Question 4 (10 points): Face Recognition using PCA (EigenFace) This problem is adapted from 08233 at Stanford University. For this question, please also refer to the slides located in http : //www. cs . unc . edu/iazebnik/SpringOQ/lec22_eigenfaces . pdf We will use the YaleFace data set with images portraying human faces. YaleFace consists of images of the faces of 15 different individuals. For each individual, 11 images are taken under a variety of conditions, i.e., the person makes a sad expression, makes a happy expression, wear glasses, and etc. There are a total of 165 grey scale images. (a) (b) Download the lef ace .Rdata from canvas and load the YaleFace dataset into R. This is a matrix with 165 images and 1024 columns corresponding to the 11 images taken for 15 different pe0ple. Each row is an image containing 1024 pixels. To recreate the image, we need to create a 32x32 matrix based on this 1024 pixels. Note that since this is a grey scale image, it has only two dimensions rather than 3 dimensions as in Question 3. Plot the images for 15 individuals that have sad expression using the following com- mand. writeJPEGO Plot the images for 15 individuals that have happy expression. Generate and plot the mean image corresponding to sad images and happy images. To do this, we basically calculate the mean of the 15 matrices for sad expression and happy expression, respectively. Plot the mean images for sad and happy expressions. Next, plot the mean image corresponding to all images of the collection. Can you tell the difference? (c) Now, load the training data settrainface.RData. Perform PCA on this train data set on the pixels. The rows of this matrix is images and the columns are the pixels