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{{Paper
|id=Vol-1351/paper3
|storemode=property
|title=None
|pdfUrl=https://ceur-ws.org/Vol-1351/paper3.pdf
|volume=Vol-1351
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==None==
https://ceur-ws.org/Vol-1351/paper3.pdf
Social Mood Revealed
Bartosz Ziembiński
Polish Academy of Sciences, Warsaw, Poland,
b.ziembinski@phd.ipipan.waw.pl
Abstract. Social mood, the aggregated mood of a society, emerges from
complex system of individual moods and their influences on each other.
The real social networks consist of millions or even billions nodes con-
stantly interacting with each other. Can such a complex system be mod-
eled by a graph consisting of a small number of agents with simple in-
teractions between them? Profile of Mood States, known and well-vetted
psychometric instrument, distinguishes seven mood dimensions (Tension,
Happiness, Calmness, Vigor, Fatigue, Confusion and Friendliness). If we
apply them to a society at large, i.e. to social mood, is it possible to
measure influences of one mood dimension on another? In addition to
this, is it possible to both maintain good approximations of social mood
changes and be able to observe such interactions at the same time? In
this work we investigate these questions and propose a framework which
can approximate or even, in some circumstances, be predictive of future
social mood states. The framework consists of a model of social influ-
ence and an evolutionary algorithm learning proper network topology
and model parameters.
Keywords: Social Mood, Collective Emotions, Social Networks, Social
Influence, Agent-Based Modeling, Complex Systems, Social Simulation,
Sentiment Analysis
1 From individual to social mood
From the psychological research it is known that the emotional state, as well as
the amount of information, play the main role in human decision-making [11,
9]. Traditionally, in theoretical considerations, the second factor played a more
important role. For instance, rational choice theory, economical perspective that
perceives people as rational actors, explains decision-making process through the
paradigm of utility maximization [13]. Agents base their actions on pragmatic
calculations of their best interests.
However, emotions can profoundly affect human decision-making process as
well, in many cases driving an individual to make a choice that seems ”irrational”
in the framework of said theory. For example, behavioral finance has provided
proofs stating that financial decisions are significantly affected also by emotion
and mood and not only by rational utility maximization [23]. Damasio states
that personally beneficial decision making requires emotion as well as reason [9].
He also proposed the somatic marker hypothesis, that describes a mechanism by
which emotional processes can guide (or bias) behavior [5]. Pfister and Böhm
have developed a classification of how emotions function in decision-making,
that conceptualizes an integral role for emotions, rather than simply influencing
decision making [29].
Thus, emotions affect individual choices and decisions. Does this also apply to
larger groups of people, i.e. can societies experience mood states that affect their
collective decision making? Prechter’s socionomic hypothesis suggests that the
social mood drives various types of social action in the areas of cultural, political
and financial behaviour [30]. However, assuming that the social mood affects
the society behaviour analogously to the way in which one’s emotions drive
his individual actions is quite unreasonable. The society is a complex system
with its emergent properties. The social mood, as a state of the whole system, is
something different than just a simple sum of its parts [2]. Therefore, researchers
attention has been focused on finding the relations between the social mood and
the behaviour of societies [23, 26, 6, 31].
The first problem with such investigations is to actually find a way to mea-
sure the social mood. Large surveys of public mood are generally expensive and
difficult to undertake. That is why there were proposed some ways to assess
the social mood indirectly. For example: from the results of football games [12]
and from weather conditions [18]. Recently though, researchers came up with
other, low-cost and very efficient, way to measure the public mood. They were
able to do it through sentiment analysis of social media content such as Twitter
feed, discussion forums or blogs [27, 34, 33]. Social mood measured by means of
Twitter turned out to be predictive of many social phenomena including stock
market [7], political elections [15, 25], box-office revenues for movies [3] etc. If
social mood can be related or even predictive of so many social matters, it is
important to have better ways to analyze it and to understand its behaviour.
In this paper we propose a framework that can translate huge, highly com-
plicated social network (of individual moods and their influences on each other)
to a fairly simple and an order of magnitude smaller graph of agents. It behaves
in a similar manner to the real network concerning dynamics and interactions of
the mood dimensions. The translated network can be then more easily analyzed.
Such a framework enhances the state of the art of social sciences, offering a
tool to measure and to interpret social mood and the interactions between the
mood dimensions. Its novelty is provided by its data-driven approach. Most of
the social influence models employ bottom-up methodology: begin with simple
rules (of agents interactions), then observe the emergent behaviour of the system
[14, 32, 24, 19, 16, 10]. The goal of such investigations is to examine how the model
behaves given particular assumptions. The model, however, may or may not re-
flect a real-life social system. We believe that we propose more holistic approach.
