def test_cca():
"""Test CCA."""
# Compare results with Matlab
# x = np.random.randn(1000, 11)
# y = np.random.randn(1000, 9)
# x = demean(x).squeeze()
# y = demean(y).squeeze()
mat = loadmat('./tests/data/ccadata.mat')
x = mat['x']
y = mat['y']
A2 = mat['A2']
B2 = mat['B2']
A1, B1, R = nt_cca(x, y) # if mean(A1(:).*A2(:))<0; A2=-A2; end
X1 = np.dot(x, A1)
Y1 = np.dot(y, B1)
C1 = tscov(np.hstack((X1, Y1)))[0]
# Sklearn CCA
cca = CCA(n_components=9, scale=False, max_iter=1e6)
X2, Y2 = cca.fit_transform(x, y)
# C2 = tscov(np.hstack((X2, Y2)).T)[0]
# import matplotlib.pyplot as plt
# f, (ax1, ax2) = plt.subplots(2, 1)
# ax1.imshow(C1)
# ax2.imshow(C2)
# plt.show()
# assert_almost_equal(C1, C2, decimal=4)
# Compare with matlab
X2 = np.dot(x, A2)
Y2 = np.dot(y, B2)
C2 = tscov(np.hstack((X2, Y2)))[0]
assert_almost_equal(C1, C2)
def test_canoncorr():
"""Compare with Matlab's canoncorr."""
x = np.array([[16, 2, 3, 13], [5, 11, 10, 8], [9, 7, 6, 12],
[4, 14, 15, 1]])
y = np.array([[1, 5, 9], [2, 6, 10], [3, 7, 11], [4, 8, 12]])
[A, B, R] = nt_cca(x, y)
canoncorr = np.array([[-0.5000, -0.6708], [-0.5000, 0.2236],
[-0.5000, -0.2236], [-0.5000, 0.6708]])
# close enough
assert_almost_equal(np.cov(np.dot(x, A).T), np.cov(canoncorr.T), decimal=4)
def test_cca_lags():
"""Test multiple lags."""
mat = loadmat('./tests/data/ccadata.mat')
x = mat['x']
y = mat['y']
y[:, :3] = x[:, :3]
lags = np.arange(-10, 11, 1)
A1, B1, R1 = nt_cca(x, y, lags)
# import matplotlib.pyplot as plt
# f, ax1 = plt.subplots(1, 1)
# ax1.plot(lags, R1.T)
# plt.show()
for c in np.arange(3): # test first 3 components have peaks at 0
assert_equal(lags[np.argmax(R1[c, :])], 0)
def test_cca2():
"""Simulate correlations."""
# import matplotlib.pyplot as plt
x = np.random.randn(10000, 20)
y = np.random.randn(10000, 8)
y[:, :2] = x[:, :2]
# perfectly correlated
y[:, 2:4] = x[:, 2:4] + np.random.randn(10000, 2)
# 1/2 correlated
y[:, 4:6] = x[:, 4:6] + np.random.randn(10000, 2) * 3
# 1/4 correlated
y[:, 6:8] = np.random.randn(10000, 2)
# uncorrelated
[A, B, R] = nt_cca(x, y)
assert_almost_equal(np.dot(np.dot(x, A).T, np.dot(x, A)), np.eye(8))
assert_almost_equal(np.dot(np.dot(y, B).T, np.dot(y, B)), np.eye(8))
def test_correlated():
"""Test x & y perfectly correlated."""
x = np.random.randn(1000, 10)
y = np.random.randn(1000, 10)
y = x[:, np.random.permutation(10)] # +0.000001*y;
[A1, B1, R1] = nt_cca(x, y)
C = tscov(np.hstack((np.dot(x, A1), np.dot(y, B1))))[0]
# import matplotlib.pyplot as plt
# f, ax1 = plt.subplots(1, 1)
# im = ax1.imshow(C)
# plt.colorbar(im)
# plt.show()
for i in np.arange(C.shape[0]):
assert_almost_equal(C[i, i], C[i, (i + 10) % 10], decimal=4)
assert_almost_equal(C[i, i], C[i, (i - 10) % 10], decimal=4)