def testCallOther(self):
Kp = poly_kernel(self.X, self.Y, degree=2)
Ki = Kinterface(data=self.X,
kernel=poly_kernel,
kernel_args={"degree": 2},
row_normalize=False)
Kr = Ki(self.X, self.Y)
self.assertAlmostEquals(np.linalg.norm(Kp - Kr), 0, delta=3)
def testCall(self):
Kp = poly_kernel(self.X, self.X, degree=2)
Ki = Kinterface(data=self.X,
kernel=poly_kernel,
kernel_args={"degree": 2})
self.assertAlmostEquals(np.linalg.norm(Ki(self.X, self.X) - Kp),
0,
delta=3)
def testKernelSum(self):
Ki = Kinterface(data=self.X,
kernel=kernel_sum,
kernel_args={
"kernels": [poly_kernel, poly_kernel, poly_kernel],
"kernels_args": [{
"degree": 2
}, {
"degree": 3
}, {
"degree": 4
}]
},
row_normalize=False)
Kc = poly_kernel(self.X, self.X, degree=2) + \
poly_kernel(self.X, self.X, degree=3) + \
poly_kernel(self.X, self.X, degree=4)
self.assertAlmostEqual(np.linalg.norm(Ki[:, :] - Kc), 0, places=3)
def testRowNorm(self):
Kp = poly_kernel(self.X, self.X, degree=2)
Kr = kernel_row_normalize(Kp)
Ki = Kinterface(data=self.X,
kernel=poly_kernel,
kernel_args={"degree": 2},
row_normalize=True)
self.assertAlmostEquals(np.linalg.norm(Ki.diag().ravel() -
np.ones((self.n, ))),
0,
delta=3)
self.assertAlmostEquals(np.linalg.norm(Ki(self.X, self.X) - Kr),
0,
delta=3)
self.assertAlmostEquals(np.linalg.norm(Ki[:, :] - Kr), 0, delta=3)
def testDeterministicDecrease(self):
"""
Test expected reconstruction properties of the Nystrom method.
"""
for d in range(1, 6):
K = poly_kernel(self.X, self.X, degree=d)
model = Nystrom(rank=self.n, random_state=42)
model.fit(K)
errors = np.zeros((self.n, ))
for i in range(self.n):
Ki = model.G[:, :i + 1].dot(model.G[:, :i + 1].T)
errors[i] = np.linalg.norm(K - Ki)
self.assertTrue(np.all(errors[:-1] > errors[1:]))
self.assertAlmostEqual(errors[-1], 0, delta=3)
def testPoly(self):
"""
Test expected reconstruction properties of the ICD.
"""
for d in range(1, 6):
K = poly_kernel(self.X, self.X, degree=d)
model = ICD(rank=self.n)
model.fit(K)
errors = np.zeros((self.n, ))
for i in range(self.n):
Ki = model.G[:, :i + 1].dot(model.G[:, :i + 1].T)
errors[i] = np.linalg.norm(K - Ki)
self.assertTrue(np.all(errors[:-1] > errors[1:]))
self.assertAlmostEqual(errors[-1], 0, delta=3)
def testPoly(self):
"""
Test expected reconstruction properties of the ICD.
"""
delta = 5
rank = self.n
for d in range(1, 6):
K = poly_kernel(self.X, self.X, degree=d)
y = np.random.rand(self.n, 1)
model = CSI(rank=rank, delta=delta, kappa=0.1)
model.fit(K, y)
errors = np.zeros((rank, ))
for i in range(rank):
Ki = model.G[:, :i + 1].dot(model.G[:, :i + 1].T)
errors[i] = np.linalg.norm(K - Ki)
self.assertAlmostEqual(errors[-1], 0, places=3)
self.assertTrue(np.all(errors[:-1] >= errors[1:]))
def testLeverage(self):
"""
Assert the leverage scores performs a better low rank approximation with incraesing number of
columns.
:return:
"""
K = poly_kernel(self.X, self.X, degree=2)
rank_range = [10, 20, 30, 50]
repeats = 10
errors_lev = np.zeros((
repeats,
len(rank_range),
))
errors_rand = np.zeros((
repeats,
len(rank_range),
))
for j in xrange(repeats):
self.X = np.random.rand(self.n, self.p)
for i, rank in enumerate(rank_range):
model_lev = Nystrom(rank=rank, random_state=j, lbd=1)
model_lev.fit(K)
model_rand = Nystrom(rank=rank, random_state=j, lbd=0)
model_rand.fit(K)
Li = model_lev.G.dot(model_lev.G.T)
Ri = model_rand.G.dot(model_rand.G.T)
errors_lev[j, i] = np.linalg.norm(K - Li)
errors_rand[j, i] = np.linalg.norm(K - Ri)
self.assertTrue(np.all(errors_lev[j, :-1] > errors_lev[j, 1:]))
lev_win = np.sum(errors_lev < errors_rand)
rand_win = np.sum(errors_lev > errors_rand)
print("Leverage win: %d, random win: %d" % (lev_win, rand_win))
self.assertTrue(lev_win > rand_win)