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: atjesetiawan@gmail.com, atje.setiawan@unpad.ac.id

SEAMS School

Spatio Temporal Data Mining and Optimization Modeling

UTC-Bandung, August 9-19, 2016

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.

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).

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.

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.

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

school and senior high school in Indonesia.

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

PREP

ROCE

SSIN

GDA

TA M

ININ

GPO

STPR

OCES

SING

HASIL SELEKSI

FAKTOR DAN SEM

INTEGRASI DATA SPASIAL & NON SPASIAL

SELEKSI INDIKATOR MENGGUNAKAN FAKTOR & SEM

DATABASE SDPN 2003

DATA MINING

INTEGRASI DATA

TRANSFORMASI DATA

SELEKSI DATA

INTERPRETASI DAN VISUALISASI HASIL

KNOWLEDGE

PROSES DATA MINING

CLEANING DATA

PENGEMBANGN APLIKASI

ScalabilityUkuran data 3,91 GB (4.178.499.369 byte)

Terukur terdiri dari struktur tabel SD/SMP/SMA

Non-traditional AnalysisMelibatkan 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 DataMelibatkan data non spasial dan data spasial

Data non spasial indikator mutu pendidikan

Data spasial koordinat kecamatan

High dimentionalityJumlah total record adalah 203.590

Jumlah variabel terdiri dari 569

DATABASE SDPN 2003

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

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

Hasil Query untuk Agregat Sarana sebagai berikut:

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 siswathp jumlah kelas

(RSTRB)

Rasio jml siswa thpjml guru(RSTGR)

Rasio jml siswa usia 7tahun thdp jml siswa

(RSBR7)

Rasio jml siswamengulang thdp jmlsiswa (RSULGTJS)

Rasio jml buku thdp jml

siswa (RSBKTS)

Rasio luas bangunanthdp jml siswa

(RSLBTS)

Rasio luas tanah thdpjml siswa (RSLTTS)

Rata-rata jumlah nilai

UAS (TOTUAS)

Rasio jml guru tetapthdp jml guru

(RSGTTG)

Rasio jml pendaftarasal TK thdp jml

pendaftar (RSDFTK)

Rasio jml siswausia 7-12 tahun thdpjml siswa (RSUM712)

Rasio jml siswa putussekolah thdp jml siswa

(RSPTSTD)

Rasio jml ruang kelasbaik thdp jml ruang

kelas (RSRB)

Rasio jml alat peragathdp jml kelas

(RSPRGTK)

Rasio jml guru >= D2thdp jml guru

(RSGLTG)

Rasio jml guru agamathdp rombel(RSGATRB)

Rata-rata Tingkat

Kelulusan siswa

(TKTLLS)

INDIKATOR PENELITIAN MUTU PENDIDIKAN JENJANG SD

Rasio jml guru kelasterhadap jml guru

(RSGKTG)

Rasio julah guru B. Ingthdp rombel

(RSGINTROM)

Rasio jml siswa baruthdp jml siswa (RSB)

RSTGR28.69

RSBR120.03

RSUM13150.01

RSDFSD0.00

INPUT

PROSES

MUTU

RSLAB 0.02

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

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

Database SDPN 2003Sihombing (2002)

Nababan (2003)

PROSES SPASIALDATA 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

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).

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 siswa (RSB)

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.

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-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:

0y 1β x (2.1)

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 2 2z z (2.2)

0 0 1 2 2( ) ( )y 1x z x z x

εXβy

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

obtained:

In general model the Casetti formulated as follows:

0ZJββ

(2.3)

where

ny

y

y

2

1

y

'

'

2

'

1

0

0

00

nx

x

x

X

n

2

1

β

y

x

0β

n

2

1

ε

kynkxn

kykx

IZIZ

IZIZ

0

011

Z

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:

22

yyixcxii zzzzd (2.4)

so the expansion SAR model can be noticed:

εXDβXβαy 0 (2.5)

In the equation (2.5), the influence of variable can be

separated between non spatial and spatial

εXDβXβαy 0

spatialspatialnon

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

iidi

yiyiyi

xixixi

D

Z

Z

0

(2.6)

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).

Assume that the regionalized variable under study has

value )( ii xZZ , each representing the value at a point

ix . Also assume that this regionalized variable is

second order stationary, with:

expectation: mxZE )]([

Covariance: )()().( 2 hCmxZhxZE

Variogram: )(2)()(2

hxZhxZE

A kriged estimator*

VZ

is a linear combination of n values of the regionalized

variable:

n

i

iiV ZZ1

* (2.7)

For two locations, we have the minimum variance of

Kriging (Armstrong, 1998):

1

2

1

12

12

1

VV

12

21

222

1

VV

To get the value of 1 and2

using ordinary Kriging method we should have the values

ofV1 , V2 and 12

The value of 12is semivariogram experimental from two sample points

and V1

is the semivariogram of the first sample point and the

unsample point which will be predicted.

For case study we use the spherical

semivariogram for two locations

rhr

rhhr

r

h

,)(ˆ

,)(ˆ

)(

(2.9)

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):

• 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

• 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.

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.

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.

Figure 3.1 Maps of Provinces in Indonesia

http://zulfadli.files.wordpress.com/2008/01/indonesia-50-provinsi-gif.gif

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

Figure 3.2 Kriging Weight and Prediction of Quality Education at 13 Provinces

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

expressed as following tables:

Table 3.1 Prediction of Quality Education for Elementary School

in Indonesia using SAR-Kriging

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:

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

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:

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

Table 3.3 Comparison of Quality Education Actual and

Prediction SAR-Kriging At Junior High School

NO PROVINCE ACTUAL PREDICTION ERROR APE

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

Table 3.4 Comparison of Quality Education Actual and

Prediction SAR-Kriging At Senior High School

NO PROVINCE ACTUAL PREDICTION ERROR APE

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

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

elementary and junior high school in Indonesia.

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.

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

Econometrics. University of Toledo.