key: cord-0979225-0qgko2ia
authors: Norwawi, Norita Md
title: Sliding window time series forecasting with multilayer perceptron and multiregression of COVID-19 outbreak in Malaysia
date: 2021-05-21
journal: Data Science for COVID-19
DOI: 10.1016/b978-0-12-824536-1.00025-3
sha: ecc8481ec2ceb808561809713630b69fdf16bac2
doc_id: 979225
cord_uid: 0qgko2ia

This study demonstrates a sliding window time series forecasting methods to predict future trends of pandemic coronavirus disease 2019 (COVID-19) reported in Malaysia using a multiple regression and single-layer feedforward artificial neural network. Data from Jan. 25 to Apr. 30 were obtained from the Malaysian Ministry of Health and Department of Statistics Malaysia website. The findings show that the Movement Control Order declared by the Malaysian government was effective in mitigating the risk for spreading COVID-19 diseases through home quarantine and isolation, and thus were able to flatten the curve. Sliding window time series forecasting with an artificial neural network performs better than multiple regression as a predictive model with a smaller residual error.

The objectives of this study are to analyze the COVID-19 outbreak in Malaysia from Jan. 2020 until end of Apr. 2020, to assess the trends in the near future, and to estimate the future trend using a sliding window time series forecasting method.

This chapter is organized into five sections. Section 2 discusses some related work with temporal data mining and time series forecasting methods. Section 3 presents the dynamic sliding window technique used in this study. Section 4 discusses the findings of the trend analysis and the sliding window time series forecasting model with temporal data analytics, and Section 5 concludes the chapter.

Time series forecasting involves time series data that have a natural temporal ordering. It is usually defined as y ¼ f(t), where time t is an independent variable and where y is the dependent variable whose value depends on time. Time series data are useful for making projections, studying trends, predicting an event, extracting meaningful statistics, and so on.

The primary purpose of time series forecasting is to understand the past and predict the future with the model developed before they are measured. It may be in the univariate or multivariate form, which requires a specific approach to manipulating and deriving solutions. With the outbreak of the coronavirus pandemic around the world, it is important for us to understand the nature of the COVID-19 outbreak and characteristics to search for solutions.

Achintya et al. [2] and Gupta and Pal [13] presented a profile of the COVID-19 situation in India with polynomial fitting parameters and predicted the future trend using the Auto Regressive Integrated Moving Average (ARIMA) model. This projection may help government agencies, businesses, and others make decisions and strategize their defensive tactical solutions in facing the spreading of disease.

On the other hand, the world came to a consensus to lock down countries to mitigate risk. An MCO was declared by most governments to slow the spread of the epidemic. Naomie et al. [9] presented an analysis of the impact of the MCO in lessening the number of infected cases. Ahmadi et al. [3] studied the impact of climatology parameters on the COVID-19 outbreak in Iran using a sensitivity analysis. They found that low values of wind speed, humidity, and solar radiation exposure to a high rate of infection may help in surviving the coronavirus. Moreover, locations with a high population density, intraprovincial movement, and a high humidity rate are more at risk. These are some of the interesting studies conducted to understand the nature of the pandemic and gathering efforts to combat the deadly infectious disease.

With advances in the sophistication of technology, the world is working closely together to overcome this dangerous situation. Thousands of data being transmitted or transported around the globe at such high speed and efficiently shared around the world. In many ways, solutions are rapidly being produced owing to the urgency of the situation for which timeliness is of prime concern. Speed in arriving at practical and realistic solutions is the new norm. An important technology that has had an important role is artificial intelligence and data analytics. For example, Rao and Vazquez [14] adopted a machine learning algorithm to speed possible case identifications of COVID-19. Abdullah Farid et al. [1] proposed predicting the probability of recurrences in no-recurrence (first-time detection) cases in screening coronavirus disease. In Wuhan, Huang [19] studies a spatiotemporal analysis of the spread of the virus that gives insight into preparing for and mitigating future virus control. They used the logistic and Susceptible, Exposed, Infectious and Removed (SIER) model to analyze and predict future trends.

In this study, an artificial neural network (ANN) is used to identify characteristics of COVID-19 time series data that may have some interesting patterns to be extracted. Hota et al. [5] mentioned that ANN is a favorable technique that can map highly nonlinear input-output data samples, unlike any statistical regression model. They used the sliding window as an estimation over the actual value of time series data. Fig. 29 .1 shows the sliding window technique being used in ANN [12] . Vafaeipour et al. [7] adopted a similar technique to predict the wind velocity time series.

The sliding window method is an approach adopted in this study. It is a common method for recording temporal sequences owing to its simplicity and intuitiveness [11] .

