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Natural, April 2018. Vol 14. No 1 ISSN:1412 – 1328 45 Natural, April 2018. Vol 14. No 1 ISSN:1412 – 1328 45 PENERAPAN ANALISIS GEROMBOL DAN BIPLOT (STUDI KASUS: HASIL PERTANIAN DAERAH TERTINGGAL DI PROVINSI PAPUA BARAT) Application Of Cluster Analysis And Biplot (Case Study: Agricultural Product Of Underdeveloped Region In West Papua Province) Indah Ratih Anggriyani1), Dariani Matualage2), Esther Ria Matulessy3) 1)2)3) Jurusan Matematika dan Statistika, Fakultas MIPA, Universitas Papua Jl. Gunung Salju Amban, Manokwari – Papua Barat 1)[email protected] 2)[email protected] 3)[email protected] ABSTRACT One of the potential of the seven districts underdeveloped areas in West Papua Province is agriculture. In order to develop agricultural potential, an overview of agricultural products is needed including the similarity of regional characteristics and the relative position of the region. The similarity of regional characteristics to agricultural product can be known by cluster analysis. The relative posistion of the area with agricultural results is known by biplot analysis. Bintuni Bay Regency, South Sorong Regency, Tambrauw Regency and Maybrat Regency have the same characteristics in producing agriculture while Teluk Wondama Regency, Sorong Regency and Raja Ampat Regency have different characteristics. The relative position of agricultural products with the regency is Sorong Regency producing the highest number of food crops while the largest producer of horticulture fruits and vegetables are Teluk Wondama Regency and Raja Ampat Regency. Keywoard: cluster analysis, biplot, underdeveloped regions PENDAHULUAN tertinggal maka diperlukan informasi dasar Berdasarkan Peraturan Pemerintah mengenai potensi daerah yang dimiliki Nomor 78 Tahun 2014 tentang Percepatan sehingga dapat dikelola dengan maksimal. Daerah Tertinggal, daerah kabupaten yang Salah satu potensi yang dimiliki oleh wilayah serta masyarakatnya kurang ketujuh daerah tersebut ditemukan pada berkembang dibandingkan dengan daerah lain sektor pertanian. Hal ini diketahui dalam skala nasional disebut sebagai daerah berdasarkan tingginya persentase kontribusi tertinggal. Provinsi Papua Barat memiliki yang diberikan sektor pertanian terhadap tujuh kabupaten yang termasuk dalam daerah PDRB ADHB daerah setempat dan/atau tertinggal yaitu Raja Ampat, Teluk persentase penduduk yang bekerja pada Wondama, Teluk Bintuni, Sorong Selatan, sektor tersebut. Guna pengembangan potensi Sorong, Tambrauw dan Maybrat (Peraturan pertanian, maka diperlukan gambaran Presiden Nomor 131 Tahun 2015). Salah satu tentang hasil pertanian meliputi kesamaan kriteria suatu daerah ditetapkan sebagai karakteristik daerah dan posisi relatif daerah. daerah tertinggal adalah perekonomian Kesamaan karakteristik daerah terhadap hasil masyarakat. Guna menunjang perekonomian pertanian dapat diketahui dengan analisis daerah pada kabupaten yang termasuk daerah gerombol sedangkan posisi relatif daerah Natural, April 2018. Vol 14. No 1 ISSN:1412 – 1328 46 dengan hasil pertanian secara keseluruhan melakukan pemetaan potensi pertanian di dapat diketahui dengan analisis biplot. Kabupaten Teluk Bintuni dengan metode Analisis gerombol mempunyai tujuan biplot dan pemetaan potensi pertanian di utama untuk mengelompokan objek-objek Kabupaten Raja Ampat (Anggriyani, I.R, berdasarkan kemiripan karakteristik yang 2017). Berbeda dengan penelitian terdahulu, dimilikinya. Karakteristik objek-objek dalam pada penelitian ini menerapkan analisis suatu gerombol memiliki tingkat kemiripan gerombol dan biplot pada daerah tertinggal di yang tinggi, sedangkan karakteristik antar Provinsi Papua Barat dengan tujuan objek pada suatu gerombol dengan gerombol mengetahui gambaran tentang hasil pertanian lain memiliki tingkat kemiripan yang rendah. meliputi karakteristik daerah dan posisi relatif Peubah-peubah yang dilibatkan dalam terhadap hasil pertanian. analisis gerombol dipilih sesuai dengan tujuan penggerombolan (Mattjik A & Sumertajaya I, 2011). Metode METODE penggerombolan terdiri dari dua yaitu Data yang digunakan dalam penelitian penggerombolan berhirarki dan tak diperoleh dari publikasi Badan Pusat Statistik berhirarki. Metode penggerombolan (BPS) tiap daerah kabupaten tertinggal di berhirarki digunakan jika banyaknya Provinsi Papua Barat yaitu Kabupaten Teluk gerombol yang diinginkan belum diketahui Wondama (TW), Kabupaten Teluk Bintuni sedangkan tak berhirarki digunakan jika (TB), Kabupaten Raja Ampat (RA), banyaknya gerombol sudah diketahui. Kabupaten Sorong Selatan (SS), Kabupaten Posisi relatif daerah dengan hasil Sorong (So), Kabupaten Tambrauw (Ta) dan pertanian dapat dilakukan dengan Kabupaten Maybrat (Ma). Peubah yang menggunakan analisis biplot. Analisis biplot digunakan meliputi produksi hasil pertanian merupakan analisis eksplorasi