red
corresponds to multiple sub-topics within this
popular topic. However, this figure only reflects
their static data and does not reveal the underlying
evolutionary mechanisms. To further understand this
process, we will introduce nonlocal Kadomtsev–
Petviashvili equation to simulate it. Partial-rogue
lump ripple theory, one topic of the soliton theory, is
one of the most important areas fields of
mathematical physics. Today, soliton theory has
multiple applications in plasma physics, matrix
model of string theory, non-linear optics and light
wave communication technology.
3 PARTIAL-ROGUE LUMP
RIPPLE MODEL
3.1 Assumptions
(1) The selected popular topics diffuse in a plane,
i.e. the space of the evolution of the popular spot on
Weibo contains two variables x and y;
(2) The new daily messages about popular topics on
Weibo will be zero when
+∞→
t
. This
assumption is reasonable and very important, and
the reason will be further explained in the end of this
section.
3.2 Nonlocal Kadomtsev-Petviashvili
Equation Model
The nonlocal Kadomtsev-Petviashvili equation is
introduced in the form as
Note that
,
,
ˆˆˆ
xy
SSd
PPT
denotes parity with a shift of the space variable x
and y reversal with a delay, and
are
coefficient. The function
is the
amplitude of the wave of the popular topics as a
function of three real variables, space x, y and time t.
3.3 Solution of Nonlocal
Kadomtsev-Petviashvili Equation
Following Hirota's bilinear transform method for the
integrable equations, we can employ the variable
transformation as
() () ()
() () ()
12
12
12
ln ln ln ,
12
ln ln ln
xx xxt xxy
xx xxt xxy
Afbfbf
Bfbfbf
β
α
β
α
=++
=−−
(2)
(1)
DMEIS 2024 - The International Conference on Data Mining, E-Learning, and Information Systems
66
to transform the nonlocal Kadomtsev-Petviashvili
equation into Hirota’s bilinear form as
()()
22
43 0,
xt x t xxxx xxx x xx yy y
ff ff f f f f f ff f
βγ
−+ − + + −=
where
and are arbitrary constants and
, satisfying the following condition as
.
Then, the following Wronskian determinant are first
introduced
()
() ( )
() ( )
() ( )
()
11
11 1
11
22 2
12
11
,, , , .
N
k
N
kj
NN j
k
N
NN N
fW
x
φφ φ
φ
φφ φ
φφ φ φ
φφ φ
−
−
−
∂
== =
∂
More specifically, the nonlocal Kadomtsev-
Petviashvili equation admits the following solutions
𝑓= 𝑓
= 𝑎
,
, 𝑎
= 𝛿
+ 𝜓
𝑥
′
, 𝑦, 𝑡
𝜓
𝑥
′
, 𝑦, 𝑡
𝑑𝑥
′
with a range functions
and
satisfying
𝑖𝜓
,
−
−
𝜓
,
=0,𝜓
,
+4𝛽𝜓
,
=0,1≤
𝑘≤𝑁, 𝛾 <0, 𝑖𝜓
,
+
−
𝜓
,
=0,𝜓
,
+
4𝛽𝜓
,
=0,1≤𝑗≤𝑁, 𝑖
= −1,
where
is Kronecker function.
Taking
, we get the partial-rogue lump ripple
solution as
𝑓= 𝛿
+
∂
∂𝑥
𝜓
⋅
∂
∂𝑥
𝜓
𝑑𝑥
′
= 𝛿
+ 𝜎
12𝛽
48𝛽𝛾𝑡
𝐴𝑖
′
𝐻
−𝐻
𝐴𝑖
𝐻
+
𝜌
18
𝛽
𝑡
𝐻
𝐴𝑖
𝐻
−𝐻
𝐴𝑖
′
𝐻
−2𝐴𝑖
𝐻
𝐴𝑖
′
𝐻
,
where
is given as
()( )
1
2
3
14
33
18 4
.
24
jj
j
xxt yy
H
t
γ
γβ
−+−
=
The partial-rogue lump ripple solution is composed
of a range of lumps as shown in Fig. 2.
Figure 2: The time evolution at t=1/2,1,40.
As can be seen from the above figure, the evolution
trend of the partial-rogue lump ripple solution to the
nonlocal Kadomtsev-Petviashvili equation is closely
aligned with the popular topic of the film Full River
Red. Based on soliton theory, we provide a
mathematical explanation for the evolution trend of
Full River Red topic.
3.4 Application on Weibo
In this subsection, we turn back to the popular topics
on Weibo. Based on the the partial-rogue lump
ripple solution to the nonlocal Kadomtsev-
Petviashvili equation, the following conclusions are
worth to point out.
(1) The wave with the highest amplitude in
Figure 2(a) represents the overall popularity of the
super hit movie Full River Red, and the waves with
slightly lower amplitudes correspond to the sub-hot
topics. It can be seen that this partial-rogue lump
ripple solution aptly simulates the status of this
popular event.
(2) Figure 2(b) shows that the amplitude of the
smaller waves decreases but becomes more stable.
By comparison, it reflects the state of the popular
event after a period of development. The reason for
this is that after a certain period of time, netizens'
discussions mainly focus on the core sub-hot topics,
such as Event 1 to Event 5.
(3) The partial-rogue lump ripple solution to the
nonlocal Kadomtsev-Petviashvili equation tends to
zero when
+∞→
t
, it is consistent with the
assumption as the same as the evolution of the
popular topics on Weibo. As we know, A is the
variable describing the new messages per 2 days.
Indeed, the new messages about the popular issue on
Data Mining and Mathematical Modeling in Big Data: Partial-rogue Lump Ripple Model on Sina Weibo Public Opinion
67
Weibo will be almost zero after a long time. This
process is shown in Figure 2(c).
(4) The partial-rogue lump ripple solution of
nonlocal Kadomtsev-Petviashvili equationn shares
multiple solitons, i.e. several events could coexist in
the system at the same time. The popular online
public opinion topic of Full River Red reflects this
point.
(5) This equation also has a solution as shown in
following figures.
Figure 3: The time evolution at t=1,2.
When applied to the popular online public opinion
topic, it indicates that the overall event is relatively
strong and dominates the absolute popularity, while
the sub-events are weaker. The image corresponding
to the following solution is even more prominent.
Figure 4: The time evolution at t=1,2.
(6)From the soliton theory, the partial-rogue lump
ripple wave is once formed, and then it will continue
for a period. This result tells us that the popular
topics will keep be popular for several days
normally.
4 CONCLUSIONS
The partial-rogue lump ripple solution theory of the
nonlocal Kadomtsev-Petviashvili equation we
introduced provides a good description and
explanation of the popular topic of the film "Full
River Red" in online public opinion. This offers a
new perspective for understanding popular topics in
online public opinion.
ACKNOWLEDGEMENTS
This work is supported by Anhui Province Higher
Education Science Research Project under Grant No.
2022AH051870 and SK2021A0777.
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