Analysison Students’ Learning Habits: Identifyingthe Contributory Factorsof Learning Duringthe Covid-19 PandemicUsing Radial Basis Function (RBF)

The Artificial Neural Network (ANN) is an Artificial Intelligence technique that offer many benefits including the ability to process a vast amount of data, the ability to learn from experiences, and the good generalization capability. It was invented based on the concept of imitation of the human brain and built up of nodes that are like human neurons. The Radial Basis Function (RBF) is one of the established types of ANN. Considering the advantages and great performance of the RBF, this study aims to investigate the contributory factors of students’ learning habits during the Coronavirus Disease 2019 (or known as COVID-19) pandemic using RBF. Responses from a total of 420 respondents were collected from Vietnamese students’ learning habits during the COVID-19 pandemic dataset that was established from the questionnaires distributed in the period of 7th February 2020 to 28th February 2020. Fifteen independent variables were used as the input for the RBF network which is based on the 15-9-1 structure. Based on the experiment conducted, the implementation of the RBF model was found to be fair and effective with the small number of Sum of Square Error (SSE) and Relative Error (RE) produced. It could also be concluded that the most contributing factor of students’ learning habits during the COVID-19 pandemic is the learning hours per day for self-learning before the pandemic.


Introduction
Online learning has started to grow in many educational institutions due to its flexibility, mobility, and effectiveness since the early stage of the 21st century [1][2][3]. Also, online learning or e-learning is not something new in higher educational institutions as this approach has been implemented in universities' distance learning process. However, recently, online learning has turned out to be an essential activity among students due to the closure of educational institutions due to the COVID-19 pandemic, thus, possible opportunities related to online learning have been explored [4]. Recently, people all over the world are struggling to cope with the new normal since COVID-19hits. Hence, the implementation of normal learning has shifted from the traditional physical classroom into a virtual classroom [5]. Due to that, enormous educational institutions worldwide have conducted online and resulting direction towards studying student's learning habits.
Students learning habits are very essentials as they affects student's attitude, knowledge, and performance [6]. It is mentioned in [7] that learning habits encompass mental, physiological, natural habits, and the preferred ways of absorbing, processing, and retaining new knowledge and skills. Learning habits reflect student's usual act of studying and serve to direct the learner's cognitive processes during learning [2]. This process includes activities that deal with time management, goal setting, appropriate study environment, using appropriate notetaking strategies, choosing main ideas, and organization [2] [8]. Studies in [1] [2] mentioned that there is a positive correlation between learning habits and learner performance. Hence, it is very important to analyse student's learning habits as it is one of the main factors affecting their performance in learning.
The Artificial Neural Network (henceforth, ANN) is an Artificial Intelligence technique that has many benefits including the ability to process a vast amount of data, the ability to learn from experiences, and the good generalization capability [9]. Initially, ANN was invented based on the concept of imitation of the human brain [10]. ANN is a built up of nodes that are like human neurons. All these nodes are interconnected to one another and build up a network. One of the established types of the neural network is based on the Radial Basis Function (RBF) network.
There are many available works related to the RBF network model. For instance, RBF is vastly applied in the engineering sector and it produces promising results. Among of the examples are the application of RBF modelling submerges breakwaters [11], monitoring tunnel ventilating system [12], estimating reinforce building's seismic damage level [13], and wind energy conversion system [14]. Meanwhile, for the prediction task, RBF is applied in estimating the chemical structure of aluminium foam [15], predicting factors that contribute to COVID-19'sdeath and spread [16][17], predicting and recognizing human activity [18], and as well in predicting construction cost [19].
Considering the advantages and great performance of Radial Basis Function (RBF) ANN, this study aims to investigate the contributory factors of students' learning habits during the COVID-19 pandemic. The implementation of RBF is expected to give insights and understandings on the factors that contribute to online learning habits among students. The structure of this paper is as the following: Section 2 discusses the data background and followed by Section 3 which elaborates on the methodology. Next, results and discussions are presented in Section 4 while Section 5 is the conclusion.

Data background
A dataset of of Vietnamese students' learning habits during the COVID-19 pandemic [20] was retrieved from the Research Gate's open source. This dataset was established from the questionnaires distributed in the period of 7th February 2020 to 28th February 2020. It comprised of three major groups of questions which are (1) student's demographic, (2) student's learning habits, and (3) student's perception of self-learning during the school closure. This dataset was composed of 460 responses from the secondary students in grades 6-12. However, only 420 data were valid after the process of data cleaning. The descriptive statistics of the dataset is illustrated in Table 1 as follows.

