def verify_kernel_matrix():
n1 = 10
n2 = 10
n = n1+n2
d = 5
degree = 3
X = randn(n,d)
Phi = poly.phi(X, degree)
(K, Kuc, Kc) = kernel_matrix(X, polyk(degree), n1, n2)
P1 = Phi[0:n1,:]
P2 = Phi[n1:n,:]
mu1 = mat.sum(P1,0) / n1
mu2 = mat.sum(P2,0) / n2
P1c = P1 - mat.tile(mu1, (n1,1))
P2c = P2 - mat.tile(mu2, (n2,1))
Pc = bmat('P1c; P2c')
KP = mat.zeros((n,n))
for i in xrange(n):
for j in xrange(i+1):
KP[i,j] = dotp(Phi[i,:], Phi[j,:])
KP[j,i] = KP[i,j]
KucP = mat.zeros((n,n))
for i in xrange(n):
for j in xrange(n):
KucP[i,j] = dotp(Phi[i,:], Pc[j,:])
KcP = mat.zeros((n,n))
for i in xrange(n):
for j in xrange(n):
KcP[i,j] = dotp(Pc[i,:], Pc[j,:])
#KcP[j,i] = KcP[i,j]
#debug()
print "Div1: " + str(sum(abs(K-KP)))
print "Div2: " + str(sum(abs(Kuc-KucP)))
print "Div3: " + str(sum(abs(Kc-KcP)))
def test_suite_1():
n1 = 100
n2 = 100
n = n1+n2
d = 5
eta = .1
degree = 3
iterations = 1
results = mat.zeros((8,5))
times = mat.zeros((1,5))
sigma = 2
# 1st col is non-kernelized
# 2nd col is poly-kernel
for itr in xrange(iterations):
X = mat.randn(n1,d)
Phi_X = poly.phi(X, degree)
D0 = X + mat.rand(n2,d) / 1000
# Verify identity K(X,X) = 1
D1 = mat.randn(n2,d)
# How does kernel perform iid data
D2 = mat.rand(n2,d)
# Uniform rather than normal distribution
D3 = mat.randn(n2,d) * 2 + 2
# Linear transformation
D4 = mat.power(mat.randn(n2,d) + 1 ,3)
#Non-linear transformation
D5 = mat.power(X+1,3)
#non-linear transformation of the D0 dataset;
D6 = mat.rand(n2,d)/100 + mat.eye(n2,d)
#Totally different data - should have low similarity
D7 = mat.rand(n2,d)/100 + mat.eye(n2,d)*5
# Scaled version of D7
Data = [D0, D1, D2, D3, D4, D5, D6, D7]
for idx in xrange(8):
D = Data[idx]
start = time.time()
results[idx, 0] += nk_bhatta(X, D, 0)
nk = time.time()
emp = time.time()
results[idx, 1] += Bhattacharrya(X,D,gaussk(sigma),eta,5)
e5 = time.time()
results[idx, 2] += Bhattacharrya(X,D,gaussk(sigma),eta,15)
e15 = time.time()
results[idx, 3] += Bhattacharrya(X,D,gaussk(sigma),eta,25)
e25 = time.time()
nktime = nk-start
emptime = emp-nk
e5time = e5-emp
e15time = e15-e5
e25time = e25-e15
print "nk: {:.1f}, emp: {:.1f}, e5: {:.1f}, e15: {:.1f}, e25: {:.1f}".format(nktime, emptime, e5time, e15time, e25time)
times[0,0]+= nktime
times[0,4]+= emptime
times[0,1]+= e5time
times[0,2]+= e15time
times[0,3]+= e25time