# This should print a validation error of 0.19
if question == '3.2':
dataset = utils.load_dataset('animals')
X = dataset['X'].astype(float)
animals = dataset['animals']
n,d = X.shape
# standardize columns
X = utils.standardize_cols(X)
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':
# Plot the matrix
plt.imshow(X)
utils.savefig('unsatisfying_visualization_1.png')
## Randomly plot two features, and label all points
x = X[:, np.random.choice(d, 2)]
fig, ax = plt.subplots()
ax.scatter(x[:, 0], x[:, 1])
for i in range(n):
ax.annotate(animals[i], (x[i, 0], x[i, 1]))
utils.savefig('unsatisfying_visualization_2.png')
# 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