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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                iteration


Perceptrone    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 samples
Associative                                          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 samples
Associative                                          -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 solve
propagation     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)
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.

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Neural network Algos formulas

  • 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 iteration Perceptrone 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 samples Associative 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 samples Associative -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 solve propagation 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. 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.