Levenberg-Marquardt Algorithm Combined with Bipolar Sigmoid

Function to Measure Open Unemployment Rate in Indonesia

Anjar Wanto, Irfan Sudahri Damanik, Indra Gunawan, Eka Irawan, Heru Satria Tambunan, Sumarno,

Zulaini Masruro Nasution

Tunas Bangsa College of Computer Science, Sudirman street Blok A Number 1, 2,

3 Pematangsiantar, North Sumatra - Indonesia

eka.irawan@amiktunasbangsa.ac.id, heru@amiktunasbangsa.ac.id, sumarno@amiktunasbangsa.ac.id,

zulaini@amiktunasbangsa.ac.id

Keywords: Levenberg-Marquardt, Combined, Sigmoid, Bipolar, Unemployment.

Abstract: The purpose of this research is to see how much open unemployment rate according to the highest education

completed in the country of Indonesia for subsequent years through predictions used on the basis of existing

data, which later as input for the government so that the government can make better policies to suppress the

unemployment rate. This research uses artificial neural network application using a combination of

Levenberg-Marquardt Algorithm with bipolar sigmoid function. Open unemployment data according to the

highest education is sourced from the National Labor Force Survey of the Republic of Indonesia, 2013-2017

in each semester. The data processing consists of two stages where the first phase of pattern recognition and

the second stage is predicted. Pattern recognition and prediction use different data from the same process that

uses data training and data testing. Data Training year 2013-2015 with target of 2016, while data testing year

2014-2016 with target year 2017. Architectural model used there are five, among others 6-2-5-2, 6-5-6-2, 6-

5-8-2, 6-5-10-2 and 6-8-12-2. From the 5 models it can be concluded that the best model is 6-5-10-2 with

epoch of 13 iterations, MSE in February 0.0109696004, MSE in August 0.0233797200. While the accuracy

rate in February and August is the same, that is equal to 88%.

1 INTRODUCTION

Unemployment is a term for people who do not work

at all, looking for work, working less than two days a

week or someone trying to get a decent job.

Unemployment is largely due to the fact that the

number of the labor force or job seekers is not

proportional to the amount of available employment

that is able to absorb it. Unemployment is often a

problem in the economy, because, with

unemployment, people's productivity and income will

be reduced so that it can cause poverty and other

social problems. Open Unemployment Rate is the

percentage of unemployment to the total labor force.

Unemployment in Indonesia includes issues that

are still difficult to overcome by the government.

Many factors affect the unemployment rate, one of

which is inflation, financial crisis to low levels of

community education (Tesfaselassie and Wolters

2017) (Carrillo-Tudela, Graber, and Waelde 2017).

Therefore, the role of government is needed in

tackling the problem of unemployment. Open

unemployment data in Indonesia according to the

highest education completed can be seen in the

following table:

Table 1: Open Unemployment According to Completed

Higher Education

Highest

Education

Completed

2013 2017

February August February August

Never

School

112.435 81.432 92.331 62.984

Hasn't

finished

primary

school

523.400 489.152 546.897 404.435

Primary

school

1.421.873 1.347.555 1.292.234 904.561

Junior

high

school

1.821.429 1.689.643 1.281.240 1.274.417

Senior

High

School

General

1.874.799 1.925.660

1.552.894 1.910.829

Wanto, A., Damanik, I., Gunawan, I., Irawan, E., Tambunan, H., Sumarno, . and Nasution, Z.

Levenberg-Marquardt Algorithm Combined with Bipolar Sigmoid Function to Measure Open Unemployment Rate in Indonesia.

DOI: 10.5220/0010037200220028

In Proceedings of the 3rd International Conference of Computer, Environment, Agriculture, Social Science, Health Science, Engineering and Technology (ICEST 2018), pages 22-28

ISBN: 978-989-758-496-1

SHS /

Vocational

School

864.64

1.258.20

1.383.02

1.621.40

Academy /

Diploma

197.27

185.10

249.70

242.93

8 University 425.04

434.18

606.93

618.75

Figure 1: Open Unemployment According to Completed

Higher Education

One way to suppress open unemployment by the

highest education completed is to forecast the

unemployment rate for subsequent years. Forecasting

results will be used as a barometer for the

Government to determine the policy as early as

possible, by applying appropriate measures

considered in overcoming unemployment. However,

the forecasting process is not easy, it takes the basic

model and time series data of those problems, which

is generally complicated by the estimation of

inaccurate accuracy, requiring more advanced

techniques (Hrasko, Pacheco, and Krohling 2015).

