
Published by the IEEE Computer Society
Article Contents  
Introduction  
Related Work  
Guided GameBased Learning Using FCM  
Driving Training Prototype System  
Evaluation  
Conclusions and Future Work  
Acknowledgments  
References  
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Abstract—Fuzzy Cognitive Maps (FCMs) can be used to design gamebased learning systems for their excellent ability of concept representation and reasoning. However, they cannot 1) acquire new knowledge from data and 2) correct false prior knowledge, thus reducing the gamebased learning ability. This paper utilizes Hebbian Learning Rule to solve the first problem and uses Unbalance Degree to solve the second problem. As a result, an improved FCM gains the ability of selflearning from both data and prior knowledge. The improved FCM, therefore, is intelligent enough to work as a teacher to guide the study process. Based on the improved FCM, a novel gamebased learning model is proposed, including a teacher submodel, a learner submodel, and a set of gamebased learning mechanisms. The teacher submodel has enough knowledge and intelligence to deduce the answers by the improved FCM. The learner submodel records students' study processes. The gamebased learning mechanism realizes the guided gamebased learning process with the support of the teacher submodel. A driving training prototype system is presented as a case study to present a way to realize a real system based on the proposed models. Extensive experimental results justify the model in terms of the controlling and guiding the study process of the student.
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1. how to make the FCM own the abilities of selflearning and knowledge acquisition,
2. how to build a guiding gamebased learning model resting on an improved FCM,
3. how to realize an actual gamebased learning system resting on the proposed model, and
4. how to verify the effectiveness of our proposed model.
3.3.1 Construction of the Teacher Submodel The initial FCM of the teacher submodel is usually constructed by domain experts. Because domain experts have abundant prior knowledge of their domains, they can build the FCM effectively, which corresponds to the real world. This work involves finding the concepts in the model and the initial weight between concepts. These weights reflect the expert knowledge and are fine adjusted by using the local and global learning described in the next section, which makes them emulate the real world effectively.
3.3.2 Local Learning of the Teacher Submodel Local learning of the teacher submodel is mostly to learn the weight value between the concepts of an FCM. We mainly use the classic Hebbian Learning Rule [ ^{16} ] and the D riveReinforcement Hebbian Learning Rule [ ^{17} ], [ ^{18} ] in the local learning process of the teacher submodel. The main steps are as follows:
1. SelfLearning Based on the Hebbian Learning Rule
Generally, for a common neural computing model , where is the concepts set, is the connection relation matrix, is the input set, is the output set, is the working algorithm, and is the organizing algorithm [ ^{19} ], we notate the output of random concept as and . According to Hebb supposition, the correction of connection weight between concept and is defined as
(2)
where is the discrete time, that is, , is the learning factor, and is the correction value of at time .
From (2), if presynaptic concept and its postsynaptic concept excite at the same time, that is, both the output of concept and the output of concept equal to 1, and the correction value (connection weight ) , then the connection weight at time will be improved. At time , if either the output of concept or of concept is zero, the correction value .
2. SelfLearning Based on the DriveReinforcement Hebbian Learning Rule
According to the drivereinforcement algorithm and the Hebbian Learning Rule [ ^{17} ], [ ^{18} ], the correction of connection weight between concept and is defined as [ ^{18} ]
(3)
where is the change of the output of presynaptic concept at time .
For the concept of , the change of its output at time is
(4)
According to (3), if and have the same sign, that is, the changes from time to of and are of the same sign, then the connection weight at the time of will be improved. On the contrary, if and have different signs, that is, the changes from time to of and are of different signs, then the connection weight at the time of will be reduced.
3. Local Learning Algorithm
Every concept has some different influences on other concepts. Through the onetoone learning between any two concepts, that is, the state value of a concept is adjusted singly on the condition that other state values are not changed, the influence on the other concept can be observed so as to learn the relation between the two concepts.
In the local learning cycles, the state value of concept is adjusted continuously. Meanwhile, the state value of the corresponding concept also varies, and its changed value is denoted by . Also, the programming output of the concept based on the expert knowledge also varies, and its changed value is denoted as . Thus, the error is . Besides, the changed value of concept is denoted by , and the modifier between concepts and is then defined as
(5)
The algorithm of the local learning between the concepts is shown as follows:
Local Learning Algorithm:
Step 1: calculate , , ;
Step 2: ;
Step 3: ;
Step 4: if round and 8
then ; go to Step 1;
else go to Step 5;
Step 5: end.
