Spatial Data Mining using SAR-Kriging Model

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Spatial Data Mining

using SAR-Kriging Model

Atje Setiawan Abdullah

A Lecturer at Informatics Engineering Study Program

Department of Computer Science FMIPA Universitas Padjadjaran Jl. Raya Bandung Sumedang Km 21 Jatinangor

e-mail: [email protected], [email protected]

SEAMS School

Spatio Temporal Data Mining and Optimization Modeling UTC-Bandung, August 9-19, 2016

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1. Introduction

In this paper

we combine the Expansion of

Spatial Autoregressive (Expansion SAR) model as

an extension of SAR model and Kriging technique

to predict a quality of education of

elementary

school.

The quality of education is defined as a

result of student on study which is measured by

National End Test (UAN). In Indonesia the score of

UAN still spreadly sparse, because there are

difference on education services based on spatial

or location.

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Education of elementary or middle level is study

process of passing school, imposed to student to be

having storey;

certain interest in cognate ability,

psycomotoric, and affective, according to specified

by a middle and elementary education curriculum.

Quality of education defined

as achievement

reached by the student and measured by pursuant

to final test value of national (UAN).

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1.1 Problems

Research about quality of education still be limited,

focused at measurement of result of education

through

UAN school, and analysis method still

limited to descriptive analysis. Considering regional

swampy forest broadness of education in Indonesia

and social condition, economic, and also culture

which

different

in

each

location,

hence

related/relevant problem with the education quality

in school at various location in Indonesia represent

the interesting study to be studied by method of

spatial of data mining.

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One of model of spatial of data mining which can be

used for the description and prediction is Expansion

Spatial Autoregressive ( Expansion SAR). The

Expansion SAR used for prediction of observation in

sample

location.

In

the

case

of

measuring

heterogeneities based on co-ordinate of location

spatial. Lack of the SAR model, it cannot be used to

predict at unsample location. Kriging method is one

of spatial analysis which can be used for prediction at

unsample location. So, we try to combine the SAR

and Kriging method to be SAR-Kriging for prediction

at unsample location using the parameter of SAR as

an input of Kriging method.

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1.2 The Aims of Research

• Studying model of combination of Expansion

SAR and Kriging method (SAR-Kriging)

• Applying concept of spatial of data mining use

the method of SAR-Kriging, for prediction at

unsample locations. For case study we use the

database of SDPN 2003 to predict quality of

education for

elementary school, junior high

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PROSES SPASIAL DATA MINING MENGGUNAKAN SAR-KRIGING DATABASE HASIL SDPN 2003 HASIL CLEANING & TRANSFORMASI HASIL DATA PREPARATION HASIL MODEL SAR-KRIGING HASIL EKSPANSI SAR

& GRAFIK HASIL MODEL SAR &

INDEKS MORAN

KNOWLEDGE PATTERN

CLEANING DATA & TRANSFORMASI KE RASIO

MODEL SAR

EVALUASI & VISUALISASI

DATA EKSTERNAL KOORDINAT KECAMATAN MODEL SAR INTERPRETASI PERHITUNGAN KRIGING

MODEL EKSPANSI SAR

HASIL PERBANDINGAN DATA AKTUAL & PREDIKSI

PERSAMAAN SAR-KRIGING DAN MUTU HASIL SAR-KRIGING

DATA MUTU HASIL EKSPANSI SAR DATA MUTU HASIL SURVEI

PR EP RO CE SS IN G DA TA M IN IN G PO ST PR OC ES SI NG HASIL SELEKSI FAKTOR DAN SEM

INTEGRASI DATA SPASIAL & NON SPASIAL SELEKSI INDIKATOR MENGGUNAKAN FAKTOR & SEM

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DATABASE SDPN 2003

DATA MINING INTEGRASI DATA TRANSFORMASI DATA

SELEKSI DATA

INTERPRETASI DAN VISUALISASI HASIL

KNOWLEDGE

PROSES DATA MINING

CLEANING DATA

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Scalability

Ukuran data 3,91 GB (4.178.499.369 byte) Terukur terdiri dari struktur tabel SD/SMP/SMA

Non-traditional Analysis

Melibatkan koordinat lokasi dan peta lokasi kecamatan, kabupaten dan provinsi di Indonesia

