PCA and Kernels: Let I be the input space, {t;}"=1 c I be the dataset, 0 : 1 F be the mapping from input space to feature space, and K be the corresponding kernel matrix. Assume that the data is centered in feature space (21=10(1;) = 0). Suppose that the data includes four points (n = 4 and d = 2): 11 = (1, 2), 12 = (2,1), 13 = (2, 2), and 24 = (1,1) and we would like to reduce the dimensionality from 2 to 1. Would you recommend to use linear PCA or kernel PCA in this case? Why? Assuming the first two data points x1 = (1, 2) and 12 = (2,1), calculate the first kernel principal component using the kernel function: Kli, tj) = (x+x;)? (hint: calculate the kernel matrix, use the determinant to find the first eigenvalue, and solve the eigenvector decomposition to find the first eigenvector. Skip centering the kernel matrix)