Understanding 3-Input Perceptron with Bias and Learning Rate
Explore an example of a 3-input perceptron with bias that outputs values based on a specified condition. Follow the training set with initial weights set to zero and observe the weight vector adjustments with each iteration. Learn about the impact of the learning rate on the convergence of the perceptron model.
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Example 2 Assume a 3 input perceptron plus bias (it outputs 1 if net > 0, else 0) Assume a learning rate of 1 and initial weights all 0: wij = c(tj zj)xi Training set 0 0 0 -> 1 1 1 0 -> 0 0 1 1 -> 0 0 1 0 -> 1 W Pattern Target Weight Vector Net Output CS 478 - Perceptrons 1
Example 2 Assume a 3 input perceptron plus bias (it outputs 1 if net > 0, else 0) Assume a learning rate of 1 and initial weights all 0: wij = c(tj zj)xi Training set 0 0 0 -> 1 1 1 0 -> 0 0 1 1 -> 0 0 1 0 -> 1 W Pattern 0 0 0 1 Target 1 Weight Vector 0 0 0 0 Net Output CS 478 - Perceptrons 2
Example 2 Assume a 3 input perceptron plus bias (it outputs 1 if net > 0, else 0) Assume a learning rate of 1 and initial weights all 0: wij = c(tj zj)xi Training set 0 0 0 -> 1 1 1 0 -> 0 0 1 1 -> 0 0 1 0 -> 1 W 0 0 0 1 -1 -1 0 -1 Pattern 0 0 0 1 1 1 0 1 0 1 1 1 Target 1 0 0 Weight Vector 0 0 0 0 0 0 0 1 -1 -1 0 0 Net 0 1 Output 0 1 CS 478 - Perceptrons 3
Example 2 Assume a 3 input perceptron plus bias (it outputs 1 if net > 0, else 0) Assume a learning rate of 1 and initial weights all 0: wij = c(tj zj)xi Training set 0 0 0 -> 1 1 1 0 -> 0 0 1 1 -> 0 0 1 0 -> 1 W 0 0 0 1 -1 -1 0 -1 0 0 0 0 0 1 0 1 Pattern 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 Target 1 0 0 1 Weight Vector 0 0 0 0 0 0 0 1 -1 -1 0 0 -1 -1 0 0 Net 0 1 -1 -1 Output 0 1 0 0 CS 478 - Perceptrons 4
Example 2 Assume a 3 input perceptron plus bias (it outputs 1 if net > 0, else 0) Assume a learning rate of 1 and initial weights all 0: wij = c(tj zj)xi Training set 0 0 0 -> 1 1 1 0 -> 0 0 1 1 -> 0 0 1 0 -> 1 W 0 0 0 1 -1 -1 0 -1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 -1 -1 -1 0 1 0 1 Pattern 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 0 1 Target 1 0 0 1 1 0 0 1 Weight Vector 0 0 0 0 0 0 0 1 -1 -1 0 0 -1 -1 0 0 -1 0 0 1 -1 0 0 1 -1 0 0 1 -1 -1 -1 0 -1 0 -1 1 Net 0 1 -1 -1 1 0 1 -1 Output 0 1 0 0 1 0 1 0 CS 478 - Perceptrons 5
