def test_alignment_value_with_normalization(self):
"""Test value of kernel target alignment with class label rescaling."""
X = [0.1, 0.4, 0.0]
Y = [1, -1, 1]
alignment = kern.target_alignment(
X,
Y,
lambda x1, x2: _mock_kernel(x1, x2, []),
rescale_class_labels=True)
alignment_assume = kern.target_alignment(
X,
Y,
lambda x1, x2: _mock_kernel(x1, x2, []),
assume_normalized_kernel=True,
rescale_class_labels=True,
)
K1 = np.array([
[
1,
0.2,
0.2,
],
[0.2, 1, 0.2],
[0.2, 0.2, 1],
])
_Y = np.array([1 / 2, -1, 1 / 2])
K2 = np.outer(_Y, _Y)
expected_alignment = np.trace(np.dot(K1, K2)) / math.sqrt(
np.trace(np.dot(K1, K1)) * np.trace(np.dot(K2, K2)))
assert alignment == expected_alignment
assert alignment == alignment_assume
def test_alignment_value_three(self):
"""Test value of kernel target alignment without class label rescaling
on more data (3/3)."""
X = [0.1, 0.4, 0.0]
Y = [1, -1, 1]
alignment = kern.target_alignment(
X,
Y,
lambda x1, x2: _mock_kernel(x1, x2, []),
rescale_class_labels=False)
alignment_assume = kern.target_alignment(
X,
Y,
lambda x1, x2: _mock_kernel(x1, x2, []),
assume_normalized_kernel=True,
rescale_class_labels=False,
)
K1 = np.array([
[
1,
0.2,
0.2,
],
[0.2, 1, 0.2],
[0.2, 0.2, 1],
])
K2 = np.array([[1, -1, 1], [-1, 1, -1], [1, -1, 1]])
expected_alignment = np.trace(np.dot(K1, K2)) / math.sqrt(
np.trace(np.dot(K1, K1)) * np.trace(np.dot(K2, K2)))
assert alignment == expected_alignment
assert alignment == alignment_assume
def test_correct_calls(self):
"""Test number and order of calls of the kernel function when computing the
kernel target alignment, including computation of the diagonal kernel matrix entries."""
X = [0.1, 0.4]
Y = [1, -1]
hist = []
kern.target_alignment(X, Y, lambda x1, x2: _mock_kernel(x1, x2, hist))
assert hist == [(0.1, 0.1), (0.1, 0.4), (0.4, 0.4)]
def test_correct_calls_normalized(self):
"""Test number and order of calls of the kernel function when computing the
kernel target alignment, assuming normalized diagonal kernel matrix entries."""
X = [0.1, 0.4]
Y = [1, -1]
hist = []
kern.target_alignment(
X, Y, lambda x1, x2: _mock_kernel(x1, x2, hist), assume_normalized_kernel=True
)
assert hist == [(0.1, 0.4)]
def test_alignment_value_other_labels(self):
"""Test value of kernel target alignment without class label rescaling (2/3)."""
X = [0.1, 0.4]
Y = [1, 1]
alignment = kern.target_alignment(
X, Y, lambda x1, x2: _mock_kernel(x1, x2, []), rescale_class_labels=False
)
alignment_assume = kern.target_alignment(
X,
Y,
lambda x1, x2: _mock_kernel(x1, x2, []),
assume_normalized_kernel=True,
rescale_class_labels=False,
)
assert alignment == 2.4 / (2 * math.sqrt(2 + 2 * 0.2 ** 2))
assert alignment == alignment_assume