It consists of two stages. We begin with measuring the actual social mood by the
means of the real-world data. Then we tune our highly customizable model of
social influence to reflect these measurements. This way we provide not only the
theoretical considerations, but also a model that can indeed approximate social
mood changes, that are happening in a day-to-day reality. On the other hand,
it is not just a numerical approximation - the construction of the model enables
one to investigate the interactions between agents, representing different mood
dimensions. To the best knowledge of this paper’s authors, models of mood di-
mension interactions have not been proposed in the scientific literature so far.
The same is for data-driven models of social influence. Therefore, the proposed
framework might be of a great interest for social scientists.
The paper is structured as follows. In Section 2 we describe our framework.
Firstly, we explain how we assess the social mood. Then, we describe our model
of social mood. The description involves a model of social influence and an
evolutionary algorithm aiming to find the best network topology and model
parameters. Section 3 describes the empirical experiments that were conducted.
In Section 4 we discuss the results of the experiments. We draw final conclusions
in Section 5.
2 Social mood translation
In a real world people affect each others individual emotional states during com-
munication. If we sum those individual emotional states up, we will receive a
global measure called social mood. The question is, if we can replace the real so-
cial network of emotional influences with its model, say with a number of nodes
two times smaller? And at the same time be able to maintain similar dynamics
of mood influences and good approximation of a global mood state? Then, could
we create a model four times smaller? How small could that model be? It is clear
that the smaller it is, the easier it would be to analyze it and to understand its
dynamics.
In this paper we propose a framework, which is able to translate huge com-
plex social network of individuals to a simple graph with fixed, small number
of nodes (not more than 50 nodes). In this graph each node is an agent which
is a representation of a class of individuals in the original network. Every agent
apart from its mood state, has its own level of impressionability and influence.
Respectively, these are the measures of how much an agent is sensitive to influ-
ence of others and how influential it is. The edge between nodes denotes their
ability to affect each other. The values of parameters and the topology of the
graph is determined by data-driven evolutionary algorithm which approximates
the social mood time series.
The next two subsections will describe the framework in detail. First, we will
describe how we measure social mood and then, how model of its dynamics is
constructed.
2.1 Assessing the social mood
We measure social mood by analyzing Twitter feed in terms of 7 mood dimen-
sions. We list them here (with explanation of what does, respectively, the low
and high score of each dimension mean):
1. Tension - relaxed or anxious,
2. Happiness - happy or depressed,
3. Calmness - calm or angry,
4. Vigor - apathetic or vital,
5. Fatigue - rested or tired,
6. Confusion - sure or confused,
7. Friendliness - aloof or kind.
We use similar mood dimensions and methodology of assessing the public mood
to the one used in [7] (namely Profile of Mood States). The motivation behind
this is that we believe we should measure social mood in more than just one
classic dimension (positive vs. negative) to obtain some number of potentially
different aspects of public mood. The efficiency of this sentiment tracking tool
was cross-validated against big socio-cultural events like the U.S presidential
election (November 4, 2008), Thanksgiving (November 27, 2008) etc. [7, 6]. In
addition to this, in [7] authors find an accuracy of 87.6% in predicting the daily
up and down changes in the closing values of the Dow Jones Industrial Average
index, which indicates that the classification can have good practical applica-
tions.
Data We recorded a collection of public tweets which were posted during 14 days
from July 7th to July 20th, 2014. We were interested only in tweets expressing
author’s mood state, thus we only tracked tweets containing words: ”feel” and
”feeling” (20,110,489 tweets). For each post, we obtained its date and time of
submission, as well as the content of the message (which is a text limited to 140
characters).
One can have an impression that the dataset is particularly small (14 days),
concerning the fact that in other papers datasets can span over several months.
The difference, though, is in temporal resolution of the datasets. Whereas re-
searchers usually measure social mood in terms of days, in this work we measure
it every 5 minutes. We do it to be able to observe the intraday dynamics of
collective emotions and to be able to track the microchanges in social mood. We
believe that such investigations may be helpful, for instance, for financial intra-
day traders, for trading algorithms or for people responsible for communication
and public relations. If we compare the sizes of the datasets, we will obtain
14d × 24h × 12 = 4032 time intervals for our dataset. In this paper experiments
were conducted for time periods between 09:30 and 16:00 EST from Monday till
Friday, as these are the times when New York Stock Exchange is opened. This
gives us 10d × 6.5h × 12 = 780 time slots. On the contrary, if we take a daily
resolution into consideration and, say, we will have a dataset of 9 months, it
gives us around 9m × 31d = 279 time intervals.