Analysis menggunakan model spasial

Data Ownership and Distribution

Tersebar secara geografis terdiri dari: provinsi,kabupaten, kecamatan dan desa

Heterogeneity and Complex Data

Melibatkan data non spasial dan data spasial Data non spasial indikator mutu pendidikan

Data spasial koordinat kecamatan

High dimentionality

Jumlah total record adalah 203.590 Jumlah variabel terdiri dari 569 DATABASE SDPN 2003

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DATA PERSEKOLAHAN TK: 54226 Record SD: 158590 Record SMP: 28949 Record SMA: 10810 Record SMK: 4753 Record DATA PENELITIAN

SD: 158.590 record dengan 122 variabel SMP: 28.949 record dengan 138 variabel SMA 10.810 record dengan 142 variabel

SELEKSI DATA

DATABASE SDPN 2003

Data Persekolahan 257660 Data Pendidikan Luar Sekolah 3047 Data Non Pendidikan 240 Data Perguruan Tinggi 13202

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SELECT left(sd_sarana.id,7) AS kdkec, Sum(jbkips_1+jbkips_2+jbkips_3+jbkips_4+jbkips_5+jbkips_6+jbkPPKN_1+jbkPPKN_2+jbkPPK N_3+jbkPPKN_4+jbkPPKN_5+jbkPPKN_6+jbkINDO_1+jbkINDO_2+jbkINDO_3+jbkINDO_4+jbkI NDO_5+jbkINDO_6+jbkMat_1+jbkMat_2+jbkMat_3+jbkMat_4+jbkMat_5+jbkMat_6+jbkipa_1+jbki pa_2+jbkipa_3+jbkipa_4+jbkipa_5+jbkipa_6)/ Sum(jsisK_tk1l+jsisK_tk1p+jsisK_tk2l+jsisK_tk2p+jsisK_tk3l+jsisK_tk3p+jsisK_tk4l+jsisK_tk4p+jsi sK_tk5l+jsisK_tk5p+jsisK_tk6l+jsisK_tk6p) AS RSBKTS, Sum(Lbangun)/ Sum(jsisK_tk1l+jsisK_tk1p+jsisK_tk2l+jsisK_tk2p+jsisK_tk3l+jsisK_tk3p+jsisK_tk4l+jsisK_tk4p+jsi sKtk5l+jsisK_tk5p+jsisK_tk6l+jsisK_tk6p) AS RSLBTS, Sum(Ltanah)/ Sum(jsisK_tk1l+jsisK_tk1p+jsisK_tk2l+jsisK_tk2p+jsisK_tk3l+jsisK_tk3p+jsisK_tk4l+jsisK_tk4p+jsi sK_tk5l+jsisK_tk5p+jsisK_tk6l+jsisK_tk6p) AS RSLTTS, Sum(jrng_baik)/ Sum(jrng_baik+jrng_rr+jrng_rb+jrng_bm) AS RSRB, Sum(jprg_ppkn+jprg_indo+jprg_mat+jprg_ipa+jprg_ips)/Sum(jrng_baik+jrng_rr+jrng_rb+jrng_bm) AS RSPRGTK FROM SD_Sarana INNER JOIN SD_SISWA ON SD_Sarana.ID=SD_SISWA.ID GROUP BY left(sd_sarana.id,7);

TRANSFORMASI DATA DARI VARIABEL KE INDIKATOR

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TRANSFORMASI DATA DASAR KE DATA INDIKATOR (QUERY)

SD: 21 Indikator SMP: 19 Indikator SMA: 20 Indikator

HASIL SELEKSI INDIKATOR MENGGUNAKAN ANALISIS FAKTOR

SD: 14 Indikator SMP: 16 Indikator SMA: 14 Indikator SELEKSI INDIKATOR DATA DASAR SD: 122 Variabel SMP: 138 Variabel SMA 142 Variabel

HASIL SELEKSI INDIKATOR MENGGUNAKAN SEM

SD: 7 Indikator SMP: 10 Indikator SMA: 13 Indikator

input proses Mutu

Rasio jumlah siswa thp jumlah kelas

(RSTRB)

