utils.savefig('q2_2_PCA_animals.png')
elif question == '3.1':
X = load_dataset('highway.pkl')['X'].astype(float) / 255
n, d = X.shape
print(n, d)
h, w = 64, 64 # height and width of each image
k = 5 # number of PCs
threshold = 0.1 # threshold for being considered "foreground"
model = AlternativePCA(k=k)
model.fit(X)
Z = model.compress(X)
Xhat_pca = model.expand(Z)
model = RobustPCA(k=k)
model.fit(X)
Z = model.compress(X)
Xhat_robust = model.expand(Z)
fig, ax = plt.subplots(2, 3)
for i in range(10):
ax[0, 0].set_title('$X$')
ax[0, 0].imshow(X[i].reshape(h, w).T, cmap='gray')
ax[0, 1].set_title('$\hat{X}$ (L2)')
ax[0, 1].imshow(Xhat_pca[i].reshape(h, w).T, cmap='gray')
ax[0, 2].set_title('$|x_i-\hat{x_i}|$>threshold (L2)')
if question == '2.1':
X = utils.load_dataset('highway')['X'].astype(float) / 255
n, d = X.shape
h, w = 64, 64 # height and width of each image
# the two variables below are parameters for the foreground/background extraction method
# you should just leave these two as default.
k = 5 # number of PCs
threshold = 0.04 # a threshold for separating foreground from background
model = RobustPCA(k=k)
model.fit(X)
Z = model.compress(X)
Xhat = model.expand(Z)
# save 10 frames for illustration purposes
for i in range(10):
plt.subplot(1, 3, 1)
plt.title('Original')
plt.imshow(X[i].reshape(h, w).T, cmap='gray')
plt.subplot(1, 3, 2)
plt.title('Reconstructed')
plt.imshow(Xhat[i].reshape(h, w).T, cmap='gray')
plt.subplot(1, 3, 3)
plt.title('Thresholded Difference')
plt.imshow(1.0 * (abs(X[i] - Xhat[i]) < threshold).reshape(h, w).T,
cmap='gray')
utils.savefig('q2.1_highway_{:03d}.pdf'.format(i))
