I K G Darmaputra <ikgdarmaputra@unud.ac.id>

Fw: [TELKOMNIKA] #5993: Foreign Tourist Arrivals Forecasting Using RecurrentNeural Network Backpropagation Through Time 1 message

Oger Vihikan <ogervihikan@outlook.com> Sun, Oct 1, 2017 at 12:27 PMTo: "ikgdarmaputra@unud.ac.id" <ikgdarmaputra@unud.ac.id>

From: Tole Sutikno <tole@journal.uad.ac.id> Sent: Sunday, August 20, 2017 11:20 PM To: Oger Vihikan Subject: [TELKOMNIKA] #5993: Foreign Tourist Arrivals Forecasting Using Recurrent Neural NetworkBackpropagation Through Time Dear Mr. Wayan Oger Vihikan, 

It is my great pleasure to inform you that your paper has been ACCEPTED and will be published on the TELKOMNIKATelecommunication  Computing  Electronics  and  Control  (ISSN  1693­6930,  SCOPUS  indexed  journal).Congratulations!

 

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TELKOMNIKA

Vol. 15, No 3: September 2017

DOI: http://dx.doi.org/10.12928/telkomnika.v15i3

List of Accepted papers dapat dilihat pada alamat:

http://journal.uad.ac.id/index.php/TELKOMNIKA/issue/view/425

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TELKOMNIKA, Vol.15, No.3, September 2017, pp. xxx~xxx ISSN: 1693-6930, accredited A by DIKTI, Decree No: 58/DIKTI/Kep/2013 DOI: 10.12928/telkomnika.v15i3.5993 xxx

Received February 23, 2014; Revised May 29, 2014; Accepted June 12, 2014

Foreign Tourist Arrivals Forecasting Using Recurrent Neural Network Backpropagation Through Time

Wayan Oger Vihikan*1, I Ketut Gede Darma Putra2, I Putu Arya Dharmaadi3 1,2,3Information Technology Department, Faculty of Engineering, Udayana University

Kampus Unud, Bukit Jimbaran, Bali, Indonesia-803611 telp/fax : (0361) 701954, 704845 / (0361) 701907

*Corresponding author, e-mail: ogervihikan@outlook.com

Abstract Bali as an icon of tourism in Indonesia has been visited by many foreign tourists. Thus,

Bali is one of the provinces that contribute huge foreign exchange for Indonesia. However, this potential could be threatened by the effectuation of the ASEAN Economic Community as it causes stricter competition among ASEAN countries including in tourism field. To resolve this issue, Balinese government need to forecast the arrival of foreign tourist to Bali in order to help them strategizing tourism plan. However, they do not have an appropriate method to do this. To overcome this problem, this study contributed a forecasting method using Recurrent Neural Network Backpropagation Through Time. We also compare this method with Single Moving Average method. The results showed that proposed method outperformed Single Moving Average in 10 countries tested with 80%, 70%, and 70% better MSE results for 1, 3 and 6 months ahead forecast respectively.

Keywords: Backpropagation Through Time, forecasting, tourism, Recurrent Neural Network 1. Introduction

The tourism industry is one of the huge industries that is growing very rapidly throughout the world. Many countries put the tourism sector as a strategic industry to increase revenue, including Indonesia, which has a great potential. Indonesia's tourism industry has become an important part of national development, as it can hold a lot of manpower, improve the local economy, and state revenues.

Bali as an icon of tourism in Indonesia and also as a world tourist destination that has a variety of art, culture and hospitality of the community has been visited by many foreign tourists. Data from Bali Tourism Office shows that since 2011 until 2015 the amount of foreign tourist arrivals to Bali is always increasing. For example, in 2011 the number of foreign tourist arrivals is 2,756,579, in 2012 it increased to 2,892,019, in 2013 it went up to 3,278,598, in 2014 it increased about 15% to 3,766,638 and in 2015 it climbed up to 4,001,835 [1]. In addition to that, Bali is the only province in Indonesia which has the highest amount of foreign tourist staying in star hotels since 2003 until 2015 [2]. Moreover, Bali won as the best island for holidaymakers and it is Bali’s 12th times [3]. These make Bali as one of the provinces that contribute huge foreign exchange for Indonesia.