Rasio jml siswa thp jml guru(RSTGR)

Rasio jml siswa usia 7 tahun thdp jml siswa (RSBR7) Rasio jml siswa mengulang thdp jml siswa (RSULGTJS) Rasio jml buku thdp jml siswa (RSBKTS) Rasio luas bangunan

thdp jml siswa (RSLBTS)

Rasio luas tanah thdp jml siswa (RSLTTS)

Rata-rata jumlah nilai UAS (TOTUAS)

Rasio jml guru tetap thdp jml guru (RSGTTG) Rasio jml pendaftar asal TK thdp jml pendaftar (RSDFTK) Rasio jml siswa usia 7-12 tahun thdp jml siswa (RSUM712)

Rasio jml siswa putus sekolah thdp jml siswa

(RSPTSTD) Rasio jml ruang kelas

baik thdp jml ruang kelas (RSRB) Rasio jml alat peraga

thdp jml kelas (RSPRGTK)

Rasio jml guru >= D2 thdp jml guru

(RSGLTG) Rasio jml guru agama

thdp rombel (RSGATRB)

Rata-rata Tingkat Kelulusan siswa (TKTLLS)

INDIKATOR PENELITIAN MUTU PENDIDIKAN JENJANG SD

Rasio jml guru kelas terhadap jml guru

(RSGKTG)

Rasio julah guru B. Ing thdp rombel (RSGINTROM) Rasio jml siswa baru

thdp jml siswa (RSB) RSTGR 28.69 RSBR12 0.03 RSUM1315 0.01 RSDFSD 0.00 INPUT PROSES MUTU RSLAB0.02 RSRB 0.03 RSGUAN0.00 RSGLTG0.01 RSPTSTS0.00 TOTUAN1.55 Chi-Square=32.88, df=27, P-value=0.20104, RMSEA=0.023 0.01 0.03 0.04 0.05 1.00 40.43 4.29 0.01 -0.00 0.03 -0.00 0.89 0.01 0.00-0.00 -0.000.03 -0.01

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Kecamatan yang tidak tersurvei pada SDPN 2003 dihilangkan dengan cara mengedit data

spasialnya.

Menggabungkan data non spasial dengan data spasial yang telah terpilih pada tabel peta spasial

sesuai dengan kecamatan masing-masing.

INTEGRASI DATA

Menghubungkan kecamatan-kecamatan pada peta spasial dengan data kecamatan yang disurvei

pada SDPN 2003.

Menjalankan program MATLAB menggunakan metode yang sesuai

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Database SDPN 2003 Sihombing (2002)

Nababan (2003)

PROSES SPASIAL DATA MINING

Cliff dan Ord (1975) Anselin, (1988) Cressie (1993) Armstrong (1998) Lazarevic (2000) Lichstein et al. (2002) Sekhar et al. (2003) LeSage (1999)

LeSage dan Pace (2004) Van Beers dan Kleijinen (2004) Celik et al. (2005)

Bronnenberg (2005) Kanazaki et al. (2006)

Kumar dan Remadevi (2006) Bakkali, S. dan Amrani, M. (2008) Lu et.al (2008)

Zhao Lu et al. (2008)

Koperski et al. (1997)

Berry dan Linoff (2000)

Soukup dan Davidson (2002)

Giudici, et al. (2003)

Han dan Kamber (2006)

Tan et al. (2006)

Olson dan Shi (2007)

Refaat (2007)

Giannotti dan Pedreschi (2008)

Maimon dan Rokach, (2008)

SPASIAL DATA MINING

DESKRIPSI

Indeks dan Plot Moran

PREDIKSI

Ordinary Kriging

MODEL KAUSAL

Model SAR Model Ekspansi SAR

MODEL SAR-KRIGING

MODEL SAR KRIGING

SELEKSI VARIABEL

Proses Input Output Analisis Faktor, SEM

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1.3 Variables of Research

In this research we use the database of SDPN 2003 from Balitbang-Depdiknas (2003), especially in elementary and indicator variables. Elementary variable represent the variable in individual raw data of school. Indicator variable is variable obtained by pursuant to elementary variables. Elementary variable cover the school identity, student indicator, medium indicator, teacher indicator, and total assess the UAN. From above indicator, builder by system of input and output of quality of education, input consisted by the student indicator, process composed by the indicator of medium and teacher indicator, output indicator of quality of education consisted by the amount assess the UAN and mean mount the pass. Indicator selection use the factor analysis and Structural Equation Model ( SEM).

