Estimating comparison indicators

Chapter 4: Recommendation of Advanced Learners 67

68 Chapter 4: Recommendation of Advanced Learners

Learning processes

& learning activities

……

……

……

Estimate comparison

indicators

Input Ex:

CoW32=0.4524 AoR32=0.7500 C3=4.2

……

Output Ex:

P1ia=0.6581 P2ia=0.7412 P3ia=0.4533

Definition & Calculation

Web Page

Abstract

Remark

Comment

Comment

å å

Î

= Î

ai ai

WP

k ki

WP

k ka

ia CoW

CoW p₁^'

å

Î

=

U i

ia ia

ia p p

p_{1 1}^' / ₁^' 1.Indicator of Comprehension of WP

å å

Î

= Î

ai ai

WP

k ki

WP

k ka

ia AoR

AoR p^'₂

å

Î

=

U i

ia ia

ia p p

p 2^'

' 2

2 /

2. Indicator of Adequacy of Remark

åÎ

=

U

i ia

ia

ia p p

p_{3 3}^' / ^'₃

å å å å

Î Î

Î Î

=

ai ai

ai ai

WP

k lNote kli

WP

k lNote

kla

ia AoC

AoC p₃^'

3. Indicator of Agreement of Comment

ia ia

ia

ia p p p

p =a´ ₁ +b´ ₂ +g´ ₃ Combination: linear regression α, β, γ: estimated

User1 User2User3…. Userm

User1 0 0 0.2334 … 0

User2 0.7531 0 0.4553 0

User3 0.2469 0.5 0 … 0.1725

…

Userm 0 0.5 0 … 0

e.g. entry1,3:

The indicator that user3 is more advanced (knowledgeable) than user1 is 0.2334

Fig.4.5 Example of estimating comparison indicators

Comparison indicators are utilized to compare the knowledge level of two learners. Comparison indicators between a pair of learners represent the amount of relationship between them. Indicator of comprehension of WP is based on analysis of web pages and abstracts which are post by both learners. Indicator of adequacy of remark is based on remarks and comments.

Indicator of agreement of comment is based on comments.

whose comments are better than the others’ comments. Fig.4.5 is the example of estimating comparison indicators.

Comparison indicators between a pair of learners represent the amount of relationship between them.

By using extracted interaction indicators described in section 4.2.1, we consider three types of comparison indicators to compare the knowledge level between two learners.

1) The comparison indicator of CoW (Comprehension of web page)

After searching, gathering and aggregating, the learner wrote the abstract. The comparison indicators of CoW are utilized to describe a knowledgeable degree of effective learners among group learner.

By using the analysis of interaction indicator CoW, we can obtain the effective learners’ comparison.

Chapter 4: Recommendation of Advanced Learners 69

å å

Î

= Î

ai ai

WP k

ki WP k

ka

ia CoW

CoW

p₁^' (4.4)

Then, we use

å

Î

=

U i

ia ia

ia p p

p_{1 1}^' / ₁^' to normalize p_1ia^' .

Where,

p

_1ia is the comparison indicator of learner

u

_a being more advanced (knowledgeable) than learner

u

_i based on the interaction indicator comprehension of web page. WP_ai is the web pages that were learned by both learner

u

_a and learner

u

_i.

2) The comparison indicator of AoR (Adequacy of remark)

After learners sought the useful or interesting topics on the web, they wrote their remarks about it.

Remarks are produced by the learners. The comparison indicators of AoR are utilized to evaluate a knowledgeable degree of effective creators among group learner. Likewise, we can obtain the effective creators’ comparisons by analyzing the interaction indicator AoR.

å å

Î

= Î

ai ai

WP k

ki WP k

ka

ia AoR

AoR

p^'₂ (4.5)

Then, we use

å

Î

=

U i

ia ia

ia p p

p_{2 2}^' / ₂^' to normalize p_2ia^' .

Where, p_2ia is the comparison indicator of learner

u

_a being more advanced (knowledgeable) than learner

u

_i based on the interaction indicator adequacy of remark. WP_ai is the web pages that were learned by both learner

u

_a and learner

u

_i.

3) The comparison indicator of AoC (Agreement of comment)

70 Chapter 4: Recommendation of Advanced Learners

In comment space, learners can communicate with each other, improvement knowledge by posting self opinions or ideas, generate production together. The comparison indicators of AoC are utilized to calculate a knowledgeable degree of effective collaborators among group learner. We can obtain the effective collaborators’ comparisons through the analysis of factor AoC.

å å å å

Î Î

Î Î

=

ai ai

ai ai

WP

k l Note

kli WP

k l Note

kla

ia AoC

AoC

p₃^' (4.6)

Then, we use

å

Î

=

U i

ia ia

ia p p

p_{3 3}^' / ₃^' to normalize p_3ia^' .