Another fact is that the volume of tweets posted nowadays is much greater
than it used to be in the past. In this paper we collected 20,110,489 tweets during
14 days and in [7] authors collected 9,853,498 tweets during over 9 months.
Generating social mood time series In order to obtain a mood score of a
tweet we compare each word from a tweet against each word from a lexicon of
so called emotional words. The lexicon is derived from an existing psychometric
instrument, namely the Profile of Mood States (POMS) [22]. It is known and
well-vetted psychometrical instrument used to measure one’s emotional state. It
consists of 65 adjectives describing the mood state which are linked with different
emotional dimensions. The examined person has to refer to these adjectives on
a five-point scale.
To create a computational version of the test, we expand the basic lexicon
of 65 adjectives from POMS with similar words, which we obtain by analysing
word co-occurrences in big collections of texts. The expanded lexicon consists
of 965 associated terms which are collected in the following procedure. We use
Bing search engine to query for phrases ”is [adj] and” and ”was [adj] and”,
where [adj] denotes a particular adjective from the original lexicon which we
want to find similar words to1 . For each of the queries, we download first 200
results. For each result, we extract the word after conjunction and. Then we sort
extracted words by most frequent occurrences. From the most frequent words
we choose similar adjectives by hand. The advantage of querying search engines
is that they are a relatively simple way of searching over a large collection of
documents. Moreover, it also enable us to retrieve similar words which actually
are in use.
Having the lexicon of emotional words, the social mood of Twitter feed is
measured in the following way. Tokenization is performed on each tweet and
then each word from a tweet is compared with each adjective from the lexicon.
If there is a match, the adjective from the lexicon is mapped back to its original
POMS term and via the POMS scoring table to its respective POMS dimension.
Then, a counter of corresponding dimension is incremented by one.
To obtain a social mood time series we split our collection of tweets into
groups of messages sent in 5 minutes long time periods. For each hour H, we
distinguish time intervals: [H:00, H:05), [H:05, H:10), ..., [H:55, H + 1:00). Then
for tweets from each of such time intervals, we employ our mood measuring
procedure. At the end, we obtain times series:
M = {Mt : t ∈ T } (1)
where t corresponds to successive time intervals and
Mt0 = [d0t,1 , d0t,2 , ..., d0t,7 ] (2)
where, d0t,1 , d0t,2 , ..., d0t,7 ∈ N are values of respective mood dimensions: Tension,
Happiness, Calmness, Vigor, Fatigue, Confusion and Friendliness.
For our social mood time series not to be dependent on the volume of tweets
in a given period of time, we then normalize the values of mood dimensions in
the following way. For each mood dimension dt,i , i ∈ 1, 2, ..., 7:
d0t,i
dt,i = P7 0
(3)
j=1 dt,j
1
Bing search engine distributes a dedicated API. For the details visit
http://www.bing.com/dev/en-us/dev-center.
Obtaining final elements of social mood time series:
Mt = [dt,1 , dt,2 , ..., dt,7 ] (4)
All mood times series in the rest of the paper are normalized in the same manner.
2.2 Model of social mood
Real-world social mood networks consist of big number of people, each of them
having their own mood state. These people can interact with their acquaintances,
affecting their moods, as well as being affected by them.
Therefore, if we want to translate such a network to a smaller graph, we need
to find a way to model 3 things:
1. Collective mood state of individuals - mostly, we already have it done. We
model it with 7-dimensional vector like in equation (4).
2. Topology of the social network - we need to find a way to translate the
connections between nodes in a big social network to analogous connections
in a small graph.
3. Social influence - we need to build a model of how agents are affecting each
others mood states in a small graph.
We will start with approaching the topology issue, then we will describe our
model of social influence and finally we will present the evolutionary algorithm
which aims to find the best topology and influence parameters. All these com-
ponents will, in the end, describe our framework.
Topology of the network We use evolutionary approach to find the best
network topology (as well as other parameters of the model). This choice is
made, because we want the algorithm:
– to be population-based - in order to be able to compare obtained solutions
at any time of the algorithm run,
– to be anytime - meaning that it can return a valid solution, even if it is
interrupted before it ends,
– not to make any assumptions about the topology and the parametrs of the
model.
However, evolutionary algorithm needs initial population in which topologies
are somehow constructed. To model the social network in the beginning stage of
the evolution, we decided to use two classes of graphs.
First class are random graphs. We believe that they are the simplest and the
most natural way to initialize network topologies, concerning the fact that we
take advantage of an evolutionary approach. To construct the particular graph,
first we draw p ∈ (0, 1) from the uniform distribution. Then, every possible edge
occurs independently with the probability p.
