Artificial emotion modeling based on container (CUP) algorithm

Abstract

Human emotion is an extremely complex social phenomenon that dominates many social phenomena. The paper proposes a method of emotional modeling in the context of complex systems based on the container model, which is more intuitive and can be solved than the conventional emotional modeling methods. Meanwhile the container algorithm also has the advantages of high parallelism, so it has practical significance for the simulation and analysis of emotions.

Keywords

Artificial emotion container algorithm STMS model

1 Introduction

1.1 General theory of emotion

Human psychology is an extremely complex phenomenon in all respects and the artificial emotion (AE) [1] is essentially a computer science method through the theoretical foundation of anthropology, psychology, neuroscience, and information science. It is a cross-cutting attempt to study human emotions.

From the perspective of complex systems, it is more focused on the mechanism of emotional formation and evolution and its complex phenomena as emerging in multiple cases. Emotional theory has many different opinions and the mechanism for the formation of emotion is not uniform. Although different genre psychology studies have given various explanations but it is also a relatively unified part: the human psychological process is usually divided into three processes as a mutual integration: the cognitive process, the emotional process and the will process. Cognitive process is an external event (as stimulus) on human ontology. The will process which reflects the active regulations (quantity, degree, duration, etc.) of people’s psychological processes and meanwhile the emotional process is a specific experience (attitude of experience). A psychological process associates with a specific behavioral response.

Specifically, emotion can be understood as a wake-up model of emotion [2]: a process of combining (specific or unspecified) stimulation in the context of recent emotions and the experience of early years (long-term emotional background), which is the root of all current actions. Through cognition and comparison it will trigger the corresponding physiological reactions (by the endocrine system and the motor system) and the priming of emotional expression. When the comparison result is consistent with the original expected judgment, the current mood or status will not change. But if it is inconsistent a change in mood will produce.

Firstly the study of emotions should clarify the compositional dimensions of emotions. (as an inherent compositional structures)A clear measure of emotional degree and composition is a precondition for quantifying the emotion. As an example, the PAD model proposed by Mehrabian and Russell in 1974 is representative. This theory decomposes emotions (in fact it also applies to emotional research) into three dimensions: pleasure, activation, and dominance, where ‘P’ stands for Pleasure-displeasure (positive or negative expression of the subject’s emotional state). ‘A’ stands for activation (arousal-no arousal, which indicates the level of neurophysiologic activation of the subject). And ‘D’ stands for Dominance-submissiveness (which represents the subject’s control state for the situation and others).

These three dimensions can be used to represent specific emotions and emotions. Schlosberg gave a three-dimensional theory of emotions in 1954 as: pleasant-unpleasant, attention-rejection and activation level. The emotional model proposed by Plutchic in 1970 advocated that emotion is with intensity and similarity as three dimensions and two polarities.In 1980 Russell proposed a circular pattern for emotional classification, which divides emotion into two relative dimensions: happiness and intensity.

Emotional (prone) classification is presented by OCC model [3] which classifies emotions into 22 categories. But in terms of classification’s dominant position is the model done by Ekman, which divides emotions into 6 categories: anger, happy, fear, disgust, sadness, and surprise.

It is to simulation and analysis by such methods as hidden Markova Chain in usual practice using, Grey System and fuzzy mathematics. Each method has its advantages and disadvantages. Hidden Markov Chain (HMM) [4] is a common state transition model. It has strong ability to model the emotional states and their transition but it is not easy to describe emotion as a value (degree) behavior; Grey system (GM) [5] is sensitive to the changing of emotional degree, but it can not able to model the change of emotional state; Fuzzy mathematics method has good modeling ability for both emotional state and degree, but the whole modeling process is too subjective.

1.2 Background of complex system

In terms of evolutionary category, individual emotional characteristic is a comprehensive reflection of individual history and social environment, which is a complex system itself. Uncertainty and complexity occur simultaneously in complex systems. Human physical and psychological processes conform to the general characteristics of container, so container algorithm can be used to simulate and analyze human emotion.