In the algorithm, round is the counter of learning cycles and is the maximum of learning cycles. If round reaches the maximum or is small enough, then the learning process will be completed.
In the local learning, from the local viewpoint of concepts, the teacher submodel can adjust the unreasonable weights of the relations in the FCM. However, because the learning is based on the local viewpoint, there may exist unreasonable points in the teacher submodel which need to be improved through the global learning.
3.3.3 Global Learning of the Teacher Submodel Global learning of the teacher submodel refers to the global learning of the FCM itself. The construction of the FCM is from the top down and is used to represent prior knowledge, but the classic FCM has three major defects, as discussed in Section 3.1.
The dynamic behaviors of an FCM are realized through the interaction of its concepts, and the dynamic behaviors will then reach a fixed point, a limit cycle, or a chaos state. The positions of concepts in the FCM are equal and each has its own local viewpoint, but there is no global concept among all the concepts which deprive the global learning ability of the FCM. In this section, we discuss how to construct a global concept for the FCM so as to enable it to possess global learning ability.
In our approach, a virtual super concept is constructed, which does not belong to any of the other types of concepts. The state value of the virtual super concept may be regarded as the energy of the FCM. Before proceeding to subsequent discussions, the following three definitions are defined as follows:
Definition 1 (Error of concept's state values ). The difference between the expectation output and the actual output of a concept's state value is denoted as , and the sum of represents the difference between the FCM and the real world. The definition of is given as
(6)
where is the actual output of at time and is the expectation output of the concept in the FCM at time .
Note that the dynamic behaviors of the system are the result of interaction between a concepts set and its state values set , which reflects the state value of each reasoning concept at time . The interaction of concepts' state values and their weights will produce the simulation of the real world. So, the sum of is an import parameter that represents whether the FCM can simulate the real world.
By comparing the actual output with the expectation output of all the concepts, the differences between the FCM and the real world can be obtained. Specifically, let
(7)
where is the number of concepts. If , the difference between the FCM and the real world is small and the FCM reflects the world factually.
Definition 2 (Concept weight adjusting variable ). The adjusting variable of concept weight is to hold the adjustment value in order to keep the minimal change of weight in the learning process of the FCM. is defined as
(8)
The weight adjustment of the FCM follows Linsker's maximum entropy principle [ ^{20} ], i.e., when the environment needs to change the weight of concepts, the change should be minimal, so it can mostly keep the original information.
In (8), is a random adjusting variable used for disturbing the learning process of the FCM. In order to prevent the FCM from being trapped in a local minimum point in the learning process, a random adjusting variable is set. If the weight of the FCM does not fit the expectation value after being trained several times, there may be an erroneous setting in the connection intensity of important causality. Hence, should be increased in positive or negative scope.
Sometimes, the random adjusting variable is added, which might cause the FCM to be in an error mode. So, the random adjusting variable is modified to to remove this fault. This modification can correct the error mode of the FCM and hold its right mode.
Definition 3 (Unbalance degree ). The unbalance degree is a measurement of the difference between the FCM and the real world at time , and is defined as
(9)
where is a random adjusting variable.
Under the unbalance degree , the closer the state value of the FCM is to the real world, the more effective the adjustment it produces, so it will be a better adjustment. The same applies to the opposite situation too. The adjustment can be completed when the system touches the minimal unbalance degree.
After is gained and is adjusted, the value of should be minimal. When reaches a specified value, the adjustment process can be terminated. A global concept of the FCM can control the learning process of the FCM.
After the combination of the concept states is given, the real output is compared from a global viewpoint with the expectant output of the teacher submodel, so as to learn all the relationships of the concepts as a whole.
Let and denote the real output and the expectant output of the teacher submodel, respectively, denote the error at time , and denote the modifier of the relationship weight between concepts and at time . The global learning algorithm of teacher submodel is as follows:
Global Learning Algorithm
Step 1: calculate , ;
Step 2: ;
Step 3: ;
Step 4: ;
Step 5: if round and 8
then ; go to Step 1;
else go to Step 6;
Step 6: end
After the local and global learning process, the teacher submodel is revised and optimized, and the final one can be used to guide the study process of the student.
