def testComponentSeparation(self):
A = generate_covsig([[10,5,2],[5,10,2],[2,2,10]], 500)
B = generate_covsig([[10,2,2],[2,10,5],[2,5,10]], 500)
X = np.dstack([A,B])
W, V = csp(X,[1,2])
C1a = np.cov(X[:,:,0].dot(W).T)
C2a = np.cov(X[:,:,1].dot(W).T)
Y = np.dstack([B,A])
W, V = csp(Y,[1,2])
C1b = np.cov(Y[:,:,0].dot(W).T)
C2b = np.cov(Y[:,:,1].dot(W).T)
# check symmetric case
self.assertTrue(np.allclose(C1a.diagonal(), C2a.diagonal()[::-1]))
self.assertTrue(np.allclose(C1b.diagonal(), C2b.diagonal()[::-1]))
# swapping class labels (or in this case, trials) should not change the result
self.assertTrue(np.allclose(C1a, C1b))
self.assertTrue(np.allclose(C2a, C2b))
# variance of first component should be greatest for class 1
self.assertTrue(C1a[0,0] > C2a[0,0])
# variance of last component should be greatest for class 1
self.assertTrue(C1a[2,2] < C2a[2,2])
# variance of central component should be equal for both classes
self.assertTrue(np.allclose(C1a[1,1], C2a[1,1]))
def testComponentSeparation(self):
A = generate_covsig([[10, 5, 2], [5, 10, 2], [2, 2, 10]], 500)
B = generate_covsig([[10, 2, 2], [2, 10, 5], [2, 5, 10]], 500)
X = np.concatenate([A[np.newaxis], B[np.newaxis]], axis=0)
W, V = csp(X, [1, 2])
C1a = np.cov(np.dot(W.T, X[0, :, :]))
C2a = np.cov(np.dot(W.T, X[1, :, :]))
Y = np.concatenate([B[np.newaxis], A[np.newaxis]], axis=0)
W, V = csp(Y, [1, 2])
C1b = np.cov(np.dot(W.T, Y[0, :, :]))
C2b = np.cov(np.dot(W.T, Y[1, :, :]))
# check symmetric case
assert_allclose(C1a.diagonal(), C2a.diagonal()[::-1])
assert_allclose(C1b.diagonal(), C2b.diagonal()[::-1])
# swapping class labels (or in this case, trials) should not change the result
assert_allclose(C1a, C1b, rtol=1e-9, atol=1e-9)
assert_allclose(C2a, C2b, rtol=1e-9, atol=1e-9)
# variance of first component should be greatest for class 1
self.assertGreater(C1a[0, 0], C2a[0, 0])
# variance of last component should be greatest for class 1
self.assertLess(C1a[2, 2], C2a[2, 2])
# variance of central component should be equal for both classes
assert_allclose(C1a[1, 1], C2a[1, 1])
def testComponentSeparation(self):
A = generate_covsig([[10, 5, 2], [5, 10, 2], [2, 2, 10]], 500)
B = generate_covsig([[10, 2, 2], [2, 10, 5], [2, 5, 10]], 500)
X = np.concatenate([A[np.newaxis], B[np.newaxis]], axis=0)
W, V = csp(X, [1, 2])
C1a = np.cov(np.dot(W.T, X[0, :, :]))
C2a = np.cov(np.dot(W.T, X[1, :, :]))
Y = np.concatenate([B[np.newaxis], A[np.newaxis]], axis=0)
W, V = csp(Y, [1, 2])
C1b = np.cov(np.dot(W.T, Y[0, :, :]))
C2b = np.cov(np.dot(W.T, Y[1, :, :]))
# check symmetric case
assert_allclose(C1a.diagonal(), C2a.diagonal()[::-1])
assert_allclose(C1b.diagonal(), C2b.diagonal()[::-1])
# swapping class labels (or in this case, trials) should not change the result
assert_allclose(C1a, C1b, rtol=1e-9, atol=1e-9)
assert_allclose(C2a, C2b, rtol=1e-9, atol=1e-9)
# variance of first component should be greatest for class 1
self.assertGreater(C1a[0, 0], C2a[0, 0])
# variance of last component should be greatest for class 1
self.assertLess(C1a[2, 2], C2a[2, 2])
# variance of central component should be equal for both classes
assert_allclose(C1a[1, 1], C2a[1, 1])
def testSorting(self):
"""components should be sorted by decreasing variance
"""
x = generate_covsig(np.diag([1, 9, 2, 6, 3, 8, 4, 5, 7]), 500)
w, v = pca(x, reducedim=5)
c = np.cov(np.dot(w.T, x))
self.assertTrue(np.allclose(c, np.diag([9, 8, 7, 6, 5]), rtol=1e-1, atol=1e-2))
def testDecorrelation(self):
"""components should be decorrelated after PCA
"""
x = generate_covsig([[3, 2, 1], [2, 3, 2], [1, 2, 3]], 500)
w, v = pca(x)
c = np.cov(np.dot(w.T, x))
c -= np.diag(c.diagonal())
self.assertTrue(np.allclose(c, np.zeros((3, 3)), rtol=1e-2, atol=1e-3))
def testIdentity(self):
"""identity covariance in -> identity covariance out
test for up to 50 dimensions
"""
for i in range(1, 50):
x = generate_covsig(np.eye(i), 500)
w, v = pca(x)
c = np.cov(np.dot(w.T, x))
self.assertTrue(np.allclose(c, np.eye(i)))
def testSorting(self):
"""components should be sorted by decreasing variance
"""
x = generate_covsig(np.diag([1, 9, 2, 6, 3, 8, 4, 5, 7]), 500)
w, v = pca(x, sort_components=True)
c = np.cov(x.dot(w).T)
self.assertTrue(np.allclose(c, np.diag([9, 8, 7, 6, 5, 4, 3, 2, 1]), rtol=1e-1, atol=1e-2))
w, v = pca(x, sort_components=True)
c = np.cov(x.dot(w).T)
self.assertTrue(np.allclose(c, np.diag([9, 8, 7, 6, 5, 4, 3, 2, 1]), rtol=1e-1, atol=1e-2))
def testSorting(self):
"""components should be sorted by decreasing variance
"""
x = generate_covsig(np.diag([1, 9, 2, 6, 3, 8, 4, 5, 7]), 500)
w, v = pca(x, sort_components=True)
c = np.cov(x.dot(w).T)
self.assertTrue(np.allclose(c, np.diag([9, 8, 7, 6, 5, 4, 3, 2, 1]), rtol=1e-1, atol=1e-2))
w, v = pca(x, sort_components=True)
c = np.cov(x.dot(w).T)
self.assertTrue(np.allclose(c, np.diag([9, 8, 7, 6, 5, 4, 3, 2, 1]), rtol=1e-1, atol=1e-2))