In the end of 2015, ASEAN Economy Community (AEC) was applied. This will cause strict competition among ASEAN countries in a lot of sectors including tourism. Indonesia as part of ASEAN had already prepared a presidential decree which ask local government to improve competitiveness in order to face AEC. It means Balinese government have a good opportunity to maintain and improve the amount of foreign tourist arrivals to Bali by promoting Bali’s tourism intensively and improving Bali’s tourism facilities. These can be achieved by strategizing Bali’s tourism based on past data of foreign tourist arrivals which lead to forecasting to get overview of foreign tourist arrivals in the future.

The problem is Balinese government do not have an appropriate method to forecast foreign tourist arrival to Bali. Their forecast for the current year is based on the last year foreign tourist arrival growth with analysis of several factors such as political situation and natural disasters. To help overcome that problem, this paper proposed Recurrent Neural Network as

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forecasting method with Backpropagation Through Time as the training algorithm. Previous researches using Recurrent Neural Network Backpropagation Through Time show good results in forecasting time series data [4-7].

Therefore, the aims of this research is to contribute an accurate forecasting method of foreign tourist arrivals for Balinese government in order to anticipate the increase or decrease in foreign tourist arrivals to Bali. This will help Balinese government in setting up tourism facilities such as accommodation facilities (hotels, villas), infrastructure (roads, water, electricity), tourist attraction, restaurants, transportation, travel agencies, money changers and others. 2. Research Method

This research uses data of foreign tourist arrivals to Bali and their factors. The factors of foreign tourist arrivals are population of origin country, Gross Domestic Product (GDP) real of origin country and Consumer Price Index (CPI) in Indonesia relative to CPI of origin country [8]. Those data are taken from 2005 to 2015 and has time series characteristic. Time series data is a set of data generated sequentially in time [9].

Before beginning the process, the data have to be normalized and scaled to range between -1 and 1 using equation below. Then, the data is divided into 2 parts, those are training and test data.

�̂� =(𝑥−𝑚𝑖𝑛𝑉𝑎𝑙)∗(𝑚𝑎𝑥𝑅𝑎𝑛𝑔𝑒−𝑚𝑖𝑛𝑅𝑎𝑛𝑔𝑒)

(𝑚𝑎𝑥𝑉𝑎𝑙−𝑚𝑖𝑛𝑉𝑎𝑙)+𝑚𝑖𝑛𝑅𝑎𝑛𝑔𝑒 (1)

With: 𝑥 : Original data.

�̂� : Normalized data. 𝑚𝑎𝑥𝑉𝑎𝑙 : The maximum value of original data.

𝑚𝑖𝑛𝑉𝑎𝑙 : The minimum value of original data.

𝑚𝑎𝑥𝑅𝑎𝑛𝑔𝑒 : The maximum value of normalized data (1).

𝑚𝑖𝑛𝑅𝑎𝑛𝑔𝑒 : The minimum value of normalized data (-1). Recurrent Neural Network is adapted from standard feed forward neural network that

can model sequential data [10]. It allows the network to map from all previous inputs to each output [11]. It is easier to understand by looking to unfolded RNN in Figure 1, where previous time step is needed to calculate current time step which is shown as t-1 and t respectively. RNN BPTT is started by doing Forward Propagation process. This process will calculate the network output from the input data given using equation below [10].

ℎ𝑡 = tanh(𝑈𝑥𝑡 +𝑊ℎ𝑡−1 + 𝑏ℎ) (2)

𝑜𝑡 = tanh(𝑉ℎ𝑡 + 𝑏𝑜) (3) With:

ℎ𝑡 : Hidden state at time step t.

