def centering(): #test
workdir = os.path.join("tkernel_new", "tkernel_new", "rodrech")
config = read_config()
freader = file_reader(config["dt"], workdir)
testfn = "data.bin"
trainfn = "train.bin"
tkernfn = "tkern.bin"
Kxfn = "Kx.bin"
train = freader(trainfn, config["dim"])
nTrain = train.shape[0]
test = freader(testfn, config["dim"])
nTest = test.shape[0]
sigma = config["sigma"]
tKernEstimed = np.array([[np.exp(-0.5 * np.dot(trEl-testEl, trEl-testEl)/sigma**2) for trEl in train] for testEl in test])
trTotalExt = 7479 # 3834
Kx = freader(Kxfn, trTotalExt)
tKernEstimedCent = mlpy.kernel_center(tKernEstimed, Kx.T)
gpuTKernCent = freader("t_kern_centr.bin", nTrain)
assert np.allclose(tKernEstimedCent, gpuTKernCent, atol=1e-5)
def estim_kbasis(self, trData):
self.trData = trData
Kx = np.mat([[self.kernel_func(np.array(xi), np.array(xj)) for xj in self.trData] for xi in self.trData])
Kx = np.mat(mlpy.kernel_center(Kx, Kx))
vals, vecs = np.linalg.eig(Kx)
norm_mat = np.mat(np.diag([1.0/np.sqrt(vals[i]) for i in range(len(vals))]))
self.vecs = vecs * norm_mat
print 'mult:', vals[0] * self.vecs[:, 0].T * self.vecs[:, 0]
def draw_data(data, clabs, kernel_func, testData):
fig = plt.figure(1) # plot
print data.shape
ax1 = plt.subplot(121)
plot1 = plt.scatter(data[:, 0], data[:, 1], c=clabs)
plot1_5 = plt.scatter(testData[:, 0], testData[:, 1])
Kx = np.mat([[kernel_func(xi, xj) for xj in data] for xi in data])
KxCopy = Kx
Kx = np.mat(mlpy.kernel_center(Kx, Kx))
print "KxCopy == Kx", np.allclose(KxCopy, Kx)
vals, vecs = np.linalg.eig(Kx)
print "mult before normalization", vals[0]*vecs[:, 0].T*vecs[:, 0]
norm_mat = np.mat(np.diag([1.0/np.sqrt(vals[i]) for i in range(len(vals))]))
vecs = vecs * norm_mat
print 'mult:', vals[0] * vecs[:, 0].T * vecs[:, 0]
# gK = mlpy.kernel_gaussian(data, data, sigma=2)
# gaussian_pca = mlpy.KPCA(mlpy.KernelGaussian(2.0))
# gaussian_pca.learn(data)
data_k_trans = np.real(Kx.T * vecs[:, :2])
data_k_trans = np.array(data_k_trans)
ax2 = plt.subplot(122)
plot2 = plt.scatter(data_k_trans[:, 0], data_k_trans[:, 1], c=clabs)
Kt = np.mat([[kernel_func(xi, xj) for xj in data] for xi in testData])
Kt = np.mat(mlpy.kernel_center(Kt, KxCopy))
kTransTestData = np.real(Kt * vecs[:, :2])
kTransTestData = np.array(kTransTestData)
plot2_5 = plt.scatter(kTransTestData[:, 0], kTransTestData[:, 1])
plt.show()
def estim_kbasis(self, trData, labels):
self.trData = trData
Y = one_of_c(labels)
Kx = np.mat([[self.kernel_func(np.array(xi), np.array(xj)) for xj in self.trData] for xi in self.trData])
Kx = np.mat(mlpy.kernel_center(Kx, Kx))
matForEig = np.mat(np.vstack([np.hstack([np.zeros(Kx.shape), Kx * Y]), np.hstack([Y.T * Kx, np.zeros((Y.shape[1], Y.shape[1]))])]))
# plt.imshow(Kx, cmap = cm.Greys_r)
# plt.show()
vals, vecs = np.linalg.eig(matForEig)
vals = vals[:Kx.shape[0]]
#print vals[:20]
vals = np.real(np.array([vals[i] for i in range(1, len(vals), 2)]))
vecs = vecs[:Kx.shape[0], :Kx.shape[0]]
self.vecs = vecs[:, 1]
for i in range(3, vecs.shape[1], 2):
