A Hidden Markov Model Approach to Predict Students' Actions in an Adaptive and Intelligent WebBased Educational system Masun Homsi
Rania Lutfi
Rosa M. Carro
Barakat Ghias
Faculty of Sciences University of Aleppo, Aleppo, Syria
[email protected]
Faculty of informatics Engineering University of Al-Baath, Homs, Syria
[email protected]
Escuela Politécnica Superior Universidad Autónoma de Madrid, Madrid, Spain
[email protected]
Faculty of Arts and Human Sciences University of Damascus Damascus, Syria
Abstract— This paper demonstrates how Hidden Markov Model (HMM) approach is used potentially as a tool for predicting the next concepts visited by students in an Adaptive and Intelligent Web-Based Educational System (AIWBES) for teaching English as Foreign Language (EFL). This tool helps teachers to provide their students with appropriate assistance during the learning process in a timely manner. The prediction process is achieved by following three phases, Initialization phase, adjustment phase and prediction phase. The experiment results are encouraging and serve to show the promise of HMM in AIWBESs and they show accuracy in the next action prediction reaching up to 92%. Keyword; Hidden Markov Model, AIWBES , Baum-Welch Algorithm, forward Algorithm.
I. INTRODUCTION AIWBESs try to be more adaptive than traditional educational systems "Just-put-it-on-the-web" by building a student model to represent goals, preferences and knowledge of each student and updating it in accordance with their knowledge acquisition process. A new quality of an educational system is reached by enhancing it by prediction of future students' actions based on current and previous information with the objective to get an improved overall system. The general architecture of our AIWBES for teaching EFL is composed of four parts [1, 2]: Knowledge Domain where the course content is organized into a concept network to represent learning objectives. A learning objective concerns several concepts which are classified in: main concepts, prerequisite concepts and sub-Concepts. A Pedagogical Module stores a set of rules. These rules represent teacher strategies used to instruct students by selecting appropriate concepts for them during course planning. A Users' Interface Module, where teachers can upload and update the course content while student's interface allows the student interacts with the different learning objectives and concepts of the course. Student model is built using HMM to compute students' knowledge status related to each concept in the domain knowledge and it consists of static and dynamic parts. Our system provides Navigation Adaptation technique by means of link sorting, link hiding and annotations [1, 2, 3]. It
also uses XML with a DTD document for representing the course knowledge semantically [2]. A Predictor is added as new tool to improve the interaction between the students and the system by foreseeing the students' desires and acts proactively. Machine learning is a branch of artificial intelligence that employs a variety of statistical, probabilistic and optimization techniques that allows computers to “learn” from past examples and to detect hard-to-discern patterns from large, noisy or complex data sets. To predict or anticipate future student's actions, many machine learning techniques as e.g. Hidden Markov Model, Bayesian Networks, neural networks are obvious candidates HMM is a probabilistic model used to align and analyze sequence datasets by generalization from a sequence profile. It is commonly used in speech recognition and its applications have been spreading steadily to other fields that include, e.g. communications, computational biology and e-learning systems[4, 5, 6]. Many educational systems use HMM. It is implemented In WELS (Web-Based English Learning System) to classify students in two groups (novice and advanced) with the objective to offer adaptive course for each group [7]. IMMEX (Interactive Multi-Media Exercises) utilizes HMM to model students' learning trajectories and to predict their future strategies [8]. HMM is extensively applied in predication applications. It is implemented in MANIC (Multimedia Asynchrously Networked Individualized Courseware) to prefetch lecture notes by predicting future browsing actions of specific users [9]. HMM predicts protein-coding genes encoded in DNA sequences of eukaryotes (plants and animals) [10]. In [11] is used for predicting RNA secondary structure. L. Terran uses HMM to detect security breaches by comparing a user’s current behavior to the HMM derived from their past behavior [12]. Reference [13] presents HMM approach for forecasting stock price for interrelated markets. Our HMM approach predicts the next concept based on the history of concepts, visited by a certain student navigating within the course. Predictor results are evaluated by some
concept sequences of real students, gathered from our system for teaching EFL. This paper is organized as follows. Section 2 presents the general prediction process. Section 3 details the proposed prediction algorithm. Section 4 evaluates the performance of the proposed algorithm. Finally the last section provides conclusions of this work. II.