𝑈 : Input to hidden state weight matrix.

𝑥𝑡 : Input vector at time step t.

𝑊 : Hidden to previous hidden state (recurrent) weight matrix.

ℎ𝑡−1 : Hidden state at previous time step.

𝑏ℎ : Bias at hidden state.

𝑉 : Hidden state to output weight matrix.

𝑏𝑜 : Bias at output state.

Figure 1. Unfolded Recurrent Neural Network

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After that the loss between network’s output and targeted output is calculated. In this case Mean Squared Error is used as the loss function. If the value close to 0, it means the network and targeted output or factual data value are close.

𝐿 =1

2𝑁∑(�̂�𝑖 − 𝑜𝑖)

2

𝑁

𝑖=1

(4)

With: 𝐿 : Loss value. 𝑁 : The amount of training data.

�̂� : Network’s output.

𝑜 : Targeted output. Each of the weight matrices have to learn from the error (loss). This can be achieved by

updating each weight matrices for each training data using Stochastic Gradient Descent. To do that, first Backpropagation Through Time should be applied. This algorithm calculates the gradient of loss function with respect to each weight matrix as formula below.

𝜕𝐿

𝜕𝑉=𝜕𝐿

𝜕�̂�

𝜕�̂�

𝜕𝑧

𝜕𝑧

𝜕𝑉 (5)

𝜕𝐿

𝜕𝑏𝑜=𝜕𝐿

𝜕�̂�

𝜕�̂�

𝜕𝑧

𝜕𝑧

𝜕𝑏𝑜 (6)

𝜕𝐿

𝜕𝑊=∑

𝜕𝐿

𝜕�̂�

𝜕�̂�

𝜕𝑧

𝜕𝑧

𝜕ℎ𝑇

𝜕ℎ𝑇𝜕ℎ𝑡

𝜕ℎ𝑡𝜕𝑊

𝑇

𝑡=0

(7)

𝜕𝐿

𝜕𝑏ℎ=𝜕𝐿

𝜕�̂�

𝜕�̂�

𝜕𝑧

𝜕𝑧

𝜕ℎ𝑇

𝜕ℎ𝑇𝜕𝑏ℎ

(8)

𝜕𝐿

𝜕𝑈=∑

𝜕𝐿

𝜕�̂�

𝜕�̂�

𝜕𝑧

𝜕𝑧

𝜕ℎ𝑇

𝜕ℎ𝑇𝜕ℎ𝑡

𝜕ℎ𝑡𝜕𝑈

𝑇

𝑡=0

(9)

With:

𝑧 : Network’s output before activation function (tanh) is applied.

T : Current time step. Finally, each weight matrix is updated with BPTT calculation results and learning rate. In

order to avoid over-fitting and improve generalization, weight decay is used by multiplying each weight with regularization parameter before updating them [12]. The new weight matrices value will be used in the next time step. Formula for updating weight matrix is shown below.

𝑈 = 𝑈 − 𝜂 ∗ (𝜕𝐿

𝜕𝑈+ 𝜆𝑈) (10)

𝑊 = 𝑊 − 𝜂 ∗ (𝜕𝐿

𝜕𝑊+ 𝜆𝑊) (11)

𝑏ℎ = 𝑏ℎ − 𝜂 ∗𝜕𝐿

𝜕𝑏ℎ (12)

𝑉 = 𝑉 − 𝜂 ∗ (𝜕𝐿

𝜕𝑉+ 𝜆𝑉) (13)

𝑏𝑜 = 𝑏𝑜 − 𝜂 ∗𝜕𝐿

𝜕𝑏𝑜 (14)

With: 𝜂 : Learning rate.

𝜆 : Regularization parameter. All these processes are repeated for all training data and epoch. The test will be done

by using test data and final weight matrices of training process into Forward Propagation process. Mean Squared Error will be used to see how good the network output when tested using test data.