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(11)
(12)
(13)
Gamebased Learning Algorithm
Step1: Input
Step2:
Step3:
Step4:
Step4:
Step5: If then goto step 6 else goto step 1.
Step6: end.
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4.2.1 Constructing the Initial Teacher Submodel The initial teacher submodel for the system ( Fig. 6 ) is built with the prior knowledge from the experts of the driving school and some senior drivers who have driven over tens of years. The initial teacher submodel, represented by the FCM, consists of concepts and relationships between them. Concepts are formed in terms of the car states, operations, and situations of the road lane when driving. The relationships among them are represented by edges. For instance, means that concept has an influence on concept . Generally, a state of a car can be affected by multiple operations or situations of the lane. For example, upgrade, downgrade, throttle, and brake all have an influence on the car speed. Herein, we use to express the degree of the effect from concepts to .
The following four steps are essential to construct the initial teacher submodel:
Step 1. Determine basic concepts in driving.
Through discussion with the experts of the driving school and some senior drivers, 48 basic concepts were selected, which are described as the nodes in Fig. 6 . These nodes are as follows:
: Steering Wheel, : LeftTurn Indicator, : Horn, : Clutch,
: Driving Brake, : Throttle, : Parking Brake, : Gears,
: Speedometer, : Fog Lamp, : Clearance Lamp,
: Hazard Warning Lamps, : Low Beam, : High Beam,
: Urban Road, : Slow Sign, : Stop Sign, : Tunnel,
: Upward Trail, : Downhill, : Right Turn Indicator,
: Fast Traffic Lane, : Slow Traffic Lane, : Crossroads,
: Heavy Road, : Snowy and Icy Road, : Rainy Road,
: Flooded Road, : Speed Up Sign, : Crosswind,
: Tire Puncture, : Steering Failure, : Braking Failure,
: Collision, : Foggy Weather, : Congestion,
: LeftHand Bend, : RightHand Bend, : U Turn,
: Night Driving, : Immovable Obstruction,
: Human, Livestock, Nonmotor Vehicle,
: RearEnd Collision Danger, : Traffic Light (Yellow to Red),
: Traffic Light (Yellow to Green), : Speed Limit Sign,
: Sidewalk, : Getting Start.
Step 2. Find the relation between concepts.
By analyzing each pair of concepts, if one concept influences another, there exists a relationship between them. Correspondingly, there exists an edge between the pair of concepts in Fig. 6 . Fig. 6 is a directed graph and the arrows of edges show the influence direction.
Step 3. Determine the weight of relation.
This step determines the degree of influence of a pair of concepts, namely, the weight of relation. The weights fall into three types as follows:
The first type is a constant weight value in the range of [0, 1]. This type of relation does not vary with the state values of other concepts.
The second type is a condition dependence whose weight is related to the state value of other concepts and the value is binary: 1 or 0. For example, the means of is that if and , then ; otherwise, .
The third type is a function whose weight is also related to the state value of concepts. To different state values, relevant weights are various. For example, the means of is that if , then ; if , then ; otherwise, .
Step 4. Build the initial FCM.
According to Fig. 6 , the initial FCM can be obtained and the part adjacency matrix of Fig. 6 is shown in Fig. 7 . Because there are so many concepts and the adjacency matrix of FCM is too big to be fully shown here, matrixes in Fig. 7 are only parts of the full matrixes.
It is unavoidable that the initial teacher submodel will have some defects resulting from the structure of the FCM or unreasonable weights in the FCM. The defects, related to unreasonable weights, can be overcome by the selflearning of the teacher submodel.
4.2.2 SelfLearning of the Teacher Submodel As mentioned in Section 3.3, after the initial teacher submodel is gained, the next step is the selflearning process of the teacher submodel to create the optimal FCM by using the local and global learning process. The learning process is based on the local learning algorithm and the global learning algorithm. In addition, based on the local and global learning, the teacher submodel can learn continuously according to real situations.
