Question

6. A perceptron is needed to classify two sets of patterns given as Class (1): 1- (2.0)". U-12,2). V -[1.3] , target value - 1 Class (2): X=(-1,0]', Y =(-2,0], Z =(-1, 21', target value 1 Determine the boundary line that separates the two classes ( 11 = 0.5).

Answer 1

Class(u : T=(2,0] I, U=(22) T, v= [13] Tangent value = -1 ClassB) = x= [-107T, Y=[-2,5)", 2=(-1,437 Tangent value = 1 Let us assume that the initial value for o is- and the values for w, and Wg are al and 1. :. The boundard Line is given initially X = x,-1, Updated boundara Xg=-3x, < ------ An -- 7X1 - ----++ original boundary Xg=X, 1 (O) Class 1=1 -- CAClass a= 1 -----

How wsing the terms of the update weight rule, We see the Botteon Tis correctly classified Since Syn (2.(-1) +0+1) = -1 , Which is ingeed Close(V). So no update is necessary for this exampleo. For Pattern U. 1. Syn (21-1)+2(1) + 1) = 1 and the boundary not Provide for a we'ght update correct clossification . So is warranted. AW, = A Wg =112)=-2. The bias update poovides for se- +1. The new values for W., Wq ondo become now -3,-) and o. The new boundary is now represented by the line Xg = -3X, A brief checking of the remaing patterns shows that no weight and bias updating is required since all the pottons are now adequately Classifled. that sebrate the .. Xg=-3x, is the boundary Line two classes.