Question

Consider a Kohonen net with two cluster units and five input units. The weights vectors for the cluster units are

W1 = (1.0, 0.9, 0.7, 0.3, 0.2)

W2 = (0.6, 0.7, 0.5, 0.4, 1.0)

Use the square of the Euclidean distance to find the winning cluster unit for the input pattern x = (0.0, 0.2, 0.1, 0.2,0.0). A learning rate of 0.2, find the

new weights for the winning unit.​

Answer 1

Answer:

Step 1: Initial weight matrix•[0.9 0.4•0.7 0.3•0.6 0.5]•Initial radius R = 0, Initial learning rate α = 0.2•Step 2: Begin training•Step 3: For the input vector (0.4, 0.2, 0.1) do steps 4-6.•Step 4: Calculate the squared Euclidean distance•D(j) = ∑(wij– xi)2•D(1) = (0.9-0.4)2+ (0.7-0.2)2+ (0.6 – 0.1)2= 0.75•D(2) = (0.4-0.4)2+ (0.3-0.2)2+ (0.5 – 0.1)2= 0.17

•Step 5: The input vector is closest to output node 2. Since D(2) is minimum J=2.• w12(new)=w12(old)+α[x1-w12(old)]•= 0.4 + 0.2*(0.4-0.4) = 0.4• w22(new)=w22(old)+ α[x2-w22(old)]•= 0.3 + 0.2*(0.2-0.3) = 0.28• w32(new)= w32(old)+ α[x3-w32(old)]•= 0.5 + 0.2*(0.1-0.5) = 0.42•This gives the new updated weight matrix•[0.90.4•0.70.28•0.60.42]

Explanation:

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