**4.1 Experiment 1 – Group X**

The learners in Group X were experimented. At first, all 50 questions were divided into three levels according to accuracy rate of Group X. As shown in Table 3, question level was defined, and all questions were classified. Moreover, the average and standard deviation of answer time in Group X were obtained, and all data were transformed by using Eq.(15). The diagnosis results are shown in Table 4.

"Others" in Table 4 indicates that the output was not any stored patterns, in other words, CNN couldn't diagnose. In the experiment, diagnosis rate, which means that CNN recalled a stored pattern, was about 93.3 %. It is recognized that learner patterns are classified into A,B in easy questions (Level I) and C,D in difficult (Level III). Hence, this result can be appropriate.

Q1

A

Input Hidden Output

Intelligent Tutoring System with Associative Cellular Neural Network 131

Associative BCNN is effective to diagnose learner's understanding level because it has a high diagnosis capability. However, it has a significant problem with lack of representable understanding levels. Though we can basically overcome it by increasing cells, and

As described above, Associative BCNN is effective for diagnosis of understanding level. However, it has a difficulty of few understanding levels. In order to overcome it, extended

The principle of Tri-valued output CNN (TCNN) is similar with that of BCNN, and we can

1 if *s* + *L* ≤ *x*

*<sup>L</sup>* if *<sup>s</sup>* <sup>&</sup>lt; *<sup>x</sup>* <sup>&</sup>lt; *<sup>s</sup>* <sup>+</sup> *<sup>L</sup>* 0 if −*s* ≤ *x* < *s*

The parameter *s* provides a new saturated region, and *L* enables us to adjust saturated regions. If *s* = 0 and *L* = 0, the function is conventional BCNN. Fig.7 shows the output function. Design method of associative TCNN is also similar with that of associative BCNN. All you

*<sup>L</sup>* if <sup>−</sup>(*<sup>s</sup>* <sup>+</sup> *<sup>L</sup>*) <sup>&</sup>lt; *<sup>x</sup>* <sup>&</sup>lt; <sup>−</sup>*<sup>s</sup>* −1 if *x* ≤ −(*s* + *L*).

Associative CNN is designed, and more versatile system is constructed.

⎧ ⎪⎪⎪⎪⎪⎪⎪⎨

*xij* − *s*

*xij* + *s*

⎪⎪⎪⎪⎪⎪⎪⎩

have to do is to change each element of α*<sup>i</sup>* in Eq.(7) is −1, 0, +1.

B

C

D

(16)

Q2

Fig. 6. Diagnosis Module by MLP

computational amount is also be increased.

**5. Extended associative CNN – TCNN**

**5.1 Tri-valued output associative CNN**

easily realize by redesigning output function as

*yij* =


Table 4. Diagnosis Result of Group X


Table 5. Diagnosis Result of Group Y


Table 6. Diagnosis Result by MLP

#### **4.2 Experiment 2 – Group Y**

We next made a similar experiment in Group Y. The same value as ¯*tk* and *σ<sup>k</sup>* of Group X were used. Experimental results are shown in Table 5. In this experiment, diagnosis rate was 100 %.

Associative CNN has a classification function of ambiguous data, and doesn't require a great number of data such as a fuzzy rule. Hence, it can be an useful model for such a problem.

Moreover, a system should immediately provide learners with feedback in real-time environment such as WBT (Web Based Training) system. As Experiment 2, if the system could classify without recalculating ¯*tk* and *σk*, its usefulness would be much higher.

#### **4.3 Experiment 3 – Comparison experiment**

In this section, multi-layered perceptron (MLP) which is one of representative neural network model was applied to this diagnosis problem in order to compare with associative CNN performance. The typical three-layered perceptron with Back Propagation Algorithm was used. Fig.6 shows MLP model used in the experiment. Training data were four stored patterns as shown in Fig.5. Learning was iterated until the mean square error between training data and the output was less than 0.001. When a value of output unit was more than 0.75, the pattern corresponding to it was the estimation result. Tables 6 (a) and (b) show the results. Most of patterns were classified as "Others", in other words, "not diagnosed". To compare with the diagnosis result by associative CNN (Tables 4 and 5), it is evident that diagnosis rate of associative CNN is superior to that of MLP in both cases.

Fig. 6. Diagnosis Module by MLP

8 Will-be-set-by-IN-TECH

Level No. A B C D Others I 10 7 3 0 0 0 II 10 2 3 2 1 2 III 10 0 0 5 5 0

Level No. A B C D Others I 5 4 1 0 0 0 II 5 3 1 0 1 0 III 5 1 0 1 3 0

(a) Group X Level No. A B C D Others I 10 2 2 0 0 6 II 10 1 0 0 0 9 III 10 1 0 1 3 5 (b) Group Y Level No. A B C D Others I 5 2 1 0 0 2 II 5 1 0 0 1 3 III 5 0 0 0 1 4

We next made a similar experiment in Group Y. The same value as ¯*tk* and *σ<sup>k</sup>* of Group X were used. Experimental results are shown in Table 5. In this experiment, diagnosis rate was 100