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Figure 1.1 Variables Reduction Process

input proses _Mutu

Rasio jumlah siswa thp jumlah kelas (RSTRB) Rasio jml siswa usia 7 tahun thdp jml siswa (RSBR7) Rata-rata jumlah nilai UAS (TOTUAS) Rasio jml ruang kelas baik thdp jml ruang kelas (RSRB) Rasio jml guru >= D2 thdp jml guru (RSGLTG) Rata-rata Tingkat Kelulusan siswa (TKTLLS) HASIL REDUKSI VARIABEL INDIKATOR PENELITIAN MUTU PENDIDIKAN JENJANG SD

MENGGUNAKAN STRUCTURAL EQUATION MODEL

Rasio jml siswa baru thdp jml

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Figure 1.1 shows the result reduces of indicator

variables having an effect on to quality, using

factor analysis and SEM. The result for input gives

3 indicators, student ratio to amount class, ratio

sum up the student old age 7 year to student at the

first class and ratio new student to all all students.

Process composed by 2 indicators that is ratio of

well classroom to all space and competent teacher

ratio to total teacher. Output composed by 2

indicators, total assess the UAN, and mount the

pass. Indicator outputs UAN try to be analyzed by

expansion SAR model.

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2. Modeling at Spatial Data Mining 2.1 The Expansion SAR Model

The expansion SAR like known the previous model spatial SAR in measuring heterogeneities spatial based on neighborhood. Model the linear spatial locally in the case of measuring heterogeneities based on

co-ordinate of location spatial or a co-co-ordinate. Model the spatial like this is first time introduced by Casetti ( 1972,

1992 in Anselin, 1988 & Lesage, 1999). Paying attention to model regression in the following is:

0

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Where abouts and each showing coefficient regression, and vector perception from free variable. Coefficient regression in the equation shows the heterogeneities spatial in perception unit. For that, in the equation require to be entangled by a number of extension variables, for example and in such a way till go into effect:

1 0 1 1

z

2 2

z

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0 0 1( ) 2( 2 )

y    x z x₁  z x 

ε

Xβ

y





If the equation (2.1) substitution into equation ( 2.2) obtained:

In general model the Casetti formulated as follows:

0

ZJβ

β



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where              n y y y  2 1 y                ' ' 2 ' 1 0 0 0 0 n x x x    X              n     2 1 β        y x   0 β              n     2 1 ε                    k yn k xn k y k x I Z I Z I Z I Z     0 0 1 1 Z

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The model appraised by using smallest square method to appraise the parameters. Pursuant to the parameter

valuation, other valuation for the dot of in space appraised to use the second equation from (2.3). Distance from

perception center formulated:





2





2 y yi xc xi i z z z z d     (2.4)

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so the expansion SAR model can be noticed:

ε

XDβ

Xβ

α

y





₀



_(2.5)

In the equation (2.5), the influence of variable can be separated between non spatial and spatial

ε

XDβ

Xβ

α

y





₀

















spatial spatial non

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Parameter β and β₀ can be used to describe marginal influence for non spatial and spatil influences. For describing independent variables individually to dependent variable also can be used graphically through equation

i i di yi y i yi xi x i xi

D

Z

0































(2.6)

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2.2 Ordinary Kriging Method

Kriging is a method of calculating estimates of a regionalized variable at a point, over an area, or within a volume, and uses as a criterion the minimization of an estimation variance Kriging interpolation involves the generation of images of the reservoir properties and commonly used to visualize reservoir heterogeneities Therefore, Kriging techniques not well suited for reproducing geological reservoir patterns where the number of data are very limited. Using Kriging technique, we can predict the observation at unsample location (Armstrong, 1998).