Second class consists of scale-free graphs, which are graphs whose degree
distribution follows the power law. The motivation behind this choice is that
many real-world social networks, as well as cyberspace networks, are conjectured
to be scale-free [4, 17, 8]. To generate graphs, whose node degrees follow the
power law distribution, we used Barabási-Albert model [1]. The algorithm uses
a preferential attachment mechanism, which means that the more connected a
node is, the more likely it is to receive new links. More formally, the probability
pi that the new added node is connected to the pre-existing node i is:
ki
pi = (5)
Σj kj
where ki is the degree of node i and the sum is made over all pre-existing
nodes j.
Model of social influence There exists a multitude of social influence models
in the sociophysics literature. They can be classified into discrete (including bi-
nary) models and continuous models depending on the representation of opinions
that are being influenced.
The typical discrete models include Ising model [14], Sznajd model [32], social
impact model [24], voter model [19], etc. These descriptions of social influence,
sometimes called the toy models, are useful for simplifying the opinion dynamics
explanations (e.g. using the temperature notion to introduce the stochastic be-
haviour [14] or proposing United we Stand, Divided we Fall rule to implement
the phenomenon of social validation [32] etc.). However in our case, the draw-
back of these models is their discrete nature, because our measurments of the
social mood have continous characteristic.
This fact brings our attention to the continuous models, that mainly include
Hegelsmann-Krause model [16], Deffuant-Weisbuch model [10] and their numer-
ous variants and extensions [28, 20, 21, 35]. These approaches, however, also pos-
sess some limitations, as far as our work is concerned. Some of them assume
bounded confidence of agents, which means that the agent adjusts its opinion
only towards the opinions that are not very distinct (that lay in the -interval
around the agents’ opinion) [10, 21, 35]. As we want to model interactions be-
tween mood dimensions, this approach is not suited for our case (for instance a
state with high value of Happiness may affect a state with low value of Friend-
liness). Other drawback is that some of the models assume influence dynamics,
that leads to a consensus [21, 16, 28]. Consensus is not a typical feature of many
social situations, neither is it a typical state of the mood dimensions dynamics.
Mood dimensions do not tend to average themselves and often tend to differenti-
ate (e.g. low value of Happiness and high value of Tension). Our model need to
have a way to describe this phenomena. Another feature that it should possess
is the ability to describe the fact that agents may not always be easily influenced
by others.
Therefore, we propose our own model of social influence, which is similar
to Hegelsmann-Krause model, but also introduces some major differences. They
enable us to model the characteristics of mood dimensions dynamics, which we
just mentioned. It is defined as follows:
1. A = {1, 2, ..., n} is the set of agents.
2. Each agent i, at discrete moment in time t, has its own mood state:
Mi,t = [di,t,1 , di,t,2 , ..., di,t,D ] (6)
where di,t,k ∈ R and D is a constant denoting the number of mood dimen-
sions2 .
3. Each agent i, at discrete moment in time t, knows if each of its mood di-
mensions increased or decreased during the last time step:
∆i,t = [∆i,t,1 , ∆i,t,2 , ..., ∆i,t,D ] (7)
where ∆i,t,k ∈ R and ∆i,t,k = di,t,k − di,t−1,k , for t > 0. For each agent i
first element of the sequence ∆i is specified at the beginning:
∆i,0 = [ai,0,1 , ai,0,2 , ..., ai,0,D ] (8)
where ai,0,1 , ai,0,2 , ..., ai,0,D are specified initial values.
4. Each agent i has its level of:
– inf luence ϕi ∈ [0, 1], which denotes how much it is affecting others,
– impressionability δi ∈ [0, 1], which denotes how much it is being affected
by others.
5. Agents are organized in the network N = (A, E), where E is a set of con-
nections or edges, which are 2-element subsets of the set A.
6. Sequence of agent’s mood states is specified as follows. For each agent i:
– First element of the sequence is specified at the beginning:
Mi,0 = [bi,0,1 , bi,0,2 , ..., bi,0,D ] (9)
where bi,0,1 , bi,0,2 , ..., bi,0,D are initial values.
– Elements of the next time steps t > 1 are defined using a recursive rule.
For each mood dimension di,t,k , k ∈ 1, 2, ..., D:
di,t,k = di,t−1,k + δi di,t−1,k Σj sgn(∆j,t−1,k )ϕj (10)
where the sum is made over all agents j connected to the agent i (indi-
cated by the set E).
7. The global social mood state, at each discrete moment in time t, is defined
as a sum of agents’ mood states:
Mt = Σi∈A Mi,t (11)
Thus, in the model in every discrete time step t part δi of agent’s i mood
can be affected by its neighbours. If their particular mood dimension went up in
the previous time step, the neighbours will try, taking their influence parameters
ϕ into consideration, to increase it. In other case, analogously, they will try to
decrease it.