Associative CNN has a classification function of ambiguous data, and doesn't require a great number of data such as a fuzzy rule. Hence, it can be an useful model for such a problem. Moreover, a system should immediately provide learners with feedback in real-time environment such as WBT (Web Based Training) system. As Experiment 2, if the system could

In this section, multi-layered perceptron (MLP) which is one of representative neural network model was applied to this diagnosis problem in order to compare with associative CNN performance. The typical three-layered perceptron with Back Propagation Algorithm was used. Fig.6 shows MLP model used in the experiment. Training data were four stored patterns as shown in Fig.5. Learning was iterated until the mean square error between training data and the output was less than 0.001. When a value of output unit was more than 0.75, the pattern corresponding to it was the estimation result. Tables 6 (a) and (b) show the results. Most of patterns were classified as "Others", in other words, "not diagnosed". To compare with the diagnosis result by associative CNN (Tables 4 and 5), it is evident that diagnosis rate

classify without recalculating ¯*tk* and *σk*, its usefulness would be much higher.

Table 4. Diagnosis Result of Group X

Table 5. Diagnosis Result of Group Y

Table 6. Diagnosis Result by MLP

**4.3 Experiment 3 – Comparison experiment**

of associative CNN is superior to that of MLP in both cases.

**4.2 Experiment 2 – Group Y**

%.

Associative BCNN is effective to diagnose learner's understanding level because it has a high diagnosis capability. However, it has a significant problem with lack of representable understanding levels. Though we can basically overcome it by increasing cells, and computational amount is also be increased.

#### **5. Extended associative CNN – TCNN**

As described above, Associative BCNN is effective for diagnosis of understanding level. However, it has a difficulty of few understanding levels. In order to overcome it, extended Associative CNN is designed, and more versatile system is constructed.

#### **5.1 Tri-valued output associative CNN**

The principle of Tri-valued output CNN (TCNN) is similar with that of BCNN, and we can easily realize by redesigning output function as

$$y\_{ij} = \begin{cases} 1 & \text{if } s+L \le x \\ \frac{\mathbf{x}\_{ij}-s}{L} & \text{if } s < x < s+L \\ 0 & \text{if } -s \le x < s \\ \frac{\mathbf{x}\_{ij}+s}{L} & \text{if } -(s+L) < x < -s \\ -1 & \text{if } x \le -(s+L) . \end{cases} \tag{16}$$

The parameter *s* provides a new saturated region, and *L* enables us to adjust saturated regions. If *s* = 0 and *L* = 0, the function is conventional BCNN. Fig.7 shows the output function. Design method of associative TCNN is also similar with that of associative BCNN. All you have to do is to change each element of α*<sup>i</sup>* in Eq.(7) is −1, 0, +1.

Label Answer Time Understanding level a Right Short Highest b Right Medium High c Right Long Medium d Wrong Short Low e Wrong Medium Low f Wrong Long Low

Intelligent Tutoring System with Associative Cellular Neural Network 133

Pattern Easy Medium Difficult A a a a b b b B c c b c c c c b c C a a f b b f c c f D a f f b f f c f f E d d d e e e f f f

understanding levels in accordance with combination of label and level as shown in Table 8,

The purpose of experiments is to evaluate how exactly associative TCNN can diagnose

1. We design stored patterns which correspond to expected understanding levels in

learner's understanding level. Experiment condition is described as follows:

Table 7. Understanding levels defined per question

and design stored patterns which correspond to them.

1. All tests are used in CBT (Computer Based Testing). 2. All 38 questions are multiple choice (eight choices).

Design of associative TCNN is described as follows:

2. We use *s* = 0.3 and *L* = 0.5 in Eq.(16), which is general value. 3. We normalize experiment data, and make answer patterns.

**6. Evaluation experiments and results**

3. 20 learners are tested in experiments. 4. Test is used in a unit ("Probablities").

accordance with prior knowledge.

**6.1 Design of associative TCNN**

Table 8. Understanding levels

Fig. 7. Output function with three saturated regions

Fig. 8. Examples of answer pattern per question

Fig. 9. Expression of answer pattern by Associative TCNN

#### **5.2 Design of associative TCNN diagnosis module**

By extending associative CNN to tri-valued output, the number of representable information for diagnosis can be increased. In other words, more prior knowledge can be realized in cell expression. Then, question level (difficulty) is newly added. That is,


Fig.8 shows examples of answer pattern per question. (a) means right/short/easy, and (b) indicates wrong/medium/difficult. Moreover, we can make a total answer pattern by arranging all answer patterns as shown in Fig.9 as is the case with associative BCNN.

We next generate stored patterns which correspond to understanding levels. This study defines six grades (four understanding levels) in a question as shown in Table 7. We define




Table 8. Understanding levels

10 Will-be-set-by-IN-TECH

+1



Fig. 7. Output function with three saturated regions

Fig. 8. Examples of answer pattern per question

Q2

Fig. 9. Expression of answer pattern by Associative TCNN

expression. Then, question level (difficulty) is newly added. That is, 1. Answer cell means that an answer is right/wrong (Discrete). 2. Time cell means that an answer time is short/long (Continuous). 3. Level cell means that a question is easy/standard/difficult (Discrete).