The sliding window is a method that can be used in the preprocessing phase to restructure data according to a time frame into a supervised classification problem. Given a time series dataset that can be explained with y ¼ f(x), using a sliding window, the data will be restructured in which the previous output or the historical data will be used to predict the next output. For example, for window width 1, the outcome of current time t is based on the output of prior time, te1 as shown in Eq. (29.1):

The window width indicates the number of previous time steps. For example, Eq. (29.2) shows the sliding window with width 2:

For example, given the following data, Tables 29.1a and 29.1b show restructuring of the data for window widths of 1 and 2.

Chapter 29 Sliding window time series forecasting with multilayer perceptron 549 The previous examples are for a univariate time series dataset where one variable is varying over time. The sliding window method may also be used for multivariate time series data. Given variable x1 and x2 at time t, where y t ¼ f(x1 t , x2 t ), we may predict x2 at time t, as shown in Eq. (29.3) and Table 29.2:

Usually, we have one variable for prediction, but we may also predict more than one output variable, such as in an ANN. We may also predict both variables x1 and x2 at time t, as shown in Eq. (29.4).

For example, given two variables in multivariate time series data and the following data, Table 29 .3 shows restructuring to predict both variables.

We may also predict more than one next step. This is called multistep forecasting. Table 29 .4 shows an example of data restructuring with a sliding window of width ¼ 1 and two-step multiforecasting.

Decisions regarding the window width and forecasting steps with acceptable model performance, good reasoning, and experimentation are needed for the specific dataset. In this study, the width of the sliding window or lag that gives the best performance will be discussed and presented.

The MOC in Malaysia was declared beginning Mar 18. The first phase of the MCO ending on Apr. 1 was extended for another 2 weeks at each phase to the second, third, and then fourth phases until May 12, 2020. Only essential services could continue operations and charges were imposed on those who did to not comply with the MCO. Only one member of the family was allowed to purchase household goods and had to observe social distancing, wear a face mask, and observe hand hygiene. This section will present the trend analysis of the COVID-19 pandemic in Malaysia, especially during the MCO phases.

As of Apr. 30, 2020, there had been 6002 confirmed cases since Jan. 25, 2020; 1729 active patients were still in treatment and quarantine and there was a fatality rate of 1.7% (102 deaths). The rate of recovery was 69.5% and around 3% people who were tested were found to be positive for COVID-19. Table 29 .5 shows the situation. In terms of sex, 77.4% of COVID-19 patients were was male (79 males and 25 females). This is consistent with statistics around the world [6] . Active cases as stated in Table 29 .5 refers to those who were still in quarantine and undergoing treatment at the hospital.

In general, the pandemic situation in Malaysia was based on new, recovered, and active cases and deaths. reported from Jan. 25 until Apr. 30, 2020. Fig. 29.2 shows an escalating rate of recovery for Malaysian cases and a much lower mortality rate compared with 3.4% declared by the WHO (Worldometer, Mar. 5, 2020). This could be evidence that the MCO manages to achieve the objective of mitigating the risk for the disease and containing its spread to all states of Malaysia with the support of Malaysian citizens and local authorities such as the police, army, and medical frontline workers.

The disease also spread across the country of Malaysia, which has 16 states, to varying degrees, as shown in Table 29 .6, which presents cases reported in various states in Malaysia. Based on the statistics, the states of Selangor and Kuala Lumpur has the most positive cases reported. This may be because of the concentration of people in industrial areas in Selangor and Kuala Lumpur, which are the central places for many organizational headquarters as well the capital of Malaysia. The progressive spread of the pandemic is shown in Fig. 29 .3AeE and occurred in five zones: northern, central, southern, and eastern zones of West Malaysia and East Malaysia. Fig. 29.3 shows that the Malaysian government also designated some states or district as red, yellow, and green zones, indicating the seriousness of pandemic cases reported.

Regarding cumulative cases, the spread of disease has managed to be controlled through the MCO declared by the government and enforcement through the police and army. Only one member of the family, preferably a male, may go out for necessities and must wear a face mask and maintain social distancing in supermarkets, retails shops, banks, and so on.

The projection of cumulative cases may be estimated from the trendline polynomial equation generated through curve-fitting of actual data using the fifth order, as shown in Fig. 29 .5. The estimated trend line equation is given by Eq. (29.5), with R 2 ¼ 0.997: y ¼ À 5E À 06x 5 þ 0:0004x 4 þ 0:0428x 3 À 3:4011x 2 þ 60:782x À 210:83 (29. 5) where y and x represent total cases and days, respectively. The number of total cases by May 12, 2020, which was the end of MCO Phase 4 (i.e., day 109 according to Eq. [29.5]), showed an estimated 965 persons to be infected. The MCO was able to flatten the curve and suppress the spread of the pandemic in an exponential pattern. The projection shows a decline in the spread of positive cases after MCO Phase 4. However, the community still had to observe social distancing and adhere to self-quarantine and heightened hygiene practices. Fig. 29.6 illustrates the pattern of new cases reported and shows that most new cases were detected during MCO Phases 1 and 2 and slowly reducing locally infected cases. However, the figure also records cases imported from Malaysians who returned from overseas regions such as Indonesia, Iran, and Italy through a special arrangement by the government, and who quarantined for 14 days in a designated location until their tests were clearly negative. Fig. 29 .7 depicts the promising trend of a slowdown in the infection, in which the peak was around the middle of Apr. during MCO Phase 2, as expected by the WHO and the Ministry of Health Malaysia, as reported in the newspaper [15] . Active cases were those found to be positive and undergoing treatment at the hospital:

