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ex6：Support Vector Machine(SVM)
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ex6：Support Vector Machine(SVM)
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# Support Vector Machine(SVM) 支持向量機
# Use SVM based on gaussian kernel (高斯核函數) to bulid junk mail classification
# Data set on 2D plane
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sb
from scipy.io import loadmat
raw_data = loadmat('/home/kesci/input/andrew_ml_ex67101/ex6data1.mat')
data = pd.DataFrame(raw_data.get('X'), columns=['X1', 'X2'])
data['y'] = raw_data.get('y')
data()
# Visualation
def plot_init_data(data, fig, ax):
positive = data[data['y'].isin([1])]
negative = data[data['y'].isin([0])]
ax.scatter(positive['X1'], positive['X2'], s=50, marker='x', label='Positive')
ax.scatter(negative['X1'], negative['X2'], s=50, marker='o', label='Negative')
# Plot the picture notice there are one unnormal point
fig, ax = plt.subplots(figsize=(12,8))
plot_init_data(data, fig, ax)
ax.legend()
plt.show()
# SVM 可被視為CA+B C為control factor
# C==1
from sklearn import svm
svc = svm.LinearSVC(C=1, loss='hinge', max_iter=1000)
svc
svc.fit(data[['X1', 'X2']], data['y'])
svc.score(data[['X1', 'X2']], data['y'])
# Visualization the classify boundary
def find_decision_boundary(svc, x1min, x1max, x2min, x2max, diff):
x1 = np.linspace(x1min, x1max, 1000)
x2 = np.linspace(x2min, x2max, 1000)
cordinates = [(x, y) for x in x1 for y in x2]
x_cord, y_cord = zip(*cordinates)
c_val = pd.DataFrame({'x1':x_cord, 'x2':y_cord})
c_val['cval'] = svc.decision_function(c_val[['x1', 'x2']])
decision = c_val[np.abs(c_val['cval']) < diff]
return decision.x1, decision.x2
# Plot the classify line and figure
x1, x2 = find_decision_boundary(svc, 0, 4, 1.5, 5, 2 * 10**-3)
fig, ax = plt.subplots(figsize=(12,8))
ax.scatter(x1, x2, s=10, c='r',label='Boundary')
plot_init_data(data, fig, ax)
ax.set_title('SVM (C=1) Decision Boundary')
ax.legend()
plt.show()
# set the C==100
svc2 = svm.LinearSVC(C=100, loss='hinge', max_iter=1000)
svc2