extension is called a Stochastic Petri nets (SPN). There are several systems such as biochemical systems, which are inherently behave stochastically (Heiner et ...
ISBN: 978-989-99864-1-1 © 2017
MOOD STATES PREDICTION BY STOCHASTIC PETRI NETS
Mani Mehraei Department of Applied Mathematics and Computer Science, Eastern Mediterranean University, North Cyprus (Turkey)
Abstract Mood states prediction is in the center of attention of various topics in several fields such as bipolar manic depression as a mood related disorder in psychology, impact of emotion on behavior in decision making, and virtual character development in artificial intelligence and artificial psychology. In this study, a Stochastic Petri nets model is created to predict mood states based on emotion interaction of an individual and his/her personality. The emotion interaction data are collected by a questionnaire containing several questions regarding random events and possible emotion states before and after the events for 108 individuals with various personality backgrounds. Simulation results in the Stochastic Petri nets model are recorded for all the individuals and compared with their expected mood states by running Chi-Square goodness of fit test with 95% confidence level. It has been observed that simulation results were suitable fit for more than 97% of total individuals. It demonstrates that Stochastic Petri nets can be applied as an appropriate graphical mathematical tool to model and predict mood states in individuals and virtual characters based on the field of study.
Keywords: mood prediction, emotion interaction, stochastic petri nets, decision making.
1. Introduction During last decades, there has been rapid growth to model and predict mood states of human beings. To model mood states can be beneficial for variety of topics from health care studies to even entertainment industries. In the field of psychology, reseachers attempted to model mood to find possible treatments for mood disorders such as depression and bipolar disorders (Daugherty et al., 2009; Ortiz et al., 2015). In the recent studies of artificial intelligence field, many researchers tried to model and predict mood to create lifelike virtual characters (Egges et al., 2003; Kazemifard et al., 2006; Gebhard, 2005; Kasap et al., 2009) to be used in humanoid robots for the advantage of education, personal assistance, and healthcare, or to be used even in entertainment industry such as virtual charachters in video games. The most well-known and basic modeling methods for predicting mood states are OCC (Ortony et al., 1990), which demonstrates the way agents, events, and objects apprise based on personality (Egges et al., 2003; Ortony et al., 1990), and Pleasure-Arousal-Dominance (PAD) model (Mehrabian, 1996), which is constructed by Mehrabian to describe different emotion states by the mentioned independent Pleasure, Arousal, and Dominance traits. During last two decades, modeling methods which are the combination of OCC and PAD are developed to predict emotion and mood states more accurately such as ALMA and WASABI (Gebhard, 2005; Becker-Asano 2014). It is shown that it is possible to exploit the mentioned modeling approaches and combine it with mathematical and statistical techniques to come up with novel methods to create models to describe and predict mood states (Mehraei & Akcay, 2016; Pracana & Wang, 2016). The mentioned modeling methods could shed light on the matter, but yet there has not been an ideal model to be able to describe and predict mood states of individuals with different personality types. In this study, a novel mathematical model is construced by Stochastic Petri nets to predict mood states of 108 individuals with different personality types based on OCC appraisal model, dimensional PAD independent traits, and ALMA’s approach. The proposed model is validated by statistical methods to compare observed data with expected ones with 95% confidence level.
ISBN: 978-989-99864-1-1 © 2017
2. Methods 2.1. Sample The sample in this study contained 108 volunteers, who were mostly students or employees at Eastern Mediterranean University. These individuals came from different countries with different backgrounds. The questionnaire, which was filled by these volunteers had three main sections. The first section contained questions to measure OCEAN main personality traits, which are Openness, Conscientiousness, Extraversion, Agreeableness, Neuroticism (Mehrabian 1996). The second section included questions regarding random events and the possible emotional interaction before and after these events. For example, the potential significant emotion states for one, who is crying and the possible emotion traits after crying. Random events or actions in the questionnaire included but not limited to listening to music, shopping, sleeping, eating, doing sport, socializing, spending time with beloved ones, crying, fighting, gossiping, being alone, watching movies, and studying. For simplicity, volunteers could only choose between these possible emotion states: anger, admiration, dislike, disappointment, sadness, fear, gloating, hate, hope, joy, like, love, pity, pride, relief, resentment, and shame. In the final section, volunteers recorded their most significant emotion state among the mentioned possible ones, hour by hour for two weeks (Mehraei & Akcay, 2016; Pracana & Wang, 2016).
2.2. Stochastic Petri nets A Petri net is a directed graph consisting of places, transitions, and arcs. Places, transitions, and arcs are illustrated by circles, boxes, and arrows, respectively. The places and transitions in a Petri net can be connected by directed arcs. However, two places and two transitions are not able to be connected by arcs. Arcs are identified by their weights. The places from which arcs run to a transition are called the input places of that transition, which are interpreted as preconditions of the model. The places which transitions are connected to them by direct arcs are called output places, which are interpreted as postconditions of the model. Transitions in a Petri net are responsible for changing the states of the model and they interpreted as actions or events. The distribution of the available data among places are called marking of a Petri net. Classical Petri nets (Murata 1989) were designed to analyze discrete-event system behavior. However, the concept was expanded with extensions such as continuity, hierarchy, fuzziness, and stochasticity. During last few decades, such extensions implemented in Petri nets to describe and analyze systems, especially in molecular biology and system biology (Matsuno et al., 2003; Doi et al., 2004; Matheu et al., 2009; Mehraei et al., 2016). A Petri net with stochasticity extension is called a Stochastic Petri nets (SPN). There are several systems such as biochemical systems, which are inherently behave stochastically (Heiner et al., 2010). In models, which attempt to describe mood and emotion, stochastic noise should be considered in their behavioral properties. Therefore, SPN as a stochastic model is a suitable alternative to describe and analyze mood states.
