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  • 1. 66//1010//20132013 Back-Propagation Algorithm • A training procedure which allows multi-layer feed forward Neural Networks to be trained • Error-correction learning algorithm – Back-propagate the error from the output layer to the hidden layers • An example of a gradient-descent technique – The back-propagation process emerges directly from a derivation of the overall error gradient • Can theoretically perform “any” input-output mapping BPA Process • Compute the values for the output units, using the observed error • Starting with output layer, repeat the following for each layer in the network, until the earliest hidden layer is reached: – Propagate the values back to the previous layer – Update the weights between the two layers
  • 2. 66//1010//20132013 Error Back-Propagation • Sum of squared Error Hidden unitsHidden units Output unitsOutput units Input unitsInput units aaii aajj aakk wwj,ij,i wwk,jk,j Error Back-Propagation • Output Layer – Multiple output units, so Erri is i th component of error vector – Modified error • Gradient in output layer • Weight update in output layer η : Learning: Learning RateRate
  • 3. 66//1010//20132013 Error Back-Propagation • Hidden Layer – Hidden node j is “ responsible” for some fraction of the error in each of the output nodes to which it connects – divided according to strength of the connection between the hidden node and the output node and are propagated back to provide the values for the hidden layer Error Back-Propagation • Gradient in hidden layer • Weight update in hidden layer – : Learning: Learning RateRate
  • 4. 66//1010//20132013 Fungsi Aktivasi (fungsi logistik/sigmoid) ∞<<∞> −+ = )(-and0 ))(exp(1 1 ))(( nva nav nvf j j jj )](1)[( ))](exp(1[ ))(exp( ))(( 2 ' nynay nav nava nvf jj j j jj −= −+ − = FungsiFungsi AktivasiAktivasi((TangenTangen hiperbolikushiperbolikus)) 0))(tanh())(( >= (a,b)nbvanvf jij )]()][([ )))((tanh1())((hsec))(( 22' nyanya a b nbvabnbvabnvf jj jjij +−= −== Parameter-parameter JST (1) • Parameter JST yang sangat penting dan sensitif pada proses pelatihan, yaitu: jumlah neuron pada hidden layer, learning rate, jumlah iterasi, dan batasan error • Belum ada formula khusus menentukan jumlah neuron pada hidden layer yang optimal • Formula untuk memperkirakan jumlah neuron pada hidden layer adalah: – Nh adalah jumlah neuron pada hidden layer – Ni jumlah node input layer atau jumlah masukan – Ni adalah jumlah neuron pada output layer
  • 5. 66//1010//20132013 Parameter-parameter JST (2) • Parameter learning rate sangat mempengaruhi proses pelatihan – Learning rate terlalu besar (misal 0,9) • MSE menurun tajam pada awal iterasi, tetapi MSE dapat berosilasi atau naik turun tidak terkendali – Learning rate terlalu kecil (misal 0,0001) • MSE menurun sangat pelan Parameter-parameter JST (3) • Jumlah iterasi dan batasan error digunakan sebagai kondisi berhenti pada proses pelatihan. • Jika batasan error yang kita definisikan terlalu kecil, JST bisa menjadi overfit, artinya JST memiliki akurasi tinggi untuk data training set tapi akurasinya sangat rendah untuk data test set • Salah satu cara untuk menghindari overfit adalah dengan membagi data-data yang ada menjadi tiga bagian: training set, validation set, dan test set. • Pada saat pelatihan, kita menggunakan training set dan validation set secara bersamaan