1. Consider a three layer neural network with one output unit, 10 hidden units at each hidden layer, and a five dimensional augmented feature vector as inputs. (a) Draw the network. (b) Write down the general expression on the derivative of the error function with respect to a weight using back error propagation (i.e., gradient decent). (c) Verify the general expression by calculating the derivative of the error function with respect to a weight that connects the 5th hidden unit at the first hidden layer with the 6 hidden unit at the second hidden layer. (d) Write a pseudo algorithm that computes the increment of a weight that connects the 4th input component with the 3rd hidden unit at the first hidden layer. 2. Consider K-Mean clustering algorithm. Eight samples are given below. Assume that there are three clusters, i.e., \k = 3. Initial partitions S1(0),S2(0), |$3(0) are also given below. Suppose Euclidian distance is used. First sketch the samples and the initial partitions. Then continue with the k-mean algorithm by finding the centroids. Do more iterations of finding both the partitions and the centroids until convergence. Provide your results by showing both the partitions and the centroids. Samples: |X1 X2 X3 X4 X5 X6 X7 X8 (0,1) (0, -1), (0, 3), (0,4), (1,3), (3,0), (3,1), (4,0) S(0) = { x1, S2(0= {[x4, S3(0) = {x7, x2, X5, x8} x3} X6 } 1. Consider a three layer neural network with one output unit, 10 hidden units at each hidden layer, and a five dimensional augmented feature vector as inputs. (a) Draw the network. (b) Write down the general expression on the derivative of the error function with respect to a weight using back error propagation (i.e., gradient decent). (c) Verify the general expression by calculating the derivative of the error function with respect to a weight that connects the 5th hidden unit at the first hidden layer with the 6 hidden unit at the second hidden layer. (d) Write a pseudo algorithm that computes the increment of a weight that connects the 4th input component with the 3rd hidden unit at the first hidden layer. 2. Consider K-Mean clustering algorithm. Eight samples are given below. Assume that there are three clusters, i.e., \k = 3. Initial partitions S1(0),S2(0), |$3(0) are also given below. Suppose Euclidian distance is used. First sketch the samples and the initial partitions. Then continue with the k-mean algorithm by finding the centroids. Do more iterations of finding both the partitions and the centroids until convergence. Provide your results by showing both the partitions and the centroids. Samples: |X1 X2 X3 X4 X5 X6 X7 X8 (0,1) (0, -1), (0, 3), (0,4), (1,3), (3,0), (3,1), (4,0) S(0) = { x1, S2(0= {[x4, S3(0) = {x7, x2, X5, x8} x3} X6 }