self.vecs = np.hstack([self.vecs, vecs[:, i]])
self.vecs = np.mat(self.vecs)
norm_mat = np.mat(np.diag([np.sqrt(2)/np.sqrt(vals[i]) for i in range(len(vals))]))
#plobj1 = pylab.plot(vecs[:, 0])
self.vecs = self.vecs * norm_mat
print 'mult:', vals[0] * self.vecs[:, 0].T * self.vecs[:, 0]
def transform(self, data, k=2):
Kx = np.mat([[self.kernel_func(np.array(xi), np.array(xj)) for xj in self.trData] for xi in self.trData])
Kt = np.mat([[self.kernel_func(np.array(xi), np.array(xj)) for xj in self.trData] for xi in data])
Kt = np.mat(mlpy.kernel_center(Kt, Kx))
kTransTestData = np.real(Kt * self.vecs[:, :k])
return np.array(kTransTestData)
def estim_kbasis(self, trData, labels, regParam, verbose=True):
self.trData = trData
subSetInds = []
while len(set(subSetInds)) < regParam: subSetInds.append(int(random.uniform(0, len(trData))))
subSetInds = sorted(list(set(subSetInds)))
if verbose:
print "The sub set of indecies for reqularization has been selected"
self.trDataSubset = np.array([trData[i] for i in subSetInds])
Y = one_of_c(labels)
Kx = np.mat([[self.kernel_func(np.array(xi), np.array(xj)) for xj in self.trData] for xi in self.trDataSubset])
self.Kx = Kx
if verbose:
print "Requralized kernel matrix has been estimated!"
print "The shape of KxReg is", self.Kx.shape
Kx = np.mat(mlpy.kernel_center(Kx, Kx))
Ky = Y * Y.T
Ky = np.mat(mlpy.kernel_center(Ky, Ky))
meval = min(np.real(np.linalg.eigvals(Kx * Kx.T)))
KxKxT = Kx * Kx.T - 1e4 * meval * np.identity(Kx.shape[0])
if verbose:
print "Valitidy Check 1: KxKxT is simmetric:", \
np.allclose(KxKxT, (KxKxT).T)
def is_pos_def(x):
return np.all(np.linalg.eigvals(x) > 0)
if verbose:
print "Validity Check 2: KxKxT is positive definite:", \
is_pos_def(KxKxT)
# plt.imshow(Kx, cmap = cm.Greys_r)
# plt.show()
vals, vecs = eigh(Kx*Ky*Kx.T, KxKxT)
vals = np.array([np.real(v) for v in vals])
print vals
# plt.plot(vals)
# plt.show()
# vecs = vecs.T
# lambdas, alphas = zip(*sorted(zip(vals, vecs), reverse=True))
# lambdas = np.array([l for l in lambdas])
# alphas = np.mat([col for col in alphas])
# args = vals.argsort(axis = 0)
# alphas = np.mat(vecs[list(reversed(args))])
# alphas = alphas.T
# lambdas = sorted(vals, reverse=True)
lambdas = vals
alphas = np.mat(vecs)
print type(lambdas), type(alphas)
# plt.plot(lambdas)
# normTerm = (alpha.T * Kx) * (Kx * alpha)
# alpha = np.mat(vecs[:, 3]).T
# print 'mult before norm:', 1.0 / ((alpha.T * Kx) * (Kx * alpha))
norm_mat = np.mat(np.diag([1.0/np.sqrt(((alphas[:, i].T * Kx) * (Kx.T * alphas[:, i]))[0,0]) for i in range(len(lambdas))]))
alphas = alphas * norm_mat
alpha = np.mat(alphas[:, 44])
# alpha = alpha / np.sqrt(normTerm)
print 'mult after norm:', (alpha.T * Kx) * (Kx.T * alpha)
self.vecs = alphas
def transform(self, data):
tKernEstimed = np.array([[np.exp(-0.5 * np.dot(trEl-el, trEl-el)/self.sigma**2) for trEl in self.train] for el in data])
tKernEstimed = mlpy.kernel_center(tKernEstimed, self.Kx.T)
return np.dot(tKernEstimed, self.eigvecs)