PREDICTION PROCESS
Figure 1 depicts general prediction process and it is divided in three phases; initialization, adjustment and prediction.
Where: t(i)=P(O1, O2, …, Ot, qt=Si, ) – the forward variable [5, 14], representing the probability of the partial observation (concept) sequence until time t, and hidden state Si ate time t, given the model =(A, B, ).
Next concept
Prediction
Adjustment
HMM , A, B
HMM , A, B
Initialization
Concepts' sequence
t(i)=P(Ot+1, Ot+2, …, OT |qt=Si, ) – the backward variable [5,14], representing the probability of the observation (concept) sequence from time t+1 to T, given hidden state Si at time t and the model =(A, B, ). t(i, j)=P(qt=Si, qt+1=Sj |O1, O2,…,OT, ): the probability of being in hidden state Si at time t and making a transition to state Sj at time t+1, given the observation sequence O= O1, O2, …, OT and the model =(A, B, ).
New concepts' sequence
t(i)=P(qt=Si|O1, O2,…,OT, ): the probability of being in state Si at time t given the observation sequence O= O1, O2, …, OT and the model =(A, B, ).
Figure 1. General prediction process
A. - Initialization Phase The initialization phase is shown in figure 2. For each student a HMM (λ) is built based on his/her previous concept access sequences. Each HMM is specified by [4, 5, 6, 14]: HMM (λ)
AIWBES
Compute , A, B
C01, C05, C11, … Concepts' Sequence
Given a new observed sequence and given a HMM (λ), the Baum-Welch algorithm is used to adjust the initialized HMM and to maximize the new observed sequence (Figure 3).
Initialization and adjustment phases can be summarized using the following steps: 1- For each student a HMM =(A, B, ) is Initialized; 2- Compute t(i), t(i), t(i, j), t(i), t=1…,T, i-0,…,N-1, j=0,…,N-1; 3- Adjust the model =(A, B, ). 4- If P(O|) increases, go to 2.
Student
Figure 2. Initialization phase
- N, the number of hidden states S= {S0, S1, …, SN-1), which represents number of concepts in the domain model of the system. qt represents the hidden state at time t.
Concepts
C05, C011,…,C 03 New Concepts' Sequence
C05, C011,…,C03,C02
C02
CN Compute ,
Compute ,
AIWBES
HMM (λ) Figure 3. Adustement phase
. . .
. . .
C05, C011,…,C03,CN
HMM
( )
HMM
Forward Algorithm Forward Algorithm
Forward Algorithm
( )
HMM
Compute
, A, B
HMM
( )
C01
B. - Adjustment Phase C05, C011,…,C03 New Concepts' Sequence
C05, C011,…,C03,C01
Get maximum Probability to predict next concept will be visited by the student
- M, the number of observable states, with V = {V0, V1, …, VM-1} the set of observable states (Symbols), and Ot the observation state at time t. - A={aij}, the transition probabilities between hidden states Si and Sj. - B={bj(k)}, the probabilities of the observable states Vk in hidden states Sj. - ∏={i}, the initial hidden state probabilities.
C. - Prediction Phase The Forward Algorithm is applied to determine the probability distribution t (i ) of each concept (state) in the course. The highest value represents the next concept will be visited by the student. Figures 4 illustrates prediction phase and section III presents detailed prediction algorithm.
Figure 4. Prediction Phase
(
)
III.
DETAILED PREDICTION ALGORITHM
1- T=1 (T is the length of the observation/concept-sequence); 2- T=T+1; 3- If T