2
In this paper D = 7.
How to construct the model from Twitter data? We only described ag-
gregated social mood M = {Mt : t ∈ T } acquired from Twitter data so far.
However, to be able to use it in our model of social influence, we need split
data. To achieve this, the idea is to split tweets into some kind of equivalence
classes associated with mood dimensions. The agents then are not representa-
tives of individuals, but representatives of mood dimensions. The easiest way to
achieve this is to employ the mood measuring procedure for each tweet, identify
its dominant mood dimension (the dimension with the highest score) and then
classify the tweet as Tension, Happiness, Calmness, Vigor, Fatigue, Confusion or
Friendliness representative. If there is more than one dimension with the high-
est score, classify the tweet randomly as a representative of one of its dominant
dimensions.
Using this procedure, we can obtain decomposition of tweets into seven dif-
ferent groups associated with mood dimensions. We can then couple each group
i ∈ {1, 2, ..., 7} with different agent, obtaining corresponding mood time series:
Mi = {Mi,t : t ∈ T } (12)
Having agents as representatives of mood dimensions, we can then apply our
social influence model to observe how different dimensions are influencing each
other. This way, we obtain a graphical representation of influence dynamics. In
this approach the influence of one mood dimension on the other is not based
on the actual Twitter social graph or other kind of individuals topology. The
influence is measured on the macro level, the same way that in a society op-
timists have an influence on pessimists or electorate of one political party has
an influence on the other electorate. The influence is measured as the change in
aggregated sum of micro-interactions among the individuals.
On the other hand, conducting such a simulation (running the model), we
are able to calculate mood estimators M d i,t - set of vectors of mood scores of
every agent i, in every time step t. Those estimators can be then summed to
obtain global social mood estimator M ct . It is then easy to assess how good is our
estimation (and all in all - simulation) calculating the mean absolute percentage
error (MAPE):
t∈T c
1 X |M t − Mt |
M AP E = (13)
|T | t Mt
We choose MAPE as a measure of performance of our simulations, because
we need to compensate for two things:
1. scores of some mood dimensions are usually much greater than scores of
other mood dimensions - therefore, we need percentage error to measure
performance of all dimensions approximations,
2. the values of estimators may be greater or less than actual mood score -
therefore, we need to measure error in absolute values.
Another thing is that, as the experiments showed, only seven agents in the
model may not be a sufficient number to approximate the global social mood M
well. We may therefore want to have more than just one representative of each
mood dimension. To achieve this, we introduce splitting parameter S. We then
employ the same grouping procedure to tweets set as before, but after obtaining
seven groups for seven different mood dimensions, we split each group into S
smaller groups of the same size. In this paper S ∈ {1, 2, ..., 5}, therefore we
conducted experiments for numbers of 7, 14, 21, ..., 35 agents in the model.
Evolutionary algorithm The main parameters that need to be adjusted in
social mood model to reflect the real-world data are the network topology, ∆0 ,
ϕ and δ parameters of the agents. In our approach, we start with a random
graph or scale-free graph network topology (with the same probability), random
values of ∆0 vector generated independently from [-1,1] interval and random
values of ϕ and δ parameters generated independently from [0, 1] interval. Then,
we adjust these parameters using an evolutionary algorithm which is defined in
the following way.
We start with population of P = 100 randomly generated models of social
mood3 . For each model we conduct the simulation and calculate the mean ab-
solute percentage error (MAPE). M AP E = [M AP E1 , M AP E2 , ..., M AP E7 ] is
also a vector, because there are 7 mood dimensions, so we calculate the mean
value of this vector coordinates obtaining our final error Er.
7
1X
Er = M AP Ei (14)
7 i=1
We then sort our models ascending by the value of Er and build next gen-
eration of models in the following way. The m fittest models (where m is equal
to 50% in our simulations) are retained in the next generation and the others
are discarded. A single mutated copy is made of each remaining model so that
the size of the population always remains constant. Mutations are applied to
r agents from a particular model (where r is equal to 10%) and can take four
forms with equal probability:
1. The agent receives new values of inf luence ϕ and impressionability δ pa-
rameters. They are generated independently and randomly from [0, 1] inter-
val.
2. A new link in the network is added between the agent and different, randomly
chosen agent.
3. An existing, randomly chosen link of the agent is removed from the network.
4. The agent receives new values of ∆0 vector. They are generated indepen-
dently and randomly from [−1, 1] interval.
After G generations, we obtain the model with the least error Er which is
the best fit to the data.
3
Some parameters of the evolutionary algorithm are constrained (eg. P = 100, m =
50%, r = 10%). The values were handpicked to optimize the performance.
