model = PCA(k=2)
model.fit(X)
Z = model.compress(X)
fig, ax = plt.subplots()
ax.scatter(Z[:,0], Z[:,1])
plt.ylabel('z2')
plt.xlabel('z1')
plt.title('PCA')
for i in range(n):
ax.annotate(animals[i], (Z[i,0], Z[i,1]))
utils.savefig('q3_2_PCA_animals.png')
# code below isn't required.
variance_explained = 1 - norm(model.expand(Z) - X, 'fro')**2 / norm(X, 'fro')**2
print('Variance explained {}'.format(variance_explained))
if question == '4.1':
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 = AlternativePCA(k=k)
model.fit(X)
# Create PCA model, fit and compress our X matrix
model = PCA(k=5)
model.fit(X)
Z = model.compress(X) # Z = (50, k)
# z = Z[:,np.random.choice(Z.shape[1], 2)]
fig_1, ax_1 = plt.subplots()
ax_1.scatter(Z[:, 0], Z[:, 1])
for i in range(Z.shape[0]):
ax_1.annotate(animals[i], (Z[i, 0], Z[i, 1]))
utils.savefig('satisfying_visualization.png')
# Print % variance
Z_new = model.expand(Z)
print(norm(Z_new - X)**2 / norm(X)**2)
if question == '4':
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)