Active Cases ¼ Total Cumulative Cases À Recovered À Death:

(29.6) Fig. 29 .8 compares new, active, and recovered cases. The trend shows a favorable situation in which fewer than 100 new cases were recorded from Apr. 17 to Apr. 30, 2020.

Regarding the mortality rate, the situation looks promising: there was a lower fatality rate in April (fewer than five cases) and an average of 1.97 people per day. The largest number of deaths recorded was on Apr. 30, seven persons, as depicted in Fig. 29.9 . The medical frontlines should be commended for this achievement for their sacrifices. 

As described in Section 3, this study conducts predictive analytics using a sliding window method. The main justifications for selecting this approach are:

a. Time series data are usually analyzed as a single variable varying over time. These data are continuously bonded to each other, meaning that what will happen at time t will strongly depend on or be influence by what happened in the previous time scale such that y(t) ¼ f(y(tÀn)), where n is the time frame that we are interested in investigating. Fig. 29.9 illustrates the sliding window concept. b. There is a time delay from one variable to another. For example, a person who is infected and his road to recovery will take some duration of time. Thus, data on new cases will eventually contribute to statistics on the number of patients who are discharged or die. This time delay must be captured so as not to lose important information. c. Many time series datasets are multivariate in nature. How can we conduct time series forecasting when we must consider prior events? How do we restructure the data? How do we run the forecasting algorithm with multivariate datasets?

Two experiments were conducted using (a) the multiple regression technique (b) the multilayer perceptron, a feedforward ANN with a restructured dataset using a sliding window approach.

In this experiment, the data on which we are focused is the number of recovered COVID-19 patients from Jan. 25 to Apr. 30, 2020. It is the cumulative number of people infected who were discharged from the hospital.

The purposes of the experiment are:

a. To identify whether there is a specific time frame that may influence the projection of future trends; b. To determine the optimum sliding window width that gives good predictive analytics performance; and c. To determine whether it is consistent with the other technique. For this study, we will compare the result of time series forecasting using multiple regression and multilayer perceptron with feedforward ANN architecture.

The Microsoft Excel Data Analysis tool was used for this experiment. Tables 29.7 and 29.8 show the data preparation using the sliding window technique. The data need to be restructured so that they represents a classification problem. However, because the data are numerals with real values, it is a regression problem.

FIGURE 29.9 Sliding window conceptual view. Table 29 .7 illustrates the restructuring process and Table 29 .8 shows the transformed data to be used for predictive analytics.

Malaysia COVID-19 data were gathered from various resources such as the Ministry of Health Malaysia, Department of Statistics Malaysia, Worldometer, and John Hopkins University from Jan. 25 to Apr. 30, 2020. Data collected were the number of cumulative cases from each state in Malaysia, total cumulative cases in Malaysia, active cases, cumulative number of patients who recovered, number of patients in the intensive care unit, number of new cases, and number who died. There were 21 variables in which 16 Table 29 .7 Example of data restructuring using a window of width 1, 2, and 3. data   0  0  0  0  0  0  0  1  1  0  0  1  1  1  0  1  1  1  1  1  1  1  2  2  1  1  2  3  3  1  2  3  7  7  2  3  7  8  8  3  7  8  7 8 8   Table 29 .8 Restructured data in sliding window format, in which xi is the predictor variable for y(t). Table 29 .8 shows three sets of data with varying window width.

Sliding window restructured data 0  0  0  0  1  0  0  1  1  0  1  0  1  1  0  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  2  1  1  2  3  1  2  1  2  3  1  2  3  7  2  3  2  3  7  2  3  7  8  3  7  3  7  8  7  8 were states and five statistics were at the national level. In this chapter, we focus only on the number of patients who recovered or were discharged from the hospital. This is an indicator of how well the pandemic was under control. More people discharged show that fewer people are infected and will become infected. From Jan. 25 to Apr. 30, there were 97 sets of daily data for the COVID-19 situation. The width in window use in the experiment is from 2 to 16 owing to the limitation of the predictor variables of the software for multiple regression. Table 29 .9 lists details about the dataset and the corresponding performance of the multiple regression according to the window width with a 95% confidence level. For the regression model with various widths of window, w is statistically significant with an F value < 0.05.

