def compute_eigen_faces(X, k=20):
'''
Compute top k eigen faces of the olivetti face image dataset using PCA.
Each eigen face corresponds to an eigen vector in the PCA on matrix X.
For example, suppose the top k eigen vectors in the PCA on matrix X are e1, e2, e3 (suppose k=3),
Then e1 is a vector of length 4096, if we reshape e1, we can get the first eigen face image is a matrix of shape 64x64.
Similar, reshaping e2, we get the second eigen face image.
Input:
X: the feature matrix, a float numpy matrix of shape (400, 4096). Here 400 is the number of images, 4096 is the number of features.
k: the number of eigen face to keep.
Output:
P_images: the eigen faces, a python list of length k.
The i-th element in the list is the i-th eigen face image, which is a numpy float matrix of shape 64 by 64.
Xp: the feature matrix with reduced dimensions, a numpy float matrix of shape n by k. (400 by k)
Note: this function may take 1-5 minutes and 1-2GB of memory to run.
'''
#########################################
## INSERT YOUR CODE HERE
Xp, p = p2.PCA(X, k)
P_images = list()
for i in range(k):
P_images.append(vector_to_image(p[:, i]))
#########################################
return P_images, Xp
'''
def compute_eigen_faces(X, k=20):
'''
Compute top k eigen faces of the olivetti face image dataset using PCA.
Input:
X: the feature matrix, a float numpy matrix of shape (400, 4096). Here 400 is the number of images, 4096 is the number of features.
k: the number of eigen face to keep.
Output:
P_images: the eigen faces, a python list of length k.
Each element in the list is an eigen face image, which is a numpy float matrix of shape 64 by 64.
Xp: the feature matrix with reduced dimensions, a numpy float matrix of shape n by k. (400 by k)
Note: this function may take 1-5 minutes to run, and 1-2GB of memory while running.
'''
#########################################
## INSERT YOUR CODE HERE
Xp, P_images_before_reshape = p2.PCA(X, k)
P_images_before_reshape = P_images_before_reshape.T
P_images = []
for row in range(k):
P_images.append(reshape_to_image(P_images_before_reshape[row, :]))
#########################################
return P_images, Xp