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Single Moving Average is a statistic method that can be used to forecasting time series data. It works by calculating the mean of a constant number of observations in a sliding time span and it will smooth the irregular fluctuation of data. The number of observations used is called the order of the series [13]. Previous researches showed that Single Moving Average can be used to forecast time series data [14-15]. In this research Single Moving Average with order 2 or SMA(2) is used and calculated with formula below.

𝑀𝐴(2) = ∑ 𝑥𝑡

𝑡2

𝑡=𝑡1

(15)

With: 𝑥𝑡 : Number at index t.

3. Results and Analysis

There are 132 monthly data of foreign tourist arrival and 11 annual data for each foreign tourist arrival factor for each country which is taken from 2005 until 2015. Foreign tourist arrival factor data are divided by 12 to get the mean value for each month. All these data are divided into training and test data after normalizing process. There are 3 types of forecasting time period tested in this research, those are 1, 3, and 6 months ahead. Each time period has different amount of training data. Forecasting 1, 3, and 6 months ahead are done using 119, 117 and 114 data respectively and then tested using 12 data outside of the training data.

Web based application written in PHP and HTML is made to implement RNN BPTT and SMA(2) method. This application will train and test the network and showed the comparison results between those 2 methods and target data in chart form as shown in Figure 2 to 6.

The network consists of 4 input states where each of them represents input for foreign tourist arrivals, population of origin country, GDP of origin country and CPI of Indonesia relative to CPI of the origin country. There is 1 hidden layer with specified number of hidden state. The number of output state depends on the time period of forecasting, for example forecasting 3 months ahead will use 3 output states.

There are 36 network test configuration for each time period. The configuration variables are the amount of hidden state, number of epoch and learning rate. The number of hidden states are 5, 10 and 15. The number of epoch are 300, 400, and 500 and learning rate is 0.01, 0.05, 0.1, and 0.5. In Backpropagation Through Time process, truncated backpropagation is applied. It reduced the calculation cost because it only calculates 𝑘2 timesteps [16]. In this

research 𝑘2 is 2, so the backpropagation process will calculate up to 2 time step only. Each of network configuration results are compared with Single Moving Average results in MSE form.

There are 10 countries tested, they are Australia, China, Malaysia, Japan, Singapore, South Korea, United Kingdom, United State of America, France and Germany. These are top 10 countries with highest foreign tourist arrival to Bali since 2011 to 2015 [1].

Table 1. Test results of 1 month ahead forecast

Country

1 Month Ahead Forecast

RNN BPTT SMA(2)

Hidden State

Epoch Learning

Rate MSE of RNN BPTT Test

Data MSE of SMA(2) Test Data

Australia 5 500 0.1 0.04835 0.08901 China 15 300 0.1 0.07835 0.09859 Malaysia 10 300 0.01 0.04479 0.09926 Japan 15 400 0.1 0.02358 0.03688 Singapore 10 300 0.01 0.06471 0.15260 South Korea 5 300 0.5 0.05690 0.10034 UK 10 400 0.01 0.09694 0.08209 USA 5 300 0.5 0.05883 0.05565 France 10 500 0.01 0.06447 0.08900 Germany 15 300 0.05 0.06988 0.09709

Table 1, 2, and 3 show the best network configuration with the smallest RNN BPTT

MSE compared with SMA(2) MSE when testing those methods to forecast foreign tourist arrival to Bali. Table 1 shows the comparison between test data MSE of RNN BPTT and SMA with

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Foreign Tourist Arrivals Forecasting Using Recurrent Neural Network… (W. Oger Vihikan)

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order 2 in 1 month ahead forecast. The comparison reveals that Australia, China, Malaysia, Japan, Singapore, South Korea, France and Germany RNN BPTT MSE are smaller than SMA(2) MSE. This means 8 out of 10 countries or 80% of them gives better results when tested using RNN BPTT method.

