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Fungsi Aktivasi

• Fungsi aktivasi dengan notasi: µ(.) mendefinisikan nilai output dari suatu neurondalam level aktivasi tertentu berdasarkan nilaioutput pengkombinasi linier ui.

• Beberapa fungsi aktivasi yg biasa digunakan:– Hardlimiter– Threshold– Sigmoid– Tangen Hiperbolik

Fungsi Aktivasi

1. Hardlimiter

2. Piecewise Linear

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Fungsi Aktivasi

3. Threshold

xx

f(.)f(.)

++11

tt

f(x) = 0 jika x ≤ tf(x) = 1 jika x > t

Fungsi Aktivasi

4. Sigmoid

5. Tangen Hiperbolik

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Arsitektur JST

Single layerSingle layer Multiple layerMultiple layerfully connectedfully connected

Recurrent networkRecurrent networkwithout hidden unitswithout hidden units

inputsinputs

outputsoutputs

{

}

Recurrent networkRecurrent networkwith hidden unitswith hidden units

Unit delayUnit delayoperatoroperator

Standard Activation Functions

• The hard-limiting threshold function– Corresponds to the biological paradigm

• either fires or not

• Sigmoid functions ('S'-shaped curves)– The logistic function– The hyperbolic tangent (symmetrical)– Both functions have a simple differential– Only the shape is important

)exp(11

)(av

vf−+

=

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• Representation of Boolean function AND

• Linear threshold is used

Perceptron Training

t = 0.0t = 0.0

YY

XX

WW11 = 1.5= 1.5

WW33 = 1= 1

--11

WW22 = 1= 1

1 1 if if ΣΣ wwiixxi i >t>tOutputOutput== {{0 0 otherwiseotherwise

Perceptron Training

• Epoch – Presentation of the entire training set to the neur al network.– In the case of the AND function an epoch consists o f four sets

of inputs being presented to the network (i.e. [0,0 ], [0,1], [1,0], [1,1])

• Error– a simple definition of error

– The error value is the amount by which the value ou tput by the network differs from the target value.

– For example, if we required the network to output 0 and it output a 1, then Error = -1

Sum of squared Sum of squared errors :errors :

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Perceptron Training

• Target Value (T)– Value required to be produced– If we present the network with [1,1] for the AND fu nction,

T will be 1

• Output (O)– The output value from the neuron

• Ij - Inputs being presented to the neuron

• Wj - Weight from input neuron (Ij) to the output neuron

• LR( ) - The learning rateThis dictates how quickly the network converges It is set by a matter of experimentation

η

Perceptron Training

• Algorithm

While epoch produces a non null errorWhile epoch produces a non null error

End WhileEnd While