Fig. 8 shows the global learning process of the teacher submodel. For this case, it needs five learning steps to reach its final state. Fig. 8 a is the result of the first learning step, Fig. 8 b is the result of the second step, and Fig. 8 c is the result of last step.
As a result, the improved FCM of the teacher submodel contains driving knowledge which consists of not only prior knowledge of experts but also the modified and the new knowledge achieved by selflearning. So, the teacher submodel is intelligent enough to reason the answer and evaluate the students' actions, that is, it can guide students' study process.
• Step 1. Generate the game scene, that is, generate street map, traffic light, passerby, roadrock, and disturbance autos.
• Step 2. Generate the right game guidance by the teacher submodel.
• Step 3. Get the operating sequence of the student.
• Step 4. Judge the veracity of the student's operation according to the gamebased learning algorithm.
• Step 5. If the error is a bit big, the right guidance to the student is presented.
• Step 6. Update the FCM of the student.
5.1.1 Experiments for Local Learning of Teacher Submodel The aim of this experiment is to guide the local learning process between concepts in the FCM. Figs. 9 , 10 , and 11 show the local learning process of relation between and , taking no account of the influence of other concepts.
Fig. 9 shows that the expectation output and actual output of before the local learning are almost equal, but those of are quite different, which means that the relation between and needs to be adjusted by local learning.
Fig. 10 shows the local learning process. In Fig. 10 , the weight of connection between and is changing along with the increase of the training process.
As a result, after the local learning, the relation between and is right, which can be reflected by the fact that the actual output of and is almost equal to the expected output, as shown in Fig. 11 .
5.1.2 Experiments for Global Learning of the Teacher Submodel In the global learning experiment, the automobile driving FCM obtained in the last experiment is used as the initial FCM. First, the initial values of concepts are set, such as setting the initial speed of auto, other autos place, the crossing, and so on. Second, assign the expectation values according to the real ones and expert knowledge. Before the training process, the actual output is different from , and is much closer to after the global learning.
In Figs. 12 , 13 , and 14 , T_state is the expected output of the concepts and O_State is the actual output of the concepts. The Xaxis represents the 48 concepts (as shown in Fig. 6 ) and the Yaxis represents the output of state values.
Fig. 12 is the actual output of concepts before global learning. Fig. 13 is the actual output of concepts after learning five times. Fig. 14 is the actual output of concepts when global learning is completed. More specifically, Fig. 12 shows that there are many differences between the expected output and actual output of some concepts before global learning. The initial FCM is imperfect and is far from reality, justifying for the need for learning.
After learning for five times, the actual output is much closer to the expected output except for and ( Fig. 13 ), which shows that our global learning process is quite effective. After the global learning process is complete, the actual output is almost consistent with the expected output.
5.2.1 Participants of the Experiments The participants of the experiment were 20 persons who were studying driving skills or were going to study driving skills. They were randomly divided into the control group and the experimental group with 10 students in each group. Group learned the concepts from the driving handbook directly, while group was trained in the simulation system when they were studying from the driving handbook.
5.2.2 Experimental Design There is much information to study in the driving study process. From the information, we selected some complex and related topics to construct six study cases: two simple ones, two mediocre ones, and two difficult ones. The students studied these cases one by one. The study process consisted of three rounds of study. The first and the second rounds were timelimited study, while the third round was a timeunlimited study. After each round of study, there was a test to evaluate the study effectiveness. During the study process, we recorded how long each student spent on each case. The study process did not end until the students got above 80 percent of the correct answers.
This experiment focused on whether the simulation system and the model can improve the efficiency of the students' study. There were only two groups, and , in experiments. Group was used as the control group and group was used as the experimental group. We made use of the ttest for computing the result of the experiment, which is shown in Table 3 .
After the study experiments, we took advantage of a questionnaire to collect subjective evaluations of the system and the model from the students. Only group studied with the help of the simulation driving system and was asked to fill in the questionnaire. The questions in the questionnaire were designed simply to see whether our design and implementation of the simulation system was effective or not in helping them study.
5.2.3 Experimental Procedures In order to ensure the correctness of the evaluation of the driving training prototype system, the following steps were carried out [ ^{23} ]:
Step 1. Introduction.