Table 2. Test results of 3 months ahead forecast

Country

3 Months Ahead Forecast

RNN BPTT SMA(2)

Hidden State

Epoch Learning

Rate MSE of RNN BPTT Test

Data MSE of SMA(2) Test Data

Australia 5 300 0.1 0.04083 0.07674 China 10 300 0.1 0.07025 0.09814 Malaysia 15 300 0.01 0.06534 0.09826 Japan 15 300 0.1 0.02654 0.03303 Singapore 15 400 0.01 0.09591 0.15136 South Korea 5 300 0.5 0.05893 0.10125 UK 15 400 0.01 0.11138 0.06971 USA 5 300 0.5 0.06250 0.05087 France 10 400 0.01 0.07302 0.08615 Germany 5 400 0.1 0.10328 0.08465

Table 2 shows the comparison between test data MSE of RNN BPTT and SMA with

order 2 in 3 months ahead forecast. The comparison reveals that Australia, China, Malaysia, Japan, Singapore, South Korea and France RNN BPTT MSE are smaller than SMA(2) MSE. This means 7 out of 10 countries or 70% of them gives better results when tested using RNN BPTT method.

Table 3. Test results of 6 months ahead forecast

Country

6 Months Ahead Forecast

RNN BPTT SMA(2)

Hidden State

Epoch Learning

Rate MSE of RNN BPTT Test

Data MSE of SMA(2) Test Data

Australia 5 400 0.5 0.03370 0.05587 China 15 300 0.1 0.06417 0.09589 Malaysia 15 300 0.01 0.06969 0.09785 Japan 5 500 0.01 0.02304 0.02689 Singapore 10 400 0.1 0.07845 0.15263 South Korea 15 300 0.5 0.05356 0.08929 UK 5 400 0.01 0.09568 0.05388 USA 10 400 0.01 0.04830 0.04301 France 10 500 0.01 0.05771 0.09155 Germany 5 500 0.1 0.08870 0.06597

Table 3 shows the comparison between test data MSE of RNN BPTT and SMA with

order 2 in 6 months ahead forecast. The comparison reveals that Australia, China, Malaysia, Japan, Singapore, South Korea and France RNN BPTT MSE are smaller than SMA(2) MSE. This means 7 out of 10 countries or 70% of them gives better results when tested using RNN BPTT method.

Figure 2. Forecast comparison chart between RNN BPTT, SMA(2), and real data of Australia

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Figure 3. Forecast comparison chart between RNN BPTT, SMA(2), and real data of China

Figure 4. Forecast comparison chart between RNN BPTT, SMA(2), and real data of Malaysia

Figure 5. Forecast comparison chart between RNN BPTT, SMA(2), and real data of Japan

Figure 6. Forecast comparison chart between RNN BPTT, SMA(2), and real data of Singapore

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Foreign Tourist Arrivals Forecasting Using Recurrent Neural Network… (W. Oger Vihikan)

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Figure 2, 3, 4, 5 and 6 show one of test data result of first 5 countries tested in chart form that represent forecast test comparisons of foreign tourist arrival to Bali by RNN BPTT, SMA(2) and real data. The green line represents real data, pink line represents RNN BPTT forecast and blue line represents SMA(2) forecast. The values of tourist arrivals are still in range between -1 to 1. 4. Conclusion

Based on the research results can be concluded some points as following: 1) Recurrent Neural Network Backpropagation Through Time can be used as forecasting method of foreign tourist arrival to Bali by Balinese government due to the forecast test results for most countries tested in 1, 3, and 6 months ahead forecast are closer to factual data than Single Moving Average method’s which is shown by their MSE value. 2) From 10 countries tested, 80% MSE of RNN BPTT for 1 month ahead forecast is smaller than MSE of SMA(2). For 3 and 6 months ahead forecast, 70% MSE of RNN BPTT is smaller than SMA(2). The smaller the MSE means the forecast test results are closer to factual data. These mean Recurrent Neural Network Backpropagation Through Time method outperformed Single Moving Average order 2 in forecasting foreign tourist arrival to Bali.

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