Therefore, forecasting techniques using the

Levenberg-Marquardt Algorithm combined with

bipolar sigmoid function. The Levenberg-Marquardt

algorithm is closer to the matrix that usually exists in

the optimization method. This reduces algorithm

complexity significantly (Sarabakha et al. 2017). This

algorithm is a powerful algorithm capable of

approaching and simplifying problems resulting in

faster and less complex convergence than standard

gradient descent or even backpropagation JST

methods. The Levenberg-Marquardt algorithm is

widely favored as a forecasting algorithm, because of

its superior performance with the use of more

consequent parameters (Castillo et al. 2013)

(Salimifard and Safavi 2013), and has many

successful implementations (Khanesar and Kayacan

2013).

In this research, the Levenberg-Marquardt

algorithm will be combined with bipolar sigmoid

function. The bipolar sigmoid function is almost the

same as the binary sigmoid function, only the output

of this function has a range between 1 to -1. The

bipolar sigmoid function is often used to predict time

series data whose value is up and down (unstable),

therefore we could readily analyze the situation of

using bipolar sigmoid activation function (Yunong

Zhang and Ke Chen 2008) (Zhang, Zhang, and Im

2017).

2 RUDIMENTARY

2.1 Artificial Intelligence

Artificial Intelligence is one area that is quite reliable

in solving problems such as prediction

(forecasting) (A. Wanto et al. 2017). AI is a very

important discipline and it includes a number of well

recognized and mature areas including Neural

Network (Chiroma et al. 2014) (Hakim, Sari, and

Herawan 2014) (Lasisi, Ghazali, and Herawan 2014).

Artificial Intelligence (AI) is a general term that

implies the use of a computer to model intelligent

behavior with minimal human intervention. AI is

generally accepted as having started with the

invention of robots. The term derives from the Czech

word robota, meaning biosynthetic machines used as

forced labor (Hamet and Tremblay 2017). AI is a field

of research based on the premise that intelligent

thought can be regarded as a form of computation -

one that can be formalized and ultimately

mechanized. To achieve this, however, two major

issues need to be addressed. The first issue is

knowledge representation, and the second is

knowledge manipulation (Sumijan et al. 2016).

2.2 Artificial Neural Networks (ANN)

Artificial Neural Network (ANN) is one of the studies

of Artificial Intelligence and is a new computing

technology in the field of computer science

research. Neural networks mostly used for problem-

solving in pattern recognition, data analysis, control

and clustering (Adnan et al. 2017). Initially ANN

were developed in the field of artificial intelligence

and were first introduced for image recognition. The

central concept was inspired by knowledge of the

nervous system, especially the human brain with its

closely connected neurons (Ehret et al. 2015).

Artificial neural network (ANN) is one of the

methods that is suitable to deal with the internal

relations of complex model because of its highly

Levenberg-Marquardt Algorithm Combined with Bipolar Sigmoid Function to Measure Open Unemployment Rate in Indonesia

nonlinear, large amounts of data parallel processing,

high robustness, and fault tolerance (Wang et al.

2017) (Anjar Wanto et al. 2017).

Figure 2: Artificial Neural Networks

The schematic representation of artificial neural

network. It consists of: (1) input layer (independent

variables), (2) hidden layers and, (3) the output layer

(dependent variable) (Parveen, Zaidi, and Danish

2017) (Putra Siregar and Wanto 2017).

2.3 Levenberg Marquardt Algorithm

In engineering and scientific computing, the

Levenberg-Marquardt algorithm (LMA or just LM) is

used to solve non-linear least squares problems. The

algorithm was first published in 1944 by Kenneth

Levenberg (Levenberg 1944) and in 1963 by Donald

Marquardt (Marquardt 1963). It is well known that

the LM method has quadratic convergence as the

Newton method if the Jacobian is Lipschitz

continuous and nonsingular at some solutions.

However, the condition on the non-singularity of the

Jacobian is very strong. (Yamashita and Fukushima

2001) (Fan and Pan 2009) (Fan and Yuan 2005)

Showed that if the LM parameter is chosen properly,

then the LM method preserves the quadratic

convergence under the local error bound condition,

which is weaker than non-singularity.