Research methodology
This section discusses the methodology used in this study that aims to assess the performance of the RBF network in investigating the contributory factors of students' learning habits during the COVID-19 pandemic. A

. Radial Basis Function (RBF) Network
The RBF network is a feed-forward neural network type. It is built of three different layers which are the input layer, the hidden layer, and the output layer [11]. The representation of input pattern used in RBF network is based on the middle layer given with a set of input units. The use of the activation functions at this middle layer is important for the purpose to characterize each of the input units used in the network.
RBF is highly successful in function approximation and pattern recognition [21]. Moreover, it is also known that the RBF structure offers a simple layout, rapid convergence speed and more important is to be able to perform universal approximation [11][12] [15]. The RBF network is widely used due to its advantages such as excellent generalization, easy structure, high input noise tolerance and online learning capabilities [16] [17]. An example of a basic structure of RBF with one hidden layer is demonstrated in  The radial basis function used in the network depends on the strategy of the network itself. The approximation function with linear combination of Radial Basis function is expressed as in Equation 1.
Where (hx) is mostly the Gaussian functions. The RBF neuron activation function is slightly different and is typically written as in Equation 2.
hj(x)= exp( -(x-cj) 2 / rj 2 ) Where cj is the centre of a region and rj is the width of the receptive field.

Result and analysis
This section discusses the results obtained from the experiment conducted. The dataset dataset of the Vietnamese students was run using SPSS 13. The case processing summary for RBF is displayed in Table 2. Based on Table 2, the dataset used in this study was divided into two groups; which are training and testing. The training set for RBF is 72.4% (304/420) and the testing set is 27.6% (116/420). The overall data from the dataset is N = 420 and there is no excluded data reported.
There were fifteen covariates used in the network which are fa_job, exam, Self_evaluation, English, Lh_before_Cov, nec_prog, nec_habit, nec_parent, eff_moti, eff_con eff_supp, eff_env, eff_obj, eff_resource, and eff_friend. Table 3 shows the descriptions of the covariates used in this study. These fifteen covariates acted as the input for the RBF network. The activation function used in the network is Softmax and there is one dependent variable which is Lh_in_Cov. To simplify the architecture, it could be addressed as the 15-9-1 RBF network architecture as portrayed in  Based on the illustration of the RBF network architecture in Fig 2, this network is composed of 15 inputs with one hidden layer with 9 nodes. Softmax is used as the hidden layer activation function. Hence, the target output of this network is the learning hours during COVID-19 (Lh_in_Cov). The identity (purelin) function is used as the activation function from the hidden layer to the output layer and the default error function applied is the sum of squares (SSE). SSE is the sum of differences between each observation group mean, and it is used to indicate the variation within a cluster. Hence, it can be concluded that the smaller the SSE, the lesser the variation between the clusters.
To simplify the configuration of the network, it is addresses as the 15-9-1 RBF network structure. Consequently, Table 4 tabulates a summary from the RBF network while Table 5 demonstrates the independent variables' importance. Dependent Variable: Lh_in_Cov a. The number of hidden units is determined by the testing data criterion: The "best" number of hidden units is the one that yields the smallest error in the testing data.  Table 5 tabulates the independent variables' importance for the RBF network constructed in this study. It is stated that the five most influential factors based in this study are Lh_before_Cov (100), eff_moti (54.9), eff_con (50.5), nec_habit (44.7), and English (40.7).  As previously mentioned, the performance evaluation was conducted on the developed RBF network model using the Sum of Square Error (SSE) and Relative Error (RE). Table 6 and Table 7 demonstrate the SSE and RE for the RBF network model, respectively.

Conclusion
This paper presented a study to investigate the contributory factors of students' learning habits during the COVID-19 pandemic using Radial Basis (RBF) network. Vietnamese secondary students' dataset was used in which it composed of a total of 420 respondents. There were fifteen independent variables used as the input for the RBF network and the network was based on the 15-9-1 structure. Based on the result obtained from the experiment, it was observed that the most contributory factor in students' learning habits during the COVID-19 pandemic was the learning hours before the COVID-19 pandemic (Lh_before_Covid). This means that students' learning behaviour before the pandemic was a necessity in maintaining their learning behaviour during the pandemic. It is also concluded that the implementation of the RBF model was fair and effective with the small number of SSE and RE produced from the developed model. On a different side, this study contributes towards the investigation of the contributory factors in students' learning habits during the pandemic. In the future, it is suggested that the exploration of the contributory factors is further investigated as it is important in preparing educational institutions and society for a better learning environment.