The first step was to make students know the objective of the experiment and to make students familiar with the basic instructions about the driving training prototype system. To do this, we let the students of group B study an irrespective concept to the following test using the simulation system.
Step 2. Pretest.
The second step was that all the students of the two groups attended an individual test. The answers of each student were analyzed by statistical methods and the statistical results were compared with the posttest.
Step 3. Firstround timelimited study and test.
In this step, group A and group B employed different methods of the leaning process. The students of group A did not use the simulation driving system and they only studied from the driving handbook. The students of group B studied from the handbook and practiced in the driving training prototype system. That is to say, group B used gamebased learning, but group A did not. The time for each case was limited to 5 minutes, and after this round of study, the test was repeated.
Step 4. Secondround timelimited study and test.
This step repeated step 3 and the test result was recorded separately.
Step 5. Timeunlimited study and test.
To get the same study effectiveness in principle, different students need different times. In addition to the individual difference, the main reason might lie in different study methods. To compare the two groups' differences, this round of study was an unlimited time study. The student could not stop studying until he got above 80 percent of the correct answers in the test. During the process, the time each student spent was recorded for the final analysis.
Step 6. Survey.
The last step was that students fulfill an individual subjective questionnaire which collected their opinions about the experiments. The questionnaire is shown in Table 1 .
Table 1. Summary of Results from the Student Responses to a Series of Questions
5.2.4 Design of the Questionnaire The questionnaire included 10 questions: questions 1 and 2 were about the knowledge of the participant, questions 3 and 5 were about using the system, and the other questions were about the learning effect of the system. By analyzing the scores students gave, the subjective estimate about the system can be achieved and the analysis is included in the following sections.
5.2.5 Experimental Results There are two aspects of the experimental results: subjective survey and objective evaluation, which are discussed in the following:
1. Results of subjective survey
The questionnaire used a fivepoint Likert Scale, with each question having five selections marked from one point to five points. One point means the least favorable to the statement. Five points means the most favorable to the statement. Each student filled in the questionnaire individually and gave each question a score. The summary of the survey is shown in Table 1 . Through analyzing the results of the questionnaire, we know that the students' opinions about the system are very positive in general. In Table 1 , except for the fifth question, most of the questions' mean value is above 4.5, which means the students agreed that the system was very helpful to improve their driving skills. Most of them thought that the system made studying interesting and that the teacher in the system guided them to study effectively. The fifth question surveyed if "the teacher" interfered the student, which is a negative question. In other words, the low score means a better result.
Furthermore, the standard deviation of each question is small, which means that all the students had a consensus opinion about this question.
2. Results of objective evaluation
The guidance ability of the model can be evaluated by the differences between the two groups' real study effectiveness. In the experiment, we consider the study effectiveness from two aspects. One is the test score and the other is the study time.
Table 2 summarizes the average results of the four tests. The pretest results show that two groups had similar knowledge levels on driving skills. After the first round of study, the test results show that group was a little better than group . The reason is that group spent some time familiarizing themselves with the game system. After the second round of study, group was better than group , obviously because of the help of the driving training prototype system. It should be noted that the result of the posttest does not mean anything because the two groups spent different amounts of time to achieve the goal.
Both gamed and nongamed students had significant improvement in the second round test compared with the pretest. However, it is very evident that the improvement of gamed students is greater than that of nongamed students. So, the driving training prototype system is effective in improving the study process of students effectively.
The test was designed so that each student must answer the questions correctly above 80 percent by continuous use of the study process. During the test, the time each student spent on each case was recorded. The time for each case consists of three parts: the first round and the second round, which are 5 minutes each, and the third round, which is different for different students. We measured how long the students spent studying to finish the test. By using an Independent Samples ttest Procedure, where is considered to be significant, the average, standard deviation, and Pvalue are computed and listed in Table 3 .
Table 3. The Results of the TTest
In Table 3 , with the difficulty level increasing, the difference between the two groups extends more and more. For the simple cases, means that the difference is small. For the mediocre cases, the average time group spent is less than that of group and means that the difference is significant. For the difficult cases, group did much better than group and the is much smaller than 0.05, which means that the difference is very significant.
In general, Tables 2 and 3 show that the driving training system is helpful in improving the study process effectiveness.