2 Methodologies

2.1 Container algorithm

2.1.1 Basic definition of CUP

The container (CUP) system [6] is a new framework for modeling the complex system by the concern of container’s(s’) overflowing phenomenon. When its content is higher than the capacity the container will overflow. At the volume of 1 (as it is called standard container), the container and are compatible with uniform distribution. Individual’s emotion can be thought of as a container combination of child emotions, and crowd emotions can be thought of as a container combination of individual emotions.

The two levels on container system by their structure: the primitive one and the paternal one. The primitive container will not be regarded as consisting of any smaller unit of cups. In this issue the container at the primitive level can be regarded as either individual emotion or group emotion. This definition of emotion is flexible. They can be defined by a unified form as: $Z_{l, b} (t) = {c_{l, b} (t), v_{l, b} (t)}$

The letters here are defined as follows: l is the indexing parameter of level. u, b ∈ B is the indexing parameter of layer inner ones. c is the container’s content level and v is the volume of the container.

A primitive container‘s container has a 0 level indexing parameter l.The paternal level CUP container is constructed by (lower level) atomic ones or containers. The level 0(primitive) CUP is defined as follows: $Z_{0, b} (t) = {c_{0, b} (t), v_{0, b} (t)}$

Emotion can be considered as an evolutionary process that is constantly influenced by external inputs. x and o are sequences of input and the output which are indexed by the l. Primitive container’s input process is defined by (t is time tick): $c_{0, b} (t) = c_{0, b} (t - 1) + x (0, b, t)$

Its process of output is: $o_{0, b} (t) = {\begin{matrix} o, & c_{0, b} (t) ⩽ v_{0, b} (t) \\ c_{0, b} (t) - v_{0, b} (t), & c_{0, b} (t) > v_{0, b} (t) \end{matrix}$ $c_{0, b} (t + 1) = c_{0, b} (t) - α_{0, b} (t) * o_{0, b} (t)$

The paternal level container (when its l is larger than or equal to 1) is defined as: $Z_{l, u} (t) = {Z_{l - 1, q} (t) | q \in Q}$

Index number set of Paternal container’s child (children) is Q. Parent container can be thought of as a combination or organization of smaller emotions. The paternal container level is similar to the primitive level from the evolution process. The only difference is in its input and output processing. The paternal container‘s input process is defined as: $Z_{l, u} (t) = {c_{l, u} (t), v_{l, u} (t)}$ $c_{l, u} (t) = A (c_{l, u} (t - 1), x (l, u, t), Q) + c_{l, u} (t - 1)$

Allocation function A which is determines how lower level (child) container(s) will get the input from paternal container. Different problems will give different allocations.

Paternal container ‘s output process is: $c_{l, u} (t) = c_{l, u} (t - 1) + \sum_{q \in Q} o_{l - 1, q} (t)$ $o_{l, u} (t) = {\begin{matrix} 0 & , & c_{l, u} (t) ⩽ v_{l, u} (t) \\ c_{l, u} (t) - v_{l, u} (t) & , & c_{l, u} (t) > v_{l, u} (t) \end{matrix}$ $c_{l, u} (t + 1) = c_{l, u} (t) - α_{l, u} (t) * o_{l, u} (t)$

Amplification factor α_l,u is some small integer (float is also useful) in usual. It can be used to describe the non-linear characteristics of emotions of different individuals.

2.1.2 Fitting algorithm

In order to get the useful mode of a sequence as emotion fitting algorithm will will used. The fitting system which is done by container system is the centre-partial (CP) mode fitting system. Define a CUP tuple CP. CP is composed by a central CUP C and m partial CUPs $\underset{1 ⩽ j ⩽ m}{P_{j}}$ : $\begin{matrix} CP & = & < C, P >; P = {P_{1}, P_{2}, \dots, P_{m}} \\ C & = & Z_{l, b, c} (t) = {c_{l, b, c} (t), v_{l, b, c} (t)} \\ P_{j} & = & Z_{l, b, j} (t) = {c_{l, b, j} (t), v_{l, b, j} (t)} \end{matrix}$