**5.2 Design of associative TCNN diagnosis module**

y ij


(a) (b)

By extending associative CNN to tri-valued output, the number of representable information for diagnosis can be increased. In other words, more prior knowledge can be realized in cell

Fig.8 shows examples of answer pattern per question. (a) means right/short/easy, and (b) indicates wrong/medium/difficult. Moreover, we can make a total answer pattern by arranging all answer patterns as shown in Fig.9 as is the case with associative BCNN. We next generate stored patterns which correspond to understanding levels. This study defines six grades (four understanding levels) in a question as shown in Table 7. We define

time level

answer

Q1

s

L

O xij

Q5

+1

understanding levels in accordance with combination of label and level as shown in Table 8, and design stored patterns which correspond to them.

#### **6. Evaluation experiments and results**

The purpose of experiments is to evaluate how exactly associative TCNN can diagnose learner's understanding level. Experiment condition is described as follows:


#### **6.1 Design of associative TCNN**

Design of associative TCNN is described as follows:


Associative TCNN Linear Model 95.0% 52.6%

Intelligent Tutoring System with Associative Cellular Neural Network 135

The early half of chapter described a new diagnosis system of learner's understanding level by using associative Binary Cellular Neural Network (BCNN). The results obtained are as

1. At first, ten learners (Group X) were divided all questions into three levels (difficulties) in accordance with accuracy rate. Their understanding levels could be appropriately diagnosed by the system in each difficulty. As a result, diagnosis rate was about 93.3%. It implies that the result can be appropriate according to the relation between question

2. Moreover, we made a similar experiment on five learners (Group Y). Consequently, diagnosis rate was 100%. It implies that associative BCNN is useful as an diagnosis module

3. The similar diagnosis experiments were performed by Multi-Layered Perceptron (MLP). Consequently, the diagnosis performance of associative BCNN is better than that of MLP. BCNN has an important problem with lack of representable understanding levels. Then, the latter half of chapter described an improved diagnosis system by using associative Tri-valued

1. We first defined five understanding levels, and designed associative TCNN according to

2. We next made a diagnosis experiment with associative TCNN. Participants were 20 learners who studied "Probabilities". Consequently, associative TCNN could completely diagnose all of them into expected understanding levels. It was recognized that the

3. In order to compare our system with conventional method, we also made a diagnosis experiment by linear function. From comparison of precision, we confirmed that associative TCNN which comprehensively diagnoses was better than linear function

The diagnosis by associative TCNN plays a role in rough-classification in pattern recognition. Standard associative TCNN is used in the experiment. Hence, optimized associative TCNN will probably provide better results. Our future work is to improve diagnosis performance

Part of this research was supported by a Grant-in-Aid for Scientific Research from the Ministry

Chua, L.O. and Yang, Y. (1988). Cellular Neural Networks. *IEEE Transaction on Circuit &*

Gunel, K (2010). Intelligent Tutoring Systems. *LAMBERT Academic Publishing*, pp.1-15.

of Education, Culture, Sports, Science and Technology (21700829), Japan.

diagnosis results were valid in accordance with accuracy and answer time.

Cellular Neural Network (TCNN). The results obtained are as follows:

Table 10. Comparison of precision

level and result of understanding level.

in terms of versatility.

which partly estimates.

**8. Acknowledgment**

**9. References**

with optimized associative TCNN.

*Systems*, pp.1257-1290.

**7. Conclusion**

follows:

them.


Table 9. Diagnosis results (Accuracy:%,Time:s)

#### **6.2 Experiment results and discussion**

Table 9 shows diagnosis results. All values in the table are average. This result shows that associative TCNN could completely diagnose all learners. We next evaluate the validity of diagnosis result. For instance, learners in the cluster "A" should have higher understanding level in all levels. It has high accuracy and short time compared with averages of all in any level. Hence, the diagnosis result of cluster "A" is valid. Learners in cluster "C" should have high or higher understanding level in Standard and Easy (Level II and I), and low in Difficult (Level III). Learners in cluster "D" should have high or higher understanding level in Easy, and low in Difficult and Standard. Learners in cluster "E" should have low understanding level in all levels. We can similarly conclude that the diagnosis results of clusters C,D, and E are valid.

#### **6.3 Comparison experiment**

In order to evaluate the accuracy of our system, we make a comparison experiment. We use a linear function according to the related work (Sumada et al., 2007) as the following:

$$
\Delta U = kL\_t + (1 - k)L\_a \tag{17}
$$

,where *Lt*, *La* are answer time and accuracy, respectively. *U* is understanding level. This equation is also based on our prior knowledge. It is appropriate as a comparison model with ours.

Comparison experiment is performed as the following:


In case of estimation by linear funcion, *k* is changed from 0.1 to 0.9, and the best is adopted as the estimation result.

Table 10 shows a comparison of precision. The precision of associative TCNN is superior to that of linear function. These results represent that synthetical diagnosis of associative TCNN is better than partial estimation of linear function.


Table 10. Comparison of precision