3 Experiments
In order to evaluate the framework, the experiments are conducted to see how
well can it approximate the social mood changes and predict the future values
of social mood.
3.1 Approximations of mood changes
To evaluate the quality of the framework’s approximations of social mood changes,
for each value of the splitting parameter S and for the number of generations
G = 300, we test it on 60 one-hour-long time intervals. They span across 10
days in July 2014, from 7th till 11th and from 14th till 18th. The periods of
time lay between 9:45 and 15:45 EST, as this is the time when New York Stock
Exchange is opened (actually it is 9:30 - 16:00, but first and last quarters are
the most unstable, that is why we do not want to include them). Much of the
research on social mood and electronic sentiment is focused on finding financial
applications, therefore we wanted to follow that trend. Each time period starts
at [H:45, H:50), which is the starting point, and then there are 11 time intervals
that are approximated [H:50, H:55), [H:55, H + 1:00], ..., [H + 1:40, H + 1:45).
Thus, we test the approximation on 10d × 6h × 11 = 660 time slots. The results
can be seen in the Table 1. They were obtained against a benchmark of G = 300
generations in the evolutionary algorithm. These outcomes can be further im-
proved if the computations are longer (e.g. for S = 1 we can achieve 2 percentage
point better results if we set G to 600).
Table 1. Two tables present mean value, median and standard deviation of: approxi-
mation MAPEs (on the left-hand side) and prediction MAPEs (on the right-hand side),
for each value of the splitting parameter S.
S Mean Median SD S Mean Median SD
1 10.69% 9.45% 4.05 1 18.63% 17.55% 8.32
2 10.11% 8.99% 3.84 2 28.38% 22.90% 17.56
3 9.49% 8.72% 3.64 3 27.75% 21.85% 16.24
4 9.49% 8.74% 3.22 4 27.30% 25.63% 12.44
5 9.19% 8.49% 3.29 5 28.30% 23.70% 14.74
3.2 Predictions of mood changes
In order to evaluate the predictive power of the models, for each value of the
splitting parameter S and for each model computed in previous subsection be-
tween 9:45 and 14:45 EST, we predict twelve following five-minutes-long time
intervals. Therefore, on each of ten days, for five different starting hours, we pre-
dict twelve time intervals. Thus, in our experiment we predict 10d×5h×12 = 600
time slots. The results can be seen in the Table 1.
4 Discussion
The comparison of social mood approximations for different values of the split-
ting parameter S confirms the intuitive anticipation that the larger the value is,
the better are the approximations (in a matter of fact concerning all comparison
indicators: mean, median and standard deviation). One could suspect this fact.
In larger graphs there are more agents and more connections among them. Thus,
it can be easier for the model to tune to the data. On the other hand, the person
studying the graphical model would like to have as small network as possible.
They are then easier to analyze and to understand. As the experiments show,
the approximations of the models with smaller splitting parameters are worse
by around one percentage point. In most cases, this should still be a satisfactory
level of error, which one can accept for the sake of the clarity of the graphical
model.
As far as the predictive power of models is concerned, the problem with social
mood assessed by the means of Twitter is that this kind of system is not closed.
In other words, external factors affect the social mood on Twitter, and not only
users influence each other. Therefore, prediction power of a particular model is
limited by the way of how the next time interval is similar to the previous one
in terms of mood changes dynamics.
During our experiments the predictive power of models with the splitting
parameter S = 1 turns out to be the best, even though they are not the best
fit to the data. Most probably it is due to the overfitting of models with greater
splitting parameter. In addition to this, in case of S = 1 there is no noise created
by the interactions between the representatives of the same mood. In the Figure
1, MAPEs of ten predicted time intervals for different values of S are presented.
One can notice said smaller amounts of noise for S = 1.
Topologies of the evolved networks are something that could be a topic of
a separate investigation. From the models that we obtained during our experi-
ments, we can state that they are different for different moments of time, con-
cerning not only their shapes but also their parameters. These facts are not
surprising and are probably due to the fact that in different moments of time
people were exposed to different external factors. The question of what kind of
social situation causes which kind of network topology would be an interesting
issue for the future research.
From our conclusions about topologies, first notable fact is that, during the
evolution, bigger networks lose their ”scale-free property” (understood as a de-
gree distribution following the power law in a graph which is not infinite). Some
models’ degree distributions look quite similar to the distributions following the
power law, but still are disturbed. Rest of the networks turn into more random
graphs.
Another fact concerning bigger networks produced by the algorithm (with
S > 2) is that they are not really easy to read and analyze. Each mood dimension
have a few representatives, but usually only some of them are connected to
others. It is not clear how someone should interpret such a graph. We can say
that only part of the people with particular dominant mood dimension is engaged
Fig. 1. Figure presents MAPEs of ten predicted time periods for different values of the
splitting parameter S.
in interactions, but still conclusions are chaotic. Another issue is the interaction
between representatives of the same mood dimension. The aim of the framework
is to translate the complexity to something simple. It is not obvious if bigger
networks can make that much of a simplification.
