X = load_dataset('highway.pkl')['X'].astype(float) / 255
#print(X[0].reshape(64,64).T)
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"
#threshold = 0.07
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)')
ax[0, 2].imshow(
(np.abs(X[i] - Xhat_pca[i]) < threshold).reshape(h, w).T,
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) # TODO: implement this class
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)')
ax[0,2].imshow((np.abs(X[i] - Xhat_pca[i])<threshold).reshape(h,w).T, cmap='gray')
io_args = parser.parse_args()
question = io_args.question
if question == '2.1':
X = utils.load_dataset('highway')['X'].astype(float) / 255
n, d = X.shape
print(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,
elif question == '4.1':
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, eps=0.0001)
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)')
ax[0, 2].imshow(
(np.abs(X[i] - Xhat_pca[i]) < threshold).reshape(h, w).T,
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 = AlternativePCA(k=k)
model.fit(X)
Z = model.compress(X)
Xhat_pca = model.expand(Z)
model_r = RobustPCA(k=k)
model_r.fit(X)
Z = model_r.compress(X)
Xhat_robust = model_r.expand(Z)
for i in range(10):
plt.subplot(2, 3, 1)
plt.title('Original')
plt.imshow(X[i].reshape(h, w).T, cmap='gray')
plt.subplot(2, 3, 2)
plt.title('PCA Reconst.') # Reconstruction
plt.imshow(Xhat_pca[i].reshape(h, w).T, cmap='gray')
plt.subplot(2, 3, 3)
plt.title('PCA Thresh. Diff.') # Thresholded Difference
plt.imshow(1.0 *
(abs(X[i] - Xhat_pca[i]) < threshold).reshape(h, w).T,