def fit(self, X, y):
# Check that X and y have correct shape
X, y = check_X_y(X, y)
# Compute the coefficients
self.kernel_fun = self._get_kernel_fun(self.kernel)
K = compute_gram_mat(X, X, self.kernel_fun, self.kernel_params)
N = K.shape[0]
total = np.zeros(self.D_max - 1)
for D in range(1, self.D_max):
coeffs, Phi = compute_coeff_fixD(K, y, D)
x_pred = Phi @ coeffs
mse = np.mean((y - x_pred)**2)
total[D - 1] = mse + pen_D(N, D, self.C)
tot_min = np.amin(total)
D_opt_lst = np.where(total == tot_min)
if (np.isnan(D_opt_lst)):
print("NaN get!")
D_opt = 0
else:
D_opt = np.where(total == tot_min)[0][0] + 1
mse_opt = tot_min - pen_D(N, D_opt, self.C)
coeffs_opt, Phi_opt = compute_coeff_fixD(K, y, D_opt)
Alpha, Lam = kpca(K, D_opt)
self.D_opt = D_opt
self.mse_opt = mse_opt
self.coeffs_opt = coeffs_opt
self.X_fit_ = X
self.Alpha = Alpha
self.Phi_opt = Phi_opt
# Return the classifier
return self
def predict(self, X):
# compute the prediction of y using kernel coefficients alpha
check_is_fitted(self, ["alpha"])
# Input validation
X = check_array(X)
train_samples = self.X_fit_.shape[0]
K_test = compute_gram_mat(X, self.X_fit_, self.kernel_fun, self.sigma)
y_pred = np.dot(K_test, self.alpha)
return y_pred
def fit(self, X, y):
# Key algorithm to compute the kernel ridge coefficients alpha given the gram matrix K,
# formula listed as equation (37) of the original paper
self.kernel_fun = self._get_kernel_fun(self.kernel)
K = compute_gram_mat(X, X, self.kernel_fun, self.sigma)
self.alpha = np.linalg.solve(
K + self.lam * y.size * np.eye(K.shape[0]), y)
self.X_fit_ = X
return self
def predict(self, X):
# Check is fit had been called
check_is_fitted(self, ["D_opt", "mse_opt", "coeffs_opt", "Alpha"])
# Input validation
X = check_array(X)
train_samples = self.X_fit_.shape[0]
K_test = compute_gram_mat(X, self.X_fit_, self.kernel_fun,
self.kernel_params)
Phi_test = K_test @ self.Alpha / np.sqrt(train_samples)
y_pred = Phi_test @ self.coeffs_opt
self.y_pred = y_pred
return self.y_pred
plt.show()
#%%
# eigenfunctions for dim = 2
N = 1000
d = eigen_n_sphere(N, 2, arccos)
X = d['data']
y = d['label']
K = d['gram_mat']
num = 20
alpha = np.linalg.solve(K, y)
theta_seq = np.linspace(start=0, stop=2 * np.pi - 1e-4, num=num)
X_seq = np.array([np.cos(theta_seq), np.sin(theta_seq)]).transpose()
K_test = compute_gram_mat(X_seq, X, arccos)
y_pred = K_test @ alpha
y_pred_lst = np.zeros((N, num))
for i in range(N):
y_pred_lst[i] = K_test[:, i]
# Plot results
fig, ax = plt.subplots()
cols = ['red', 'blue', 'purple', 'orange']
print(theta_seq)
print(y_pred)
ax.plot(theta_seq, y_pred, label='actual function')
for i in range(N):
ax.plot(theta_seq,
y_pred_lst[i].astype(float),