All regression models that use the sliding window perform far better than a typical y ¼ f(t), which consider each type of data as discrete. By using the sliding window, the model indicates that the historical time series or temporal data influence the current outcome owing to continuity in the time line. Upon examining the performance evaluation metrics in this experiment, the window of widths 5 and 14 gave the best performance and were statistically significant. This is also consistent where the P value at every window width is less than 0.05.

Thus, the regression model for the window of width 5 with significant predictor variables is given by Eq. (29.7) , where recovery r is:

For the window of width 14:

rðtÞ ¼ 1:00999 Ã rðt À 1Þ À 0:5743 Ã rðt À 5Þ þ 0:5353 Ã rðt À 7Þ À 0:6185 Ã rðt À 10Þ þ 0:5469 Ã rðt À 14Þ (29.8)

The predicted value for recovered cases using a window with widths 5 and 15 is shown in Table 29 .10. Data with the window of width 14 was chosen because of better performance in predicting future trends compared with the window of width 5. The experiment was conducted using Weka 3.8.3. Data from Excel was converted to CSV format and save into the .arff extension. In Weka, the sliding window can be implemented using a lag. Thus, a sliding window width is the same as the lag size where prior time steps will be used to predict the next time step. Four experiments were carried out (Table 29 .11):

a. The original data on the number of patients being discharged without a lag b. The original data on the number of patients being discharged with a lag with a minimum of 1 and a maximum of 14 c. The original data on the number of patients being discharged with a lag with a minimum of 5 and a maximum of 14 (based on regression model performance) d. With restructures, discharge data with window width ¼ 14 based on the performance in the regression model.

Based on Table 29 .11, the best result with the lowest mean square error uses the original discharge data with the lag set to 5 at the minimum and 14 at the maximum based on the regression model. Table 29 .12 lists details of the multilayer perceptron architecture neural network architecture. 

Comparing the performance in terms of the predictive values of discharge cases from May 1e4, 2020, the multilayer perceptron architecture model with a lag of 5e14 performs much better than the regression model in projecting future trends. The window width of 14 implies that the historical event 2 weeks before the next time scale correlates with the outcome. According to Worldometer [18] , on Mar. 12, the current official estimated range for the incubation of COVID-19 was 2e14 days. An evaluation is needed to confirm whether the window width or lag size represents the incubation period of the coronavirus.

The sliding window is a convenient method for conducting time series forecasting. The data need to be restructured to be represented as a temporal classification or regression problem. In time series data, historical data are important in determining future trends. This is also in line with work conducted by Norwawi et al. [10] and Wan Hussain et al. [16] , which adopted the sliding window method for time series data for early decision-making for flood emergency management of a water reservoir.

This study presented trend analysis on the COVID-19 situation in Malaysia from Jan. 25, 2020 to Apr. 30, 2020. The MCO had an impact on flattening the pandemic curve from spreading exponentially and helped improve the recovery of many infected patients. There was a 1.79% fatality rate, which was at the lower end from of the global rate.

Time series forecasting was also carried out using multiple regression and ANN employing a sliding window approach or lag. ANN is a black box approach that outperformed multiple regression in predictive analytics with these data that were gathered from various resources. Number of lags (minimum) 5 3

Number of lags (maximum) 14 4 Number of transformed input data 23 5

Number of hidden nodes 12 6 Number of outputs 1 7

Activation function Sigmoid 8

Number of instances 97

As for future work, a multivariate analysis for the time series data with more than one predictor variables or outcome can be explored. Studying the movement of the epidemic and the relationship among those variables would give more insight into how to fight this pandemic or how to be better situated for preparedness strategies in defending the community and society at large from the spread of disease, especially fatal ones.

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COVID-19 by State in Malaysia

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Why Are More Men than Women Dying of COVID-19? Science and Health

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COVID-19: Maklumat Terkini

COVID-19 epidemic in Malaysia: impact of lockdown on infection dynamics, medRxiv

Recognition decision-making model using temporal data mining technique

Computational Recognition-Primed Decision Model Based on Temporal Data Mining Approach in a Multiagent Environment for Reservoir Flood Control Decision

Forecasting of preprocessed daily solar radiation time series using neural networks

Trend analysis and forecasting of COVID-19 outbreak in India, medRxiv

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The Star, WHO Expects Malaysia's Covid-19 Cases to Peak in Mid-April

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World Health Organization

Covid-19 Coronavirus Pandemic

Spatial-temporal distribution of COVID-19 in China and its prediction: a data-driven modelling analysis

The author would like to thank the Ministry of Health, Malaysia, and the Department of Statistics, Malaysia, and John Hopkins University for publicly releasing the updated datasets related to COVID-19 in Malaysia and around the world.