This brings our attention to smaller networks. Small graphs, with only one
representative for each mood dimension (S = 1), do not possess the problems
stated above. They also have bigger predictive power of social mood changes
(only the approximation is a little bit worse, but as it was stated earlier - it is
satisfactory). Thus, we may recommend them as a better source of information
and a better tool to investigate social mood. We can see an example of such a
network in Figure 2.
5 Conclusion
In this paper, we investigate whether a complex network of individual emotions
influencing each other can be approximated by a small graph with similar prop-
erties. Our experiments show that small networks can indeed approximate social
mood with reasonable mean absolute percentage errors ranging from 9.19% to
10.69%. These results can be further improved using longer computations. Our
studies show also that if the following period of time is similar to the previous
one, meaning that it is not affected by big amount of external factors, models
can be even predictive of the future social mood states. The models with the
Fig. 2. Figure presents a simple graph (graphical model for case of S = 1) in which each
node is an agent representing one of the mood dimensions: 0 - Tension, 1 - Happiness,
2 - Calmness, 3 - Vigor, 4 - Fatigue, 5 - Confusion and 6 - Friendliness. Values of
impressionability parameters are presented inside of the nodes. Influence parameters
are placed next to the edges.
splitting parameter S = 1 can predict following twelve intervals of time with
mean MAPE = 18.63%.
In the literature, there are hardly any data-driven models of social mood
dynamics, as well as data-driven models of social influence (there are models of
these phenomena, but they are not data-driven). Thus, our attempt proposes
quite complete framework of assessing and analyzing social mood based on the
real-world data. One could argue, that other techniques could be used to ap-
proximate/predict social mood like Markov Models, Conditional Random Fields
etc. Although, the benefit of our approach is that it creates ”the map” of inter-
actions between the mood dimensions. We are able to notice which dimension
is connected to which one. We can therefore infer where the influences are and
how strong they are (looking at the values of influence and impressionability
parameters).
Presented framework may be useful in situations where quick information
about emotion dynamics is needed. For instance, for people responsible for com-
munication or public relations. Different situations may include, for example,
financial intraday trading: algorithmic as well as conducted by human. On the
other hand, when the temporal resolution of mood measurements is changed to
longer periods of time, like days for instance, the framework can also be useful
for long-term analysis of social mood dynamics. Such investigations might be of
high interest for variety of institutions monitoring societies.
As far as future work in concerned, one can notice, that during the evolution
most of the networks lose their scale-free property. Therefore, it is not clear if this
is a good starting point of evolutionary algorithm. One could consider different
initial topologies. Another interesting question is what types of graphs are being
produced by the framework. Is it a single class or a group of them?
Apart from further work on the framework itself or studying types of networks
that it produces, there are also issues more of a sociological nature. One could
investigate whether different network topologies and model parameters are some-
how related to the nature of real-world social events. We hypothesize that deeper
studies of graphs’ ”shapes” and distributions of influence/impressionability mea-
sures can give interesting conclusions about society dynamics, as well as reflect
its qualitative properties. Such correlations between social reality and topologies
of small graphs could be of a great interest for social scientists.
6 Acknowledgments
The paper is cofounded by the European Union from resources of the European
Social Fund. Project PO KL ”Information technologies: Research and their in-
terdisciplinary applications”.
References
1. R. Albert and A.-L. Barabási. Statistical mechanics of complex networks. Reviews
of modern physics, 74(1):47, 2002.
2. P. W. Anderson. More is different. Science, 177(4047):393–396, 1972.
3. S. Asur and B. A. Huberman. Predicting the future with social media. In Web
Intelligence and Intelligent Agent Technology (WI-IAT), 2010 IEEE/WIC/ACM
International Conference on, volume 1, pages 492–499. IEEE, 2010.
4. A.-L. Barabâsi, H. Jeong, Z. Néda, E. Ravasz, A. Schubert, and T. Vicsek. Evo-
lution of the social network of scientific collaborations. Physica A: Statistical me-
chanics and its applications, 311(3):590–614, 2002.
5. A. Bechara and A. R. Damasio. The somatic marker hypothesis: A neural theory
of economic decision. Games and economic behavior, 52(2):336–372, 2005.
6. J. Bollen, H. Mao, and A. Pepe. Modeling public mood and emotion: Twitter
sentiment and socio-economic phenomena. In ICWSM, 2011.