For individuals, emotion is a physical and mental process, and for groups, it also has a clear direction of action. Therefore, the CP algorithm is applicable. The input x will be put into the centre container C, and it will make the evolution by time tick and its output will be get. Then that centre container’s output o_l,b,c (t) will be put as the inputs x_l,b,j (t) of each P by some way, then the evolution of everyone of partial container will be generated and their outputs are also be obtained. Main output y is done the sum of all the outputs of each P: $\begin{matrix} y^{'} (t) & = & \sum_{1 ⩽ j ⩽ m} q_{j} (t) o_{l, b, j} (t) \\ Q & = & {q_{j} | 1 ⩽ j ⩽ m} \end{matrix}$

The weighting factor q_j (t) of each P’s output can be fitted to the value y * (t) which has the minimum error distance to the true valuez (t), which can be get as: $argmin Q : | y^{'} (t) - y (t) |$

The fitting result (show by Fig. 1) of container algorithm, the target series is part of the Lorentz curve, a typical representative of complex system. It used the candidate coefficient set {0.0, 0.5, 1.0} (there are only three elements). Accuracy can be improved by further increasing the scale of candidate coefficients (in more detail), but it will consume more computing resources.

Fig.1

The result of container fitting.

Fig.2

The result of emotion evolution by container.

Fig.3

The result of stock market evolution.

The fitting result meets the needs basically.

2.1.3 Probability structure analysis and prediction

CUP’s input and output process can be coded to states by an interval range splitting algorithm, and the states sequence S = {s_j|0 ⩽ j ⩽ u} will be obtained. Being constructed by traversing the result of fitting to the CP structure and input-output sequence, it will obtain different peripheral coefficients of output corresponding to each central output state as a table:

$ST (t) = {\begin{matrix} s_{0} : [[Q_{00}, q_{00}], [Q_{01}, q_{01}], \dots, [Q_{0 k_{0}}, q_{0 k_{0}}]] \\ s_{1} : [[Q_{10}, q_{10}], [Q_{11}, q_{11}], \dots, [Q_{1 k_{1}}, q_{1 k_{1}}]] \\ \dots \dots \dots \\ s_{u} : [[Q_{u 0}, q_{u 0}], [Q_{u 1}, q_{u 1}], \dots, [Q_{{uk}_{u}}, q_{{uk}_{u}}]] \end{matrix}}$

Here q_uv is frequency of the v-th coefficients combinations Q_a,b corresponding to the state s_u. Sequences can be probabilized by ST tables. The problem of state transition can be effectively dealt with by Markov chain equal probability method.

2.2 Artificial emotion modeling based by container algorithm

Emotion recognition is the process of recognizing emotion through external representations (such as facial expression, emotional vocabulary, etc.). This paper does not deal with the part of emotional recognition, but only focuses on the process of emotional evolution and its fitting and simulation. The result of emotion recognition can be handled as the some input (known or unknown) can be classified into two categories: the amount or the states. Emotion is a complex systemic phenomenon that is constantly affected by various factors at any time. In addition, emotional varies greatly between different individuals. The application of container models for emotional modeling has high response and scalability by the model of STMS.

2.2.1 STMS model

The emotional modeling the paper introduced by the container algorithm is called STMS (Strength, Threshold, Multi-container, and State). The emotion is regarded as a process of by reactions by multi-containers. Each container has its own strength of emotion. When the strength is higher than its threshold (overflowing) the emotional state will change.

From the point of view of container modeling it is not to distinguish the state between emotions by form clearly. Partial containers can be considered as different emotional types (states) or different constituent structures.

The latter point of view is adopted in this paper. In order to maintain compatibility of state and value (degree) synchronously, STMS takes the corresponding specific spillover as a sign of state changing. The key problem which that makes the common methods difficult to model emotion(s) is state and value cannot be operated together while CUP system can do it well: by ST table the degree of emotion can be transformed into the states. And the process of fitting can give the information which analysis of emotion needs.

2.2.2 Group emotion phenomenon

Another issue of emotional simulation and analysis is the study of group emotions.Emotionalization of the crowd is very obvious but not easy to fitting and describing. Emotionalization of the crowd drives most of the social phenomena. Because of the fractal symmetry of container model, there is no distinction between individual emotion and group emotion in the modeling of group emotion. It establishes a multi-level emotional driving structure based on fractal unification by container: the group is the parent container of the individual, and the individual is the child container(s) of the group.

