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Judul : Analisis Diskriminan pada Klasifikasi Desa di Kabupaten

Tabanan Menggunakan Metode K-Fold Cross Validation

Nama : Ida Ayu Made Supartini

Pembimbing : 1. Ir. I Komang Gde Sukarsa, M.Si

2. I Gusti Ayu Made Srinadi, S.Si, M.Si

ABSTRAK

Kabupaten Tabanan merupakan salah satu kabupaten dari kabupaten dan kota yang ada di Provinsi Bali. Secara administratif Kabupaten Tabanan dibagi

menjadi kecamatan dan desa. Wilayah kabupaten mempunyai bagian-bagian yang merupakan kawasan perdesaan dan kawasan perkotaan. Analisis

Diskriminan adalah metode analisis peubah ganda yang bertujuan untuk

memisahkan objek pengamatan yang berbeda dan mengalokasikan objek

pengamatan baru ke dalam kelompok yang telah didefinisikan, sehingga analisis

diskriminan dapat digunakan untuk mengelompokkan desa ke dalam kelompok perkotaan atau perdesaan. Analisis diskriminan linear mengasumsikan

bahwa matriks ragam-peragam adalah homogen, jika asumsi kehomogenan ragam

tidak terpenuhi maka dapat digunakan analisis diskriminan kuadratik untuk

pengelompokkan. Penelitian ini menggunakan metode k-fold cross validation

untuk menghitung keakuratan fungsi diskriminan kuadratik dengan . Fungsi diskriminan kuadratik diperoleh pada dengan nilai APER terkecil ( ). Semua hasil klasifikasi yang diperoleh adalah stabil dan konsisten.

Kata kunci: analisis diskriminan kuadratik, k-fold cross validation

klasifikasi, perdesaan, perkotaan

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Title : Discriminant Analysis in Villages Classification at Tabanan

Regency Using K-Fold Cross Validation Method

Name : Ida Ayu Made Supartini

Supervisors : 1. Ir. I Komang Gde Sukarsa, M.Si

2. I Gusti Ayu Made Srinadi, S.Si, M.Si

ABSTRACT

Tabanan Regency is one of regencies and town in Bali Province. Administratively, it is divided into districs and villages. Discriminant analysis is a technique related to the separation of objects into different groups

that have been set previously, thus discriminant analysis can be used to classify

villlages into urban or rural groups. Linear discriminant analysis assumes that the covariance matrix of the two groups are equals, if the assumption of

equality covariance matrix is denied, quadratic discriminant analysis can be used

for classification. This research used k-fold crosss validation method for

calculating the accuracy of quadratic discriminant function where . Quadratic discriminant function is obtained by with the smallest APER value ( ). All of classification results are stable and consistence.

Keywords: Quadratic Disciminant Analysis, K-Fold Cross Validation, classification, rural, urban

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DAFTAR ISI

LEMBAR JUDUL ................................................................................................... i

LEMBAR PERSEMBAHAN ................................................................................. ii

LEMBAR PERNYATAAN ................................................................................... iii

LEMBAR PENGESAHAN TUGAS AKHIR ....................................................... iv

ABSTRAK ............................................................................................................... v

ABSTRACT ............................................................................................................. vi

BIODATA ALUMNI ............................................................................................ vii

KATA PENGANTAR ......................................................................................... viii

DAFTAR ISI ............................................................................................................ x

DAFTAR TABEL ................................................................................................ xiii

DAFTAR GAMBAR ............................................................................................. xv

BAB I PENDAHULUAN ....................................................................................... 1

1.1 Latar Belakang .......................................................................................... 1

1.2 Rumusan Masalah ..................................................................................... 4

1.3 Batasan Masalah ........................................................................................ 5

1.4 Tujuan Penelitian ....................................................................................... 5

1.5 Manfaat Penelitian ..................................................................................... 5

BAB II TINJAUAN PUSTAKA ............................................................................. 7

2.1 Penelitian Sebelumnya .............................................................................. 7

2.2 Analisis Peubah Ganda .............................................................................. 8

2.3 Analisis Diskriminan ............................................................................... 10

2.3.1 Signifikansi Fungsi Diskriminan .................................................... 18

2.3.2 Uji Distribusi Normal Ganda .......................................................... 19

2.3.3 Uji Vektor Nilai Rata-Rata ............................................................. 20

2.3.4 Uji Kehomogenan Ragam (Box's M) ............................................. 21

2.3.5 Pencilan Peubah Ganda .................................................................. 22

2.3.6 Penduga Maximum Likelihood Estimation (MLE) ......................... 23

2.3.7 Metode Cross Validation ................................................................ 25

2.3.8 Mengalokasikan Individu Baru untuk Analisis Diskriminan dengan

Dua Kelompok ......................................................................................... 27

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2.4 Uji Ketepatan Klasifikasi ........................................................................ 28

2.4.1 Apparent Error Rate (APER) ......................................................... 29

2.4.2 Uji Keakuratan ................................................................................ 29

2.4.3 Uji Kestabilan .................................................................................. 31

2.5 Penentuan Status Daerah ......................................................................... 31

2.5.1 Daerah Perkotaan dan Daerah Perdesaan ....................................... 32

2.5.2 Kriteria Desa Perkotaan ................................................................ 32

BAB III METODE PENELITIAN ........................................................................ 35

3.1 Sumber Data ............................................................................................ 35

3.2 Identifikasi Peubah Penelitian ................................................................. 35

3.3 Metode Analisis Data ............................................................................. 35

BAB IV HASIL DAN PEMBAHASAN ............................................................... 37

4.1 Statistik Deskriptif ................................................................................... 37

4.2 Uji Asumsi Dasar Analisis Diskriminan ................................................. 38

4.2.1 Uji Distribusi Normal Ganda ......................................................... 38

4.2.2 Uji Vektor Nilai Rata-Rata ............................................................. 41

4.2.3 Uji Kehomogenan Matriks Ragam Peragam .................................. 42

4.2.4 Uji Pencilan (Outlier) ..................................................................... 43

4.3 Analisis Diskriminan Bertatar (Stepwise Discriminant Analysis) ........... 45

4.4 Metode K-Fold Cross Validation ............................................................ 47

4.4.1 Metode 2-Fold Cross Validation .................................................... 48

4.4.2 Metode 3-Fold Cross Validation .................................................... 53

4.4.3 Metode 4-Fold Cross Validation .................................................... 63

4.5 Uji Ketepatan Klasifikasi ........................................................................ 77

4.5.1 Peluang Kesalahan Klasifikasi (APER) ......................................... 77

4.5.2 Uji Keakuratan ............................................................................... 83

4.5.3 Uji Kestabilan ................................................................................. 85

BAB V SIMPULAN DAN SARAN ...................................................................... 87

5.1 Simpulan .................................................................................................. 87

5.2 Saran ........................................................................................................ 88

DAFTAR PUSTAKA ............................................................................................ 89

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LAMPIRAN ........................................................................................................... 91

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DAFTAR TABEL

Tabel 2.1 Tabel Kesalahan Klasifikasi ................................................................. 29

Tabel 2.2 Variabel, Klasifikasi, Skor, da