7. J. Bollen, H. Mao, and X. Zeng. Twitter mood predicts the stock market. Journal
of Computational Science, 2(1):1–8, 2011.
8. A. Clauset, C. R. Shalizi, and M. E. Newman. Power-law distributions in empirical
data. SIAM review, 51(4):661–703, 2009.
9. A. Damasio. Descartes’ error: Emotion, reason and the human brain. Random
House, 2008.
10. G. Deffuant, D. Neau, F. Amblard, and G. Weisbuch. Mixing beliefs among inter-
acting agents. Advances in Complex Systems, 3(01n04):87–98, 2000.
11. R. J. Dolan. Emotion, cognition, and behavior. Science, 298(5596):1191–1194,
2002.
12. A. Edmans, D. Garcia, and Ø. Norli. Sports sentiment and stock returns. The
Journal of Finance, 62(4):1967–1998, 2007.
13. M. Friedman. Essays in positive economics. University of Chicago Press, 1953.
14. S. Galam, Y. Gefen, and Y. Shapir. Sociophysics: A new approach of sociological
collective behaviour. Journal of Mathematical Sociology, 9(1):1–13, 1982.
15. D. Gayo-Avello, P. Metaxas, and E. Mustafaraj. Limits of electoral predictions
using Twitter. International AAAI Conference on Weblogs and Social Media, 2011.
16. R. Hegselmann and U. Krause. Opinion dynamics and bounded confidence models,
analysis, and simulation. Journal of Artificial Societies and Social Simulation, 5(3),
2002.
17. D.-I. O. Hein, D.-W.-I. M. Schwind, and W. König. Scale-free networks.
Wirtschaftsinformatik, 48(4):267–275, 2006.
18. D. Hirshleifer and T. Shumway. Good day sunshine: Stock returns and the weather.
The Journal of Finance, 58(3):1009–1032, 2003.
19. R. A. Holley and T. M. Liggett. Ergodic theorems for weakly interacting infinite
systems and the voter model. The annals of probability, pages 643–663, 1975.
20. E. Kurmyshev, H. A. Juárez, and R. A. González-Silva. Dynamics of bounded con-
fidence opinion in heterogeneous social networks: Concord against partial antag-
onism. Physica A: Statistical Mechanics and its Applications, 390(16):2945–2955,
2011.
21. J. Lorenz. Heterogeneous bounds of confidence: Meet, discuss and find consensus!
Complexity, 15(4):43–52, 2010.
22. D. McNair, M. Lorr, and L. Droppleman. Profile of mood states. San Diego, CA:
Educational and Industrial Testing Service., 1971.
23. J. R. Nofsinger. Social mood and financial economics. The Journal of Behavioral
Finance, 6(3):144–160, 2005.
24. A. Nowak, J. Szamrej, and B. Latané. From private attitude to public opinion: A
dynamic theory of social impact. Psychological Review, 97(3):362, 1990.
25. B. O’Connor, R. Balasubramanyan, B. Routledge, and N. Smith. From tweets to
polls: Linking text sentiment to public opinion time series. International AAAI
Conference on Weblogs and Social Media, 2010.
26. K. R. Olson. A literature review of social mood. The Journal of Behavioral Finance,
7(4):193–203, 2006.
27. A. Pak and P. Paroubek. Twitter as a corpus for sentiment analysis and opinion
mining. In LREC, 2010.
28. Z. Pan. Trust, influence, and convergence of behavior in social networks. Mathe-
matical Social Sciences, 60(1):69–78, 2010.
29. H.-R. Pfister and G. Böhm. The multiplicity of emotions: A framework of emotional
functions in decision making. Judgment and Decision Making, 3(1):5–17, 2008.
30. R. R. Prechter Jr. Whats going on? Pioneering studies in socionomics, page 1,
1979.
31. W. M. Rahn, B. Kroeger, and C. M. Kite. A framework for the study of public
mood. Political Psychology, pages 29–58, 1996.
32. K. Sznajd-Weron and J. Sznajd. Opinion evolution in closed community. Interna-
tional Journal of Modern Physics C, 11(06):1157–1165, 2000.
33. M. Thelwall, K. Buckley, and G. Paltoglou. Sentiment strength detection for the
social web. Journal of the American Society for Information Science and Technol-
ogy, 63(1):163–173, 2012.
34. M. Thelwall, K. Buckley, G. Paltoglou, D. Cai, and A. Kappas. Sentiment strength
detection in short informal text. Journal of the American Society for Information
Science and Technology, 61(12):2544–2558, 2010.
35. D. Urbig, J. Lorenz, and H. Herzberg. Opinion dynamics: The effect of the number
of peers met at once. Journal of Artificial Societies and Social Simulation, 11(2),
2008.