3 Results and discussion

3.1 Evolution

The simulation experiment uses the CP fitting algorithm of the container model: there are six partial containers and one core container and the the evolution coefficient of the outer containers is the multiple of 0.5(by the index number of partial container);The input here is a constant base value (0.3) pulsing a random value between 0 and 0.05 by uniform distribution.

From the simulation experiment, we can see that the basic mood of human is also changing at any time, even if it is only a very small disturbance (0.3 as a maintenance input).

3.2 Fitting and analysis

It uses the evolution of financial markets as an example of emotion modeling by CUP. In the classical financial theory, investors are rational and they do not have emotions, the prediction of the future by them is unbiased. So relatively, in the financial market we can define the mood as the return of future equity investment is too optimistic or too pessimistic biased estimates. The theory is a model of DSSW noise traders, established by De Long and others in 1990, which theoretically proves that overly optimistic emotional investors tend to buy too much, leading to higher asset prices and subsequent collapses brought about by the bursting of the bubble. Financial market is the concentrated expression of people’s emotion and it is a typical complex system. In order to avoid affecting the intuitiveness of modeling, this paper describes the financial market in the following ways (as it is by the price’s open, close, high and low): $u (t) = (c (t) - o (t)) / (h (t) - l (t))$

Fitting parameters: the candidate coefficients set is from 0.0 to 10.0 by the step 0.5; there are 3 partial container with volumes of 0.5, 1.0 and 1.5 by the amplification factors 1.0, 2.0 and 3.0.

And through fitting it can get the ST table as:

(0.0, 0.0, 0.0)	15
(9.5, 0.0, 0.0)	5
(2.5, 0.0, 0.0)	1
(3.0, 0.0, 0.0)	1
(8.5, 0.0, 0.0)	1
(8.5, 1.0, 0.0)	1
(9.0, 6.0, 0.0)	1
(0.0, 1.5, 0.0)	1
(8.0, 4.0, 0.0)	1
(1.5, 0.0, 0.0)	1
(9.5, 9.5, 0.0)	15
(9.5, 7.5, 0.0)	1
(7.0, 9.0, 0.0)	1
(6.5, 0.0, 0.0)	1
(1.5, 5.0, 0.0)	1
(9.0, 6.5, 0.0)	1
(0.0, 9.0, 0.0)	1
(3.0, 3.0, 0.0)	1
(9.0, 0.0, 0.0)	1
(1.5, 3.5, 0.0)	1
(8.5, 8.5, 0.0)	1
s_1	(8.5, 8.0, 0.0)	1
(0.0, 6.5, 0.0)	1
(3.5, 6.0, 0.0)	1
(2.5, 7.5, 0.0)	1
(1.0, 0.0, 0.0)	1
(4.0, 0.0, 1.5)	1
(4.0, 0.0, 0.0)	1
(8.5, 2.0, 0.0)	1
(5.5, 6.5, 4.0)	1
(7.5, 4.5, 0.0)	1
(9.0, 9.0, 0.0)	1
(5.5, 8.5, 0.0)	1
(0.0, 1.5, 3.0)	1
(6.0, 0.0, 0.0)	1
(3.5, 3.0, 6.0)	1
(9.5, 0.0, 9.5)	1
(0.0, 2.0, 0.0)	1
(9.5, 8.0, 0.0)	1
(1.5, 6.0, 0.0)	1
(5.5, 5.0, 0.5)	1

