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kernel_trick.py
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kernel_trick.py
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import random
import numpy as np
import matplotlib.pyplot as plt
import math
from sklearn.linear_model import Ridge
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import make_pipeline
from mpl_toolkits.mplot3d import Axes3D
import matplotlib
matplotlib.rcParams['mathtext.fontset'] = 'stix'
matplotlib.rcParams['font.family'] = 'STIXGeneral'
matplotlib.rcParams.update({'font.size': 18})
def f_outer(x1):
result = []
for x in x1:
side = random.uniform(0, 1)
sq = math.sqrt(10 * 10 - x * x)
if side > 0.5:
sq = sq * (-1)
result.append(sq)
return np.asarray(result)
def f_inner(x1):
result = []
for x in x1:
side = random.uniform(0, 1)
sq = math.sqrt(3 * 3 - x * x)
if side > 0.5:
sq = sq * (-1)
result.append(sq)
return np.asarray(result)
# generate points and keep a subset of them
x_inner = np.linspace(-3, 3, 100)
x_outer = np.linspace(-10, 10, 100)
rng = np.random.RandomState(0)
rng.shuffle(x_inner)
rng.shuffle(x_outer)
x_inner = np.sort(x_inner[:30])
x_outer = np.sort(x_outer[:30])
noize = [(-1 + np.random.random()) for i in range(len(x_inner))]
y_inner = f_inner(x_inner) + noize
noize = [(-1 + np.random.random()) for i in range(len(x_outer))]
y_outer = f_outer(x_outer) + noize
colors = ['blue', 'red']#, 'orange'
lw = 2
type_of_regression = ["linear regression", "regression of degree 10"]
fit = ["fit", "overfit"]
plt.figure(1)
axes = plt.gca()
axes.set_xlim([-11,11])
axes.set_ylim([-11,11])
plt.scatter(x_inner, y_inner, color='navy', s=30, marker='o')
plt.scatter(x_outer, y_outer, color='red', s=30, marker='o')
fig1 = plt.gcf()
fig1.subplots_adjust(top = 0.98, bottom = 0.1, right = 0.98, left = 0.08, hspace = 0, wspace = 0)
fig1.savefig('../../Illustrations/kernel-trick-0.eps', format='eps', dpi=1000, bbox_inches = 'tight', pad_inches = 0)
fig1.savefig('../../Illustrations/kernel-trick-0.pdf', format='pdf', dpi=1000, bbox_inches = 'tight', pad_inches = 0)
fig1.savefig('../../Illustrations/kernel-trick-0.png', dpi=1000, bbox_inches = 'tight', pad_inches = 0)
x_inner_transformed = np.asarray([x * x for x in x_inner])
y_inner_transformed = np.asarray([math.sqrt(2) * x * y for x, y in zip(x_inner, y_inner)])
z_inner_transformed = np.asarray([y * y for y in y_inner])
x_outer_transformed = np.asarray([x * x for x in x_outer])
y_outer_transformed = np.asarray([math.sqrt(2) * x * y for x, y in zip(x_outer, y_outer)])
z_outer_transformed = np.asarray([y * y for y in y_outer])
fig = plt.figure(2)
ax = Axes3D(fig)
ax.set_yticks([-75, 0, 75])
#ax.set_xlim([-10,120])
#$ax.set_ylim([-120,120])
#ax.set_zlim([-120,120])
ax.scatter(x_inner_transformed, y_inner_transformed, z_inner_transformed, color='navy', marker='o')
ax.scatter(x_outer_transformed, y_outer_transformed, z_outer_transformed, color='red', marker='o')
ax.view_init(14, -77)
fig.subplots_adjust(top = 0.98, bottom = 0.1, right = 0.98, left = 0.08, hspace = 0, wspace = 0)
fig.savefig('../../Illustrations/kernel-trick-1.eps', format='eps', dpi=1000, bbox_inches = 'tight', pad_inches = 0)
fig.savefig('../../Illustrations/kernel-trick-1.pdf', format='pdf', dpi=1000, bbox_inches = 'tight', pad_inches = 0)
fig.savefig('../../Illustrations/kernel-trick-1.png', dpi=1000, bbox_inches = 'tight', pad_inches = 0)
#plt.show()