def test_load(self): x = load_and_center_dataset(mnist_path) # The dataset needs to have the correct shape self.assertEqual(np.shape(x), (2000, 784)) # The dataset should not be constant-valued self.assertNotAlmostEqual(np.max(x) - np.min(x), 0)
def test_values(self): x = load_and_center_dataset(mnist_path) S = get_covariance(x) # S should be symmetric self.assertTrue(np.all(np.isclose(S, S.T))) # S should have non-negative values on the diagonal self.assertTrue(np.min(np.diagonal(S)) >= 0)
def test_larger(self):
x = load_and_center_dataset(mnist_path)
S = get_covariance(x)
Lambda, U = get_eig(S, 20)
self.check_eigen(S, Lambda, U, 20)
Lambda, U = get_eig(S, 784)
self.check_eigen(S, Lambda, U, 784)
def test_shape(self): x = load_and_center_dataset(mnist_path) S = get_covariance(x) _, U = get_eig(S, 2) # This is the image of the "9" in the spec projected = project_image(x[3], U) self.assertEqual(np.shape(projected), (784,)) self.assertAlmostEqual(np.min(projected), -113.79455198736488) self.assertAlmostEqual(np.max(projected), 120.0658469887994)
def test_larger(self):
x = load_and_center_dataset(mnist_path)
S = get_covariance(x)
# A value of perc=0.011 should yield 20 eigenvectors
Lambda, U = get_eig_perc(S, 0.011)
self.check_eigen(S, Lambda, U, 20)
# This will select all eigenvalues/eigenvectors
Lambda, U = get_eig_perc(S, -1)
self.check_eigen(S, Lambda, U, 784)
def test_small(self): x = load_and_center_dataset(mnist_path) S = get_covariance(x) Lambda, U = get_eig_perc(S, .07) self.assertEqual(np.shape(Lambda), (2, 2)) self.assertTrue(np.all(np.isclose( Lambda, [[350880.76329673, 0], [0, 245632.27295307]]))) # The eigenvectors should be the columns self.assertEqual(np.shape(U), (784, 2)) self.assertTrue(np.all(np.isclose(S @ U, U @ Lambda)))
def test_large(self): x = load_and_center_dataset(mnist_path) S = get_covariance(x) Lambda, U = get_eig(S, 784) self.assertEqual(np.shape(Lambda), (784, 784)) # Check that Lambda is diagonal self.assertEqual(np.count_nonzero( Lambda - np.diag(np.diagonal(Lambda))), 0) # Check that Lambda is sorted in decreasing order self.assertTrue(np.all(np.equal(np.diagonal(Lambda), sorted(np.diagonal(Lambda), reverse=True)))) # The eigenvectors should be the columns self.assertEqual(np.shape(U), (784, 784)) self.assertTrue(np.all(np.isclose(S @ U, U @ Lambda)))
def test_shape(self): x = load_and_center_dataset(mnist_path) S = get_covariance(x) # S should be square and have side length d self.assertEqual(np.shape(S), (784, 784))
def test_center(self): x = load_and_center_dataset(mnist_path) # Each coordinate of our dataset should average to 0 for i in range(np.shape(x)[1]): self.assertAlmostEqual(np.sum(x[:, i]), 0)
# generates and displays the relevant plot
fig, axs = plt.subplots(ncols=len(projs) + 1)
a1 = axs[0].imshow(orig.reshape((28, 28)), aspect='equal', cmap='gray')
axs[0].set_title("Original")
for i in range(len(projs)):
a = axs[i + 1].imshow(projs[i].reshape((28, 28)),
aspect='equal',
cmap='gray')
axs[i + 1].set_title(titles[i])
plt.show()
if __name__ == '__main__':
data = pca.load_and_center_dataset("mnist.npy")
cov = pca.get_covariance(data)
_, eig10 = pca.get_eig(cov, 10)
_, eig25 = pca.get_eig(cov, 25)
_, eig100 = pca.get_eig(cov, 100)
_, eig250 = pca.get_eig(cov, 250)
_, eig500 = pca.get_eig(cov, 500)
image = data[782]
projs = (pca.project_image(image,
eig500), pca.project_image(image, eig250),
pca.project_image(image, eig100), pca.project_image(image, eig25),
pca.project_image(image, eig10))
titles = ("n_components=500", "n_components=250", "n_components=100",
"n_components=25", "n_components=10")