Where, p_3ia is the comparison indicator of learner

u

_a being more advanced (knowledgeable) than learner

u

_i based on the interaction indicator agreement of comment. WP_ai are the web pages that were learned by both learner

u

_a and learner

u

_i. Note_ai are the notes that were wrote comments by both learner

u

_a and learner

u

_i.

4) Combining comparison indicators

In order to combine the three indicators described above to obtain final result, there are several methods. For example we can use Bayesian or probabilistic networks. However, Bayesian network requires intensive data collection. In addition, computation of prior probabilities, conditional and joint probabilities and relationships among various learner interactions in real time is intensive especially if the network is large and updates are frequent. The simplest way to combine multiple classifiers is by voting, which corresponds to taking a linear combination of the indicators. This is also known as ensembles and linear opinion pools. Here we adopt this simplest way to our approach.

) 1 , 0 ( , ,

1

3 2

1

Î

= + +

´ +

´ +

´

=

g b a

g b a

g b

a _{ia ia ia}

ia p p p

p

(4.7)

Chapter 4: Recommendation of Advanced Learners 71

User1 User2 User3 …. Userm User1

User2 User3

… Userm

……

U1 U2

Um ……

……

…… ……

U1 U2

Um

……

U1 U2

Um

……

User1 User2 User3 …. Userm User1

User2 User3

… Userm

User1 User2 User3 …. Userm User1 0.0167 0.6945 0.2389 … 0.0167 User2 0.1667 0.1667 0.1667 0.1667 User3 0.2268 0.4265 0.0167 … 0.4474

…

Userm0.0167 0.0167 0.1720 … 0.0167

Learning resource

Transition probability matrix indicates changes in knowledge-level comparison of learners over time (with regards to learning process)

Based on comparison indicators

Time = 1 Time = n (future)

Entry 3,1:

The probability that user3 is more advanced (knowledgeable) than user1 is 0.2268

learning process

Time = 2

Learners’ comparison

÷÷

÷÷

÷÷

÷÷

ø ö

çç çç çç çç

è æ

=

0 0 8275 . 0 1725 . 0 0 0

6175 . 0 0 3825 . 0 0 0 0

4785 . 0 5215 . 0 0 0 0 0

0 3113 . 0 0 0 4553 . 0 2334 . 0

0 0 0 0 0 0

0 0 0 2469 . 0 7531 . 0 0 P

÷÷

÷÷

÷÷

÷÷

ø ö

çç çç çç çç

è æ

= -+

=

0167 . 0 0167 . 0 7615 . 0 1720 . 0 0167 . 0 0167 . 0

5725 . 0 0167 . 0 3610 . 0 0167 . 0 0167 . 0 0167 . 0

4474 . 0 4861 . 0 0167 . 0 0167 . 0 0167 . 0 0167 . 0

0167 . 0 2967 . 0 0167 . 0 0167 . 0 4265 . 0 2268 . 0

1667 . 0 1667 . 0 1667 . 0 1667 . 0 1667 . 0 1667 . 0

0167 . 0 0167 . 0 0167 . 0 2389 . 0 6945 . 0 0167 . 0

) 1

( M

P ee P

T

a

& a

&

&

÷÷

÷÷

÷÷

÷÷

ø ö

çç çç çç çç

è æ

= ïî ïí

ì >

= å

0 0 8275 . 0 1725 . 0 0 0

6175 . 0 0 3825 . 0 0 0 0

4785 . 0 5215 . 0 0 0 0 0

0 3113 . 0 0 0 4553 . 0 2334 . 0

1667 . 0 1667 . 0 1667 . 0 1667 . 0 1667 . 0 1667 . 0

0 0 0 2469 . 0 7531 . 0 0

1 .

, 0 otherwise M

P if P

P ^l

il il

state1 state2 staten

Fig.4.6 Example of estimating learners’ comparison

The learning processes change with regards to time and learning steps. For this reason, we identify the relationship of learners by using Markov Chain Model which includes the learning processes of every learner. Transition probability matrix indicates changes in knowledge level comparison of learners over time (with regards to learning process). P is the translation matrix of combination of three comparison indicators. Pis the revised transition probability matrix. P&&& is the primitive stochastic matrix.

a,b,g are parameter representing the impact of indicator of CoW, the impact of indicator of AoR and the impact of indicator of AoC, repressively.

p

_ia is the indicator that learner a is more advanced (knowledgeable) than learner i. For example, a,b,g are based on least square method.

ドキュメント内 COLLABORATION AND RECOMMENDATION FOR GROUP LEARNING USING IN e-NOTEBOOK SYSTEM (ページ 81-85)