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# Neural network Algos formulas

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Perceptrone
Hetero
Associative
Auto
Associative
Discrete Hopfield
Back propagation

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### Neural network Algos formulas

1. 1. Algorithm Architectur Net Input Activation Weight Update Stopping name e Function Condition AND Biased update Hebb-Net Single Layer, wij(new)=wij(old)+xi y Only one Feed-forward - - bj(new)=bj(old)+y iterationPerceptrone Dual layer y_in= bj+Σxiwij y= 1 if y_in>θ wij(new)=wij(old)+ α txi If y=t, for all Feed-forward y= 0 if bj(new)=bj(old)+ α t samples -θ ≤y_in≤ θ where t=target y= -1 if y_in< -θ Adaline Feed-forward y_in=Σxiwi + b y= 1 if y_in≥ θ b(new)=b(old)+α(t-y_in), If the greatest y=-1 if y_in < θ wi(new)=wi(old)+α(t-y_in)xi weight change is smaller then the applied threshold. Madaline Dual Layer Z_inj=bj+∑xi wij f (x)=1 if x>0 When t=-1 If weight y_in=b3+z1v1+z2v2 -1 if x<0 bj(new)=bj(old)+α(-1-z_inj), changes have wij(new)=wij(old)+ α(-1- stopped so z_inj)xi one Iteration is complete when t=1 bj(new)=bj(old)+α(1-z_inj), wij(new)=wij(old)+ α(1- z_inj)xi Hetero Single Layer Y_inj=Σxiwij Yj=1 if y_inj>θj All samplesAssociative Yj if y_inj= θj wij(new)=wij(old)+sitj have been -1 if y_inj< θj processed Auto Single Layer Y_inj=Σxiwij Yj=1 if y_inj>0 All samplesAssociative -1 if y_inj<0 wij(new)=wij(old)+xiyj have been processed Discrete Unsupervised Y_inj = xi + Σyiwji 1 if y-ini> θ Hopfield Learning yi if y-ini= θ 0 if y-ini< θ Feedbackward Back Multi-layer Wij(new) = wij(old) + α Errj Oi We will solvepropagation supervised Y_inj = Σwijxi + bj bj = bj(old) + α Errj it until the learning Yj=1/1-e-Y_in error is zero Errors: Err=0 Feed-forward For hidden layers Errj = Oj (1-Oj) ∑ Errk wjk For output layer Errj = Oj (1-Oj) (Tj-Oj)
2. 2. Self unsupervised Dj=∑(wij-xi)2 Choose the Wij(new)= Wij(old)+α[xi-wij(old)]Organization learning minimum Dj (new)= 0.5 α (old) map and set the If Feed- value of j convergence Forward according to criterion met, it. STOP. Or When cluster 1 and cluster 2 is inverse of each other.