Explain: Perceptron Learning Algorithm.

       ·    The Perceptron Learning Algorithm is a search algorithm.

       ·    It begins in a random initial state and finds a solution state.

       ·    The search space is simply all possible assignments of real values to the weights of the perceptron.

       ·    The search strategy is gradient descent.

       ·    The perceptron learning rule is guaranteed to converge to a solution in a finite no. of steps, as long as a solution exists.

   ·     The perceptron can be used to classify input vectors that can be separated by a linear boundary. Such vectors are called Linearly Separable.

Algorithm:

Given: A classification problem with n input features (x1, x2, …, xn) and two output classes. 

Compute: A set of weights (w0, w1, w2, …, wn) that will cause a perceptron to fire whenever the input falls into the first output class.

       1.      Create a perceptron with n+1 input and n+1 weight, where x0 is always set to 1.

       2.     Initialize weights (w0, w1, w2, …, wn) to random real values.

       3.     Iterate through the training set, collecting all examples misclassified by the current set of weights.

       4.     If all examples are classified correctly, output the weights, and quit.

       5.     Otherwise, compute the vector sum S, of the misclassified input vectors. Multiply the sum by a scale factor η.

       6.     Modify the weights (w0, w1, w2, …, wn) by adding the elements of the vector S to them. Go to step 3.