Bayesian classification
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BAYESIAN CLASSIFICATION. Overview. Bayesian classification adalah pengklasifikasian statistik yang dapat digunakan untuk memprediksi probabilitas keanggotaan suatu class. BC didasarkan pada teorema Bayes yg memiliki kemampuan klasifikasi serupa dengan decision tree dan neural network

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BAYESIAN CLASSIFICATION

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BAYESIAN CLASSIFICATION


Overview

  • Bayesian classification adalah pengklasifikasian statistik yang dapat digunakan untuk memprediksi probabilitas keanggotaan suatu class.

  • BC didasarkan pada teorema Bayes yg memiliki kemampuan klasifikasi serupa dengan decision tree dan neural network

  • Memiliki akurasi dan kecepatan yg tinggi saat diaplikasikan ke dalam database yg besar


Bentuk umum teorema Bayes

P(H I X) = P(X I H) P(H)

P(X)

Keterangan :

X:data dgn class yg belum diketahui

H:hipotesis data X

P(HIX) :probabilitas hipotesis H berdasar kondisi X (posteriori probability)

P(H):probabilitas hipotesis H (prior porbability)

P(XIH) :probabilitas X berdasar kondisi pada hipotesis H

P(X):probabilitas dari X


Contoh


Contoh

  • Dari tabel diatas, terdpt 2 class dari klasifikasi yg dibentuk, yaitu:

    • C1 = buys_computer = yes

    • C2 = buys_cumputer = no

  • Misalnya, terdapat data X yg belum diketahui class-nya dgn data sbb:

    • X=(age=“<=30”, income=“medium”, student=“yes”, credit_rating=“fair”)

    • Buys_computer ?


Penyelesaian

  • Dibutuhkan utk memaksimalkan:

    P(XICi) P(Ci) utk i=1,2

  • P(Ci) merupakan prior probability utk setiap class berdasarkan data, contoh:

    • P(buys_computer=“yes”)= 9/14 = 0,643

    • P(buys_computer=“no”)= 5/14 = 0,357


Hitung P(XICi) utk i=1,2

  • P(age=“<30” I buys_computer=“yes”)=2/9=0,222

  • P(age=“<30” I buys_computer=“no”)=3/5=0,6

  • P(income=“medium” I buys_computer=“yes”)=4/9=0,444

  • P(income=“medium” I buys_computer=“no”)=2/5=0,4


Hitung P(XICi) utk i=1,2

  • P(student=“yes” I buys_computer=“yes”)=6/9=0,667

  • P(student=“yes” I buys_computer=“no”)=1/5=0,2

  • P(credit-rating=“fair” I buys_computer=“yes”)=6/9=0,667

  • P(credit-rating=“fair” I buys_computer=“no”)=2/5=0,4


Hitung P(XICi) utk i=1,2

  • P(X I buys_computer=“yes”)

    = 0,222 x 0,444 x 0,677 x 0,677 = 0,044

  • P(XI buys_computer=“no”)

    = 0,600 x 0,400 x 0,200 x 0,400 = 0,019

  • P(X I buys_computer=“yes”) P(buys_computer=“yes”)

    = 0,044 x 0,643 = 0,028

  • P(X I buys_computer=“no”) P(buys_computer=“no”)

    = 0,019 x 0,357 = 0,007


Hasil

  • Berdasarkan perhitungan, P(XICi) P(Ci) utk i=1,2

  • Maka :

    P(X I buys_computer=“yes”) P(buys_computer=“yes”)

    = 0,044 x 0,643 = 0,028

    P(X I buys_computer=“no”) P(buys_computer=“no”)

    = 0,019 x 0,357 = 0,007

    Nilai yg tertinggi adalah 0,028  Untuk kasus:

    X=(age = “<=30”,

    income = “medium”,

    student = “yes”,

    credit_rating = “fair”)

    Maka  buys_computer  “Yes”


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