2.3. Creating the model The proposed model in this study is conducted in terms of quantitative modeling with SPN on Snoopy platform (Heiner et al., 2012). The model contains 17 continuous places as possible emotion states, and 3 continuous places as PAD independent mood traits. Emotion states can interact with each other through 48 stochastic transitions, connected by arcs. Emotion states can influence the mood states by 35 continuous transitions, connected with arcs. There are totally 404 arcs in this model. The structure of the SPN model is the same for all the individuals, but the behavior of the model is personalized. For example, the relative frequency of changing “anger” state to “regret” state differs from one person to another. Therefore, the process rates in the stochastic transitions of the proposed SPN model is estimated based on the probability of an individual emotion interactions. For simplicity, a part of such emotion interactions is illustrated in Figure 1. “Anger”, “Relief”, and “Regret” are represented as continuous places, and there are two transitions which can change “Anger” state into either “Relief” or “Regret” state. Baes on the filled questionnaire by 108 volunteers, it is observed that the relative frequency of these events or actions (transitions) are significantly different for one individual to another. Therefore, personalizing the process rates of these individuals was essential. For example, the probability of changing “Anger” state to “Regret” state is considered twice bigger than changing “Anger” state to “Relief” state in a specific individual in Figure 1. The initial marking of three mood continuous places (PAD) for each of the individuals in the proposed SPN model can be defined by mapping from OCEAN personality traits to PAD space (Mehrabian, 1996; Gebhard, 2005). The possible values that these independent PAD traits can get are from -1 to 1. Since the marking of places in a Petri net cannot accept negative values, there had to be another mapping from -1 to the minimum value, and 1 to the maximum value that the proposed SPN model could possibly have for the marking of the places.
ISBN: 978-989-99864-1-1 © 2017
Figure 1. A part of emotion interactions in the proposed SPN model
As it is mentioned in several studies, mood states can be updated by a function in terms of emotion and mood history (Mehrabian, 1996; Gebhard, 2005; Mehraei & Akcay, 2016; Pracana & Wang, 2016). Therefore, ALMA’s approach is used for mapping from OCC emotion traits into PAD mood space in the proposed SPN model (Gebhard, 2005) to constantly update the mood states based on the previous emotion and mood states. So, there should be transitions in the SPN model which connects emotions traits to mood independents traits through arcs. In the proposed SPN model, 35 continuous transitions are constructed to update three PAD mood continuous places based on the emotion and mood history. The process rates for these continuous transitions are the same for all the individuals since the mapping from OCC to PAD in ALMA’s approach is defined the same for all individuals even for different personality types. For simplicity, a part of such transitions is illustrated in Figure 2. This figure shows that when an individual is angry, it negatively influences the pleasure mood trait, and positively influences arousal and dominance mood traits. The process rates are determined the way to have agreement with Alma’s mapping from OCC emotion traits to PAD mood space. Figure 2. A part mood updating in the proposed SPN model
3. Discussion 3.1. Simulation results The simulation results obtained by getting the average point of 38000 stochastic runs in the proposed SPN model on Snoopy platform (Heiner et al., 2012). The reason to select such big number of simulation runs is explained in a study by Liu et al. (Liu et al., 2016) based on the formula provided in a work by Sandmann and Maier (Sandmann et al., 2008). Clearly, one might decrease the number of simulation runs by sacrificing the accuracy. In this study, coefficient of variation is calculated to be approximately equal to 1. Thus, based on the mentioned formula (Sandmann et al., 2008), the confidence level for the results obtained by the average of these 38000 stochastic runs is 95%. The SPN simulation results as observed values for Pleasure (P), Arousal (A), and Dominance (D) mood traits are illustrated in Figure 3. The interval end point of Petri time is considered as 500 Petri time, and for simplicity the trends are represented at every 50 points for better comparison.
ISBN: 978-989-99864-1-1 © 2017
Figure 3. Simulation results for mood states prediction
3.2. Model validation The expected values for mood states are calculated based on the most significant emotion states of each volunteer hour by hour, which are recorded in the third section of the questionnaire, and the suggested formula for updating mood states in the previous related work (Mehraei & Akcay, 2016; Pracana & Wang, 2016). The expected mood state values are updated twice a day, and each day corresponds to 100 Petri time. The closest possible fit for ten points in a row for comparing observed and expected values for mood states are considered. The trends for both observed and expected values are illustrated in Figure 3. Chi-Square goodness of fit test with 95% confidence level is applied to compare observed and expected values of mood states. It is observed that for 97.2% of cases, SPN simulation results are suitable fit for the expected mood state values for all Pleasure, Arousal, and Dominance mood traits with P-value equal to 0.05.
4. Conclusion This study demonstrates that SPN can be used as a mathematical tool to describe systems psychology. The proposed SPN model reveals that mood states can be predicted in short term by high accuracy to be used in various purposes. For example, this model can be used for the aim of healthcare to treat mood disorders, or designing human-like virtual characters in the field of artificial intelligence. As future studies, we are planning to identify potential treatments for mood disorders such as depression, mania, and different types of bipolar disorders by using extended version of Stochastic Hybrid Functional Petri nets. This proposed mathematical model can be used to identify novel treatments as gene therapy, drug therapy, or psychotherapy for such specific patients.
References Becker-Asano, C. (2014). WASABI for affect simulation in human-computer interaction. In Proc. International Workshop on Emotion Representations and Modelling for HCI Systems.
ISBN: 978-989-99864-1-1 © 2017
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