(7.5, 0.5, 0.5)	1
(3.5, 8.5, 5.0)	1
(0.0, 0.0, 0.0)	2
(0.0, 2.0, 0.0)	1
(2.5, 1.5, 9.0)	1
(0.0, 0.0, 5.0)	1
(2.5, 2.0, 0.0)	1
(0.5, 3.5, 6.5)	1
s_3	(0.0, 9.5, 0.0)	1
(2.0, 0.5, 9.0)	1
(0.0, 2.5, 0.0)	1
(0.5, 3.0, 9.5)	1
(1.0, 4.5, 1.5)	1
(2.0, 9.0, 3.0)	1
(2.5, 9.5, 0.0)	1
(0.0, 0.5, 0.0)	1
(0.0, 0.0, 0.0)	2
(5.0, 0.0, 0.0)	1
(1.0, 0.0, 0.0)	3
(3.0, 0.0, 0.0)	1
(3.5, 0.0, 0.0)	1
(1.5, 0.0, 0.0)	1
(7.5, 0.0, 0.0)	2
(5.5, 9.0, 0.0)	1
(2.0, 9.5, 0.0)	2
(7.0, 2.0, 0.0)	1
(0.5, 0.5, 0.0)	1
(4.5, 0.0, 0.0)	2
(5.5, 4.5, 2.0)	1
(0.0, 6.0, 1.5)	1
(4.5, 0.5, 3.0)	1
(5.5, 3.5, 1.0)	1
(0.0, 6.5, 0.0)	1
(0.5, 8.5, 1.5)	1
(4.0, 3.5, 0.0)	1
(1.0, 1.0, 0.0)	2
(0.5, 4.0, 0.0)	1
(5.0, 3.0, 0.0)	1
(3.5, 4.5, 0.0)	1
(2.0, 8.0, 0.5)	1
s_2	(4.5, 7.5, 1.0)	1
(0.0, 0.5, 8.0)	1
(6.5, 8.0, 0.5)	1
(5.0, 0.0, 2.0)	1
(5.0, 0.5, 7.5)	1
(0.0, 0.0, 9.0)	1
(2.5, 4.0, 7.0)	1
(0.0, 2.0, 0.0)	1
(3.0, 3.5, 2.5)	1
(4.0, 3.0, 3.0)	1
(1.5, 9.5, 0.0)	1
(1.5, 2.0, 5.0)	1
(2.0, 0.0, 0.0)	1
(6.5, 0.5, 0.0)	1
(0.0, 0.0, 5.5)	1
(5.5, 1.5, 3.0)	1
(3.0, 8.5, 0.0)	1
(0.0, 3.0, 0.0)	1
(2.5, 5.0, 1.5)	1
(3.5, 5.5, 0.0)	1
(1.5, 1.0, 1.5)	1
(2.0, 8.0, 0.0)	1
(0.5, 5.5, 5.5)	1
(5.0, 5.0, 3.0)	1

(3.0, 5.0, 5.5)	1
(1.0, 0.0, 6.5)	1
(1.0, 0.0, 0.0)	1
s_5	(1.0, 4.0, 3.5)	1
(1.5, 0.5, 0.0)	1
(0.0, 1.5, 2.5)	1
(0.5, 4.5, 9.0)	1
(0.5, 5.0, 0.0)	1
(0.0, 8.5, 5.5)	1
s_4	(2.5, 0.0, 1.0)	1
(2.5, 1.0, 1.0)	1
(1.0, 3.5, 1.0)	1
(0.0, 9.0, 0.0)	1
(1.5, 0.0, 0.0)	1
s_7	(1.0, 0.0, 1.5)	1
(0.5, 1.5, 0.5)	1
(0.5, 0.0, 0.5)	2
(1.0, 1.5, 0.0)	1
(1.5, 0.0, 0.0)	1
(0.5, 0.0, 0.0)	1
s_6	(0.0, 2.5, 0.0)	2
(0.5, 1.5, 0.0)	1
(0.0, 0.5, 0.0)	1
(0.0, 7.0, 0.0)	1
(0.5, 1.0, 1.5)	1
s_9	(0.0, 0.5, 3.0)	1
(0.0, 0.0, 3.5)	1
s_8	(0.5, 0.5, 0.0)	1
(0.0, 0.0, 0.0)	1
s_11	(0.0, 4.0, 0.0)	1
(0.0, 4.0, 0.0)	1
s_10	(0.5, 0.5, 1.0)	1
(0.0, 0.0, 1.0)	1

4 Conclusion

CUP method is essentially a numerical method, but because of the construction of ST table, it also has the ability to model the complex system events by probability. Therefore CUP method is both numerical and probabilistic. It is compatible with two different methods of complex system modeling. At the same time the computational strength of CUP (fitting) algorithm can be controlled according to different computational requirements. Because of its weak coupling modeling characteristics, its parallelism is also fine.

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