peubah ganda yaitu tanaman pangan, hortikultura buah dan yang ditujukan untuk menyajikan data peubah hortikultura sayur. ganda dalam peta dua dimensi sehingga Tahapan penelitian yang dilakukan perilaku data mudah dilihat dan yaitu mengelompokan kabupaten daerah diinterpretasikan. Informasi yang dapat tertinggal, selanjutnya membuat posisi relatif diperoleh dari analisis biplot yaitu kedekatan daerah dengan hasil pertanian. antar objek, keragaman peubah, korelasi antar Pengelompokan kabupaten daerah peubah dan keterkaitan antar objek. Dua tertinggal mengikuti algoritma metode objek dengan karakteristik yang sama akan berhirarki (Johnson & Wichern, 2002) yaitu: digambarkan sebagai dua titik yang posisinya 1. Bentuk n gerombol yang masing- berdekatan. Peubah dengan keragaman kecil masing beranggotakan satu individu. digambarkan sebagai vektor yang pendek. 2. Gabungkan antara dua individu yang Begitu pula sebaliknya, peubah dengan memiliki jarak terdekat menjadi keragaman besar digambarkan sebagai vektor gerombol baru. Perhitungan jarak pada yang panjang. Peubah digambarkan sebagai penelitian ini menggunakan jarak euclid vektor. Jika sudut dua peubah lancip ( ) dikarenakan satuan yang digunakan maka korelasinya bernilai positif, jika sudut sama yaitu dua peubah tumpul ) maka korelasinya bernilai negatif dan jika sudut dua peubah (1) siku-siku maka tidak saling berkorelasi. [∑( ) ] Karakteristik suatu objek bisa disimpulkan dari posisi relatifnya terhadap suatu peubah. 3. Memperbaharui matriks jarak antar Jika posisi objek searah dengan arah vektor gerombol dengan memakai metode peubah maka objek tersebut bernilai di atas yang dipilih. Metode yang digunakan rata-rata, jika berlawanan maka nilainya di pada penelitian ini adalah metode bawah rata-rata, dan jika hampir di tengah- pautan tunggal (single linkage) guna tengah maka nilainya mendekati rata-rata cenderung mempertinggi hubungan (Grenacre, 2010). dalam arti kedekatan, dengan formula: Beberapa penelitian terkait kabupaten ) (2) daerah tertinggal di Provinsi Papua Barat dengan telah dilakukan. Anggriyani, I.R (2016) ) = jarak antar amatan ke-k Natural, April 2018. Vol 14. No 1 ISSN:1412 – 1328 47 dengan gerombol (i,j) (√ √ √ ) (5) = jarak antara amatan ke-i dan ) (6) amatan ke-k = jarak antara amatan ke-j dan ) amatan ke-k (7) ( ) 4. Mengulangi langkah 2 dan 3 sampai √ √ √ terbentuk hanya satu gerombol yang dengan dan beranggotakan n individu merupakan nilai eigen dari matriks Penentuan jumlah gerombol pada metode atau berhirarki dapat dilakukan dengan memotong Mencari koordinat biplot, dengan dendogram yang memiliki selisih jarak 6. dekomposisi nilai singular atau terbesar. Singular Value Decomposition (SVD). Penentuan posisi relatif mengikuti SVD mengorientasikan kembali sumbu algoritma analisis biplot (Grenacre, 2010), koordinat sehingga membuat data yaitu: matriks lebih mengikuti untuk 1. Membuat matriks data asal ( ) mendekatkan diri terhadap pola yang berukuran dengan objek dan dibuat dari titik matriks itu sendiri. peubah. Dengan demikian SVD membantu 2. Mencari koreksi terhadap rataan untuk memahami struktur data matriks masing – masing peubah ( ) yaitu secara lebih baik. Penerapan SVD yaitu menguraikan persamaan (4) menjadi ( ) (3) (8) dengan adalah vektor berdimensi dengan . Menurut Jollife yang semua elemennya bernilai (1986) jika definisikan 3. Menghitung matriks koragam ( ) yaitu - [ ] dan 4. Mencari akar ciri (nilai eigen) dan [ ], maka persamaan (8) vektor ciri (vektor eigen). Nilai eigen dapat ditulis sebagai (λ) merupakan nilai karakteristik dari (9) matriks yang diperoleh dengan dengan demikian setiap elemen ke( ) t -λ . Vektor eigen atau vektor unsur matriks dapat dinyatakan karakteristik matriks yang sebagai (10) berpadanan dengan λ. 5. Mencari matriks U, L dan A. Matriks dengan dan yang berdimensi dengan . Vektor adalah banyaknya objek dan adalah merepresentasikan objek ke- matriks banyaknya peubah serta berpangkat dan vektor merepresentasikan dengan { } yang dapat peubah ke- matriks . Jika dinyatakan sebagai dekomposisi nilai berpangkat dua, maka vektor pengaruh singular yaitu baris dan vektor pengaruh kolom (4) dapat digambarkan pada ruang dimensi dengan dan merupakan matriks dua, sedangkan matriks yang kolom ortonormal sehingga berpangkat lebih dari dua dapat didekati dengan matriks berpangkat . Matriks adalah matriks dua sehingga persamaan (10) menjadi yang kolom – kolomnya terdiri dari vektor eigen yang berpadanan (11) dengan nilai eigen dari matriks dengan masing – masing dan . Matriks adalah matriks yang mengandung dua unsur pertama vektor kolom – kolomnya merupakan vektor dan . Dengan pendekatan tersebut eigen yang berpadanan dengan nilai maka matriks dapat disajikan dalam eigen dari matriks dengan ruang berdimensi dua. hubungan Natural, April 2018. Vol
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