5.2.6 Discussion of External Factors Although the experimental results are satisfactory, some external factors, which may have influenced the experimental results, should be further discussed. Here, we only discuss the following three factors:
1. Difference of participants
It is inevitable that the knowledge of participants varies from person to person. For example, some participants have acquired some driving knowledge, so their experimental results are influenced by their prior knowledge.
2. Motivation of participants
During the experiment, each participant has different motivations. For example, some participants may be absentminded in the experiments, which will influence the results.
3. Group of participants
If participants are not divided into groups randomly and different participants are not in a fairly equal manner, the groups will influence the results to a great extent.
The difference of participants is an objective factor, while the motivation of participants is a subjective factor. The influence of both is difficult to eliminate, so we tried to minimize the influence in our experiments.
Our method was to divide the participants into groups as randomly as possible. In the next step, we will increase the number of participants and groups, which may get more convincing results.
5.2.7 Comparison with Traditional Driving Simulation Based on the proposed model, the prototype system is different from traditional driving simulations in the two main aspects as follows:
1. Efficiency
Since the proposed model is based on the improved FCM which has the abilities of reasoning and selflearning, it can automatically generate the scenario and deduce the answer to the generated scenario by the FCM's reasoning. But, for most of the traditional driving simulations, they need the programmer to design the scenario by hand. They also need to define the conditions for the scenario to judge the operator's actions. So, it is more efficient to develop the system based on our model than on the traditional methods.
2. Precision
It is for the same reason that our system may have lower precision than traditional systems. Because our model generates scenarios and reasons the answers automatically, it is certain that its precision is lower than those by hand. It requires a further study in order to improve the precision in sophisticated studying environments.
In conclusion, compared with traditional simulations, our model is highly automatic in generating study scenarios and reasoning the answers. But the procession of the system is lower than traditional simulations and needs to be improved.
1. Taking advantage of the Hebbian learning rule and unbalance degree to extend the FCM in order to equip it with the abilities of selflearning and knowledge acquisition from both data and prior knowledge, which makes the FCM more suitable for designing a gamebased learning system.
2. Proposing a new guided gamebased learning model based on the improved FCM including the teacher submodel, the learner submodel, and a set of learning mechanisms. The model provides a workable method to help design a gamebased learning system.
3. Giving a case study of the proposed model in which a driving training prototype system was implemented according to the proposed model. Experimental results show that the proposed model is effective and valid in terms of controlling and guiding students' study process.
Acknowledgments
• The authors are with the High Performance Computing Center, School of Computer Engineering and Science, Shanghai University, Room 303, Xingjian Building, No. 149 Yanchang Rd, Shanghai 200072, P.R. China. Email: {luoxf, xwei, zhangjun_haha}@shu.edu.cn.
Manuscript received 1 Dec. 2009; revised 16 Apr. 2010; accepted 30 July 2010; published online 17 Aug. 2010.
For information on obtaining reprints of this article, please send email to: lt@computer.org, and reference IEEECS Log Number TLTSI2009120164.
Digital Object Identifier no. 10.1109/TLT.2010.26.
1. Learning falls into two categories in this paper. One is human learning and the other is machine learning. In order to avoid confusion with these two categories of learning, we use the word "studying" to represent human learning (except for gamebased learning) and "learning" to represent machine learning.
References
Xiangfeng Luo received the master's and PhD degrees from the Hefei University of Technology in 2000 and 2003, respectively. He was a postdoctoral researcher with the China Knowledge Grid Research Group, Institute of Computing Technology (ICT), Chinese Academy of Sciences (CAS), from 2003 to 2005. He is currently an associate professor in the School of Computers, Shanghai University. His main research interests include web content analysis, Semantic Networks, web knowledge flow, Semantic Grid, and Knowledge Grid. His publications have appeared in Concurrency and Computation: Practice and Experience, the Journal of Systems and Software, and the Journal of Computer Science and Technology.
Xiao Wei is currently working toward the PhD degree at Shanghai University. His main research interests include gamebased learning, interactive computing, and web content analysis.
Jun Zhang received the bachelor's degree in 2008 from Shanghai University, where he is currently working toward the graduate degree in the School of Computers. His main research interests include online word relation discovery and topic detection and tracking.
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