Use python

Problem 1: (PCA on Olivetti dataset) Load the Olivetti face images dataset from sklearn. (sklearn.datasets.fetch_olivetti_faces). Vectorize the images and apply PCA. Plot the eigenvalues. Display the mean image and first 20 principal components. Represent a face image using different numbers of principal components (say, 5, 10,40, 200) and compare the representations with the original image. Use scatter plot to represent all images on a 3D space using the first 3 principal components. Problem 2: (PCA exercise) We have the following the training samples: {(2,1), (2,28.(3,2), (3,3), (4,1),(6,57. (7,4. (7,5). (8,5), (8,6). (7,71). (a) Use PCA to find the principal components (eigenvectors) and the eigenvalues. (b) Project all the samples on to the first principal component, and calculate the variance. (c) Project all the samples on to the second principal component, and calculate the variance