In this paper, we propose an LM algorithm to

predict the time series data to be combined with the

bipolar sigmoid activation function, to see how well

the accuracy and quality of these algorithms are in

forecasting the times series data

2.4 Fungsi Sigmoid Bipolar

The activation function is used to build training

networks on artificial neural networks. Determining

the optimal activation function of artificial neural

networks is important because it is directly related to

the success rate obtained. But, unfortunately, there is

no way to determine it analytically, the optimal

activation function is generally determined by testing

or adjustment. This paper discusses a simpler and

more effective approach for optimal activation

functionality. In this approach, which can be referred

to as a trained activation function, the activation

function is trained for each particular neuron. The

training process is based on the training dataset,

which consists of the number of inputs of each neuron

in the hidden layer and the desired output. In this way,

different activation functions are generated for each

neuron in the hidden layer (Ertugrul 2018).

In artificial neural networks, the activation

function used must meet several conditions, namely:

continuous, can be derived and is a function that does

not go down. One of the activation functions that

meet the characteristics of artificial neural networks

is the function of bipolar sigmoid function. The

derivative of this activation function is required by

the update weight rule, due to the condition of the

differentialization that requires the requirements

(Mishra et al. 2017). This paper uses bipolar sigmoid

Function because time series data to be processed up

and down value (unstable), therefore we could readily

analyze the situation of using bipolar sigmoid

activation function.

3 RESULT AND DISCUSSION

3.1 Data Collection

Data to be processed is unemployment data in

Indonesia according to the highest the education year

2013-2017. Data source from the National Labor

Force Survey and Indonesian Central Bureau of

Statistics. The data can be seen in table 1 in the

previous discussion.

3.2 Data Training and Testing

The dataset year 2013-2015 is used as training with

target 2016. While the dataset year 2014-2016 used

as testing with a target of 2017.

3.3 Normalization Data

The data will be normalized using the following

formula.

(1)

0.8( )

'0.1







ICEST 2018 - 3rd International Conference of Computer, Environment, Agriculture, Social Science, Health Science, Engineering and

Technology

Table 2: Normalization of training data

Nu.

Highest Education

Completed

2013 ... 2017

Feb Aug ... Feb Aug

1 Never School 0,1205 0,1093 ... 0,1139 0,1014

Hasn't finished

primary school

0,2683 0,2559 ... 0,2805 0,2181

3 Primary school 0,5914 0,5646 ... 0,5184 0,4525

4 Junior high school 0,7351 0,6877 ... 0,5525 0,5456

Senior High School

/ General

0,7543 0,7726 ... 0,6363 0,7815

SHS / Vocational

School

0,3910 0,5325 ... 0,5649 0,6269

7 Academy / Diploma 0,1510 0,1466 ... 0,1697 0,1590

8 University 0,2329 0,2362 ... 0,3301 0,2840

Table 3: Normalization of testing data

Nu.

Highest

Education

Completed

2013 ... 2017

Feb Aug ... Feb Aug

1 Never School

0,1282 0,1070 ... 0,1132 0,1027

Hasn't finished

primary school

0,2996 0,2201 ... 0,2767 0,2255

3 Primary school

0,5745 0,5222 ... 0,5448 0,4053

Junior high

school

0,6890 0,6435 ... 0,5408 0,5383

Senior High

School / General

0,7610 0,7859 ... 0,6385 0,7672

SHS / Vocational

School

0,3848 0,5592 ... 0,5774 0,6631

Academy /

Diploma

0,1502 0,1496 ... 0,1698 0,1674

8 University

0,2233 0,2581 ... 0,2983 0,3025

3.4 Analysis and Results

3.4.1 Analysis

This research uses 5 architectural models with 2

hidden and 2 outputs, among others: 6-2-5-2, 6-5-6-

2, 6-5-8-2, 6-5-10-2 and 6- 8-12-2. Training and test

parameters using Target Minimum Error = 0.001 -

0.05, Maximum Epoch = 1000, and Learning Rate =

0.001. The Levenberg-Marquardt (trainlm) algorithm

will be combined with the bipolar sigmoid activation

function (tansig). Broadly speaking, the analysis of

this combination will be applied using Matlab 2011.