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Assume that the regionalized variable under study has

value ₍ ₎

i i Z x

Z  , each representing the value at a point

i

x

. Also assume that this regionalized variable is second order stationary, with:

expectation: _E_[_Z₍_x_)] _ _m

Covariance: E



Z(x  h).Z(x)



 m2  C(h)

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A kriged estimator

Z

_V*

is a linear combination of n values of the regionalized variable:





n i i i V

Z

1 *



(2.7) For two locations, we have the minimum variance of Kriging (Armstrong, 1998):          1 2 1 12 1 2 1     V V _         12 2 1 2 2 2 1     V V

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To get the value of



₁ and

2



using ordinary Kriging method we should have the values of V 1



,



₂_V and 12



The value of



₁₂

is semivariogram experimental from two sample points and



₁

_V

is the semivariogram of the first sample point and the unsample point which will be predicted.

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For case study we use the spherical semivariogram for two locations















r

h

r

h

r

h

,

)

(

ˆ

,

)

(

ˆ

)

(



(2.9)

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2.3 SAR-Kriging Method

Method of SAR-Kriging in this study represent the combination model the Expansion SAR with the technique Kriging addressed for the prediction of quality of education unsample locations. Stages in explainable SAR-Kriging model as follows (Abdullah, A.S.-2009):

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• Determining variable dependent and independent to model the Ekspansi SAR entangling region data through distance between location center with the perception location

• Conducting parameter estimating model the Expansion SAR with the Maximum Likelihood method

• Determining location which unsample , around two sample location of co-ordinate and also apart to location sample

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• Parameter valuation model the Expansion SAR made by input at Kriging method to obtain; get weight in location to be predicted of quality of education

• The weight of Kriging represent the parameter valuation in unsample location

• The weight of Kriging obtained become the coefficient model of the Expansion SAR in unsample location

• Because model of Expansion SAR represent the model for the data of cross sectional, hence method of SAR Kriging got applicable to predict of quality of education if known by the independent values variable.

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The Result of SAR-Kriging

In this paper, we implemented spatial data mining using SAR-Kriging method to predict quality of education at 13 provinces in Indonesia included Aceh Province. In the base survey of education year 2003, Aceh didn’t included as a survey location, because of the situation and condition was very dangerous. So, for predicting of quality education we can use SAR-Kriging method.

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For the method of SAR-Kriging, selected by data input-proses of quality of storey; level of elementary school, junior high school, and senior high school from two provinces in region of Indonesia, that is Banten Province and South Sulawesi Province.

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Figure 3.1 Maps of Provinces in Indonesia

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Following the SAR-Kriging procedure, we have:

(1). Location co-ordinate which unsample selected by 13 provinces around Banten and South Sulawesi

(2). It ’ s obtained by a parameter valuation model the Expansion SAR through technique Kriging to 13 new locations by its co-ordinate

(3). Position of 13 locations between Banten and South Sulawesi Provinces

(4). Pursuant to weight Kriging at step 2, can be expressed by model of prediction expansion SAR through Kriging to quality of education at 13 unsample locations for elementary school

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Pursuant to inferential result that to 13 locations

among Banten and South Sulawesi, obtained by

model prediction of quality of education for

elementary school through method of SAR Kriging.

If known by the values from input variable and

process the education and also co-ordinate of

each;every location, hence quality of education

measured by totalizing UAN will be able to predict.

Model the prediction of quality of education to 13

locations

among Banten and South Sulawesi

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Table 3.1 Prediction of Quality Education for Elementary School in Indonesia using SAR-Kriging

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From Table 3.1 we can explain that quality of

education

in

13 provinces

influenced

by

component of non spatial with five variables and

five components spatial with five the variable

including distance of perception location to center

location. If we a selected Aceh Provinces between

Banten and South Sulawesi, pursuant to data

SDPN 2003 obtained by the following model

Expansion SAR:

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Quality of Education at Aceh

=

25.61 +

0.02RSTRB

+

5.88RSB

-2.87RSBR7

– 6.31RSRB + 1.77RSGLTG +

0.22d-RSTRB -7.81d-RSB

-11.39d-RSBR7-1.53d-RSRB+0.57d-RSGLTG

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For predicting of quality education on elementary

school, junior high school and senior high school

at

13 Provinces

in

Indonesia,

we

have

a

comparison between actual and prediction

SAR-Kriging as follows:

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Table 3.2 Comparison of Quality Education Actual and Prediction SAR-Kriging At Elementary School

NO PROVINCE ACTUAL PREDICTION ERROR APE

1 DKI 26.85 23.81 3.04 11.32 2 JABAR 31.73 26.04 5.69 17.93 3 JATENG 26.15 27.44 -1.29 4.93 4 DIY 26.47 26.76 -0.29 1.10 5 JATIM 26.83 28.19 -1.36 5.07 6 ACEH 25.94 24.27 1.67 6.44 7 SUMUT 24.22 24.54 -0.32 1.32 8 SUMBAR 23.13 29.13 -6 25.94 9 SULUT 24.95 25.96 -1.01 4.05 10 SULBAR 25.39 25.48 -0.09 0.35 11 KALBAR 24.09 24.1 -0.01 0.04 12 KALTENG 23.43 26.52 -3.09 13.19 13 KALTIM 23.57 26.68 -3.11 13.19 MAPE 8.07

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Table 3.3 Comparison of Quality Education Actual and Prediction SAR-Kriging At Junior High School

1 DKI 18.54 16.99 1.55 8.36 2 JABAR 17.85 16.82 1.03 5.77 3 JATENG 17.65 18.00 -0.35 1.98 4 DIY 18.99 17.98 1.01 5.31 5 JATIM 16.46 16.97 -0.51 3.10 6 ACEH 14.47 15.23 -0.76 5.25 7 SUMUT 18.53 15.11 3.42 18.46 8 SUMBAR 19.20 16.57 2.63 13.69 9 SULUT 14.13 17.30 -3.17 22.43 10 SULBAR 18.02 17.36 0.66 3.66 11 KALBAR 16.15 16.07 0.08 0.50 12 KALTENG 18.20 16.94 1.26 6.92 13 KALTIM 16.42 16.71 -0.29 1.77 MAPE 7.48

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Table 3.4 Comparison of Quality Education Actual and

Prediction SAR-Kriging At Senior High School

1 DKI 36.74 16.90 19.84 54.00 2 JABAR 36.30 31.20 5.10 14.04 3 JATENG 39.54 29.92 9.62 24.33 4 DIY 40.30 29.25 11.05 27.43 5 JATIM 45.34 29.55 15.79 34.82 6 ACEH 17.16 28.93 -11.77 68.61 7 SUMUT 31.90 38.66 -6.76 21.19 8 SUMBAR 33.22 35.46 -2.24 6.73 9 SULUT 45.48 38.54 6.94 15.26 10 SULBAR 20.78 37.17 -16.39 78.87 11 KALBAR 16.58 16.70 -0.12 0.72 12 KALTENG 39.09 37.96 1.13 2.89 13 KALTIM 25.48 33.33 -7.85 30.81 MAPE 29.21

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From three tables above, we can conclude that

Mean Average Percentage Error (MAPE) for

prediction of quality education at 13 provinces I

Indonesia for elementary school and junior high

school are less than 10%. But for senior high

school more than 10%. It means that the

SAR-Kriging method fit a good model for prediction of

quality

education

at

unsample

locations

on

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4. Conclusion

1). SAR-Kriging model is one of tools in spatial data

mining which combines expansion SAR model and

Kriging method.

2).

An

application

of

SAR-Kriging

model

for

prediction of quality of education at unsample

locations in Indonesia show that it gave a good result

for elementary and junior high school at 13 provinces

which are located in among two selected provinces.

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References

• Abdullah, A. S. 2009. Spatial Data Mining using

SAR-Kriging Model (Spatial Autoregressive-Kriging) for Mapping Quality of Education in Indonesia. Unpublished

Dissertation. Yogyakarta: Universitas Gadjah Mada.

• Anselin, L. 1988, Spatial Econometrics : Method and

Models, London: Kluwer Academic publisher.

• Armstrong, M. 1998. Basic Liniear Geostatistic, New York: Springer Verlag.

• Balitbang Depdiknas, 2003, Survei Dasar Pendidikan Nasional Tahun 2003, Jakarta.

• Han, J., and Kamber, M., 2006, Data Mining, Concept

and Techniques, USA: Academic Press.

• LeSage, J. P. 1999. The Theory and Practice of Spatial