The program listing can be seen as follows:

>>net=newff(minmax(P),[Hidden,Target],{'tansig','pureli

n','tansig'},'trainlm');

>> net.IW{1,1};

>> net.b{1};

>> net.LW{2,1};

>> net.b{2};

>> net.LW{3,2};

>> net.trainparam.epochs=1000;

>> net.trainparam.LR=0.001;

>> net.trainParam.goal = 0.001;

>> net.trainParam.show = 1000;

>> net.b{3};

>> net=train(net,P,T)

3.4.2 Results

Overall, the best results of the 5 network architecture

models used are 6-5-10-2, with the accuracy of output

in semester 1 (February) at 88% and in the 2nd

semester (August) also equal 88%. Actually, the

architecture model 6-5-8-2 produces 100% accuracy

in semester 1 (February), but in the 2nd semester

(August) its accuracy is low ie 75%. So we chose 6-

5-10-2 as the best model, with consideration of stable

accuracy.

For more details can be seen in the following

picture:

Figure 3: Training with architecture 6-5-10-2

Comparison of standard gradient descent training

functions with gradient descent with momentum and

adaptive LR can be seen in the following table:

Table 4: Results Levenberg-Marquardt + Bipolar

Arsitektur Epoch

MSE Akurasi

Feb Agu Feb Agu

6-2-5-2 14 0,0022588499 0,0065650062 63% 75%

6-5-6-2 6 0,0126063807 0,0680858800 75% 63%

6-5-8-2 6 0,0004848094 0,0043782187 100% 75%

6-5-10-2 13 0,0109696004 0,0233797200 88% 88%

Levenberg-Marquardt Algorithm Combined with Bipolar Sigmoid Function to Measure Open Unemployment Rate in Indonesia

Arsitektur Epoch

MSE Akurasi

Feb Agu Feb Agu

6-8-12-2 9 0,1704704039 0,1267147790 75% 75%

Comparison of each Epoch from the 5 architecture

models can be seen in the following figure:

Figure 4: Comparison of Epoch

Comparison of MSE from the 5 architectural

models can be seen in the following figure:

Figure 5: Comparison of MSE

Perbandingan tingkat akurasi dari ke 5 model

arsitektur dapat dilihat pada gambar berikut:

Figure 6: Comparison of Accuracy

The overall comparison (Epoch, MSE, and

Accuracy) of the 5 architectural models can be seen

in the following figure:

Figure 7: Comparison of Epoch, MSE, and Accuracy

From forecasting calculations using the

Levenberg-Marquardt algorithm combined with the

bipolar sigmoid activation function, it will show the

results of open unemployment forecasting in

Indonesia according to the highest education

completed as follows (2018-2020):

Table 5: Results of Open unemployment forecast by highest

education completed (2018-2020)

2018 2019 2020

February August February August February August

119.343 68.989 117.641 97.529 138.002 125.775

449.646 353.327 311.097 183.148 179.698 145.338

1.181.392 771.864 787.267 597.450 418.745 374.848

1.185.781 1.079.299 810.060 783.436 416.299 398.325

1.173.308 1.601.315 727.889 1.075.727 394.290 537.841

141.894 1.363.174 741.489 881.314 403.950 458.484

232.986 218.665 203.260 169.740 157.444 141.670

521.019 532.568 392.693 421.999 296.837 276.906

4 CONCLUSIONS

From the previous explanation, it can be concluded as

follows:

1. The accuracy, MSE and Epoch levels of the

Levenberg-Marquardt Algorithm combined

with bipolar sigmoid depend on the

architectural model used.

2. Determination of the parameters of optimum

network can only be done based on the

learning process and the determination of the

6-2-5-2 6-5-6-2 6-5-8-2 6-5-10-

6-8-12-

Epoch

0,0000000000

0,1000000000

0,2000000000

0,3000000000

0,4000000000

MSE

MSE Feb MSE Aug

100

200

LevelofAccuracy

AccuracyFeb AccuracyAug

200

Feb Aug Feb Aug

Epoch MSE Accuracy

Levenberg-Marquardt + Sigmoid

Bipolar

6‐2‐5‐2 6‐5‐6‐2 6‐5‐8‐2

6‐5‐10‐2 6‐8‐12‐2

ICEST 2018 - 3rd International Conference of Computer, Environment, Agriculture, Social Science, Health Science, Engineering and

Technology

error so that the length of research time can’t

be determined with certainty.

3. The number of iterations can’t be determined

by the size of the desired pattern recognition

accuracy but is determined by the parameters

of the network used, the initial conditions of

the network and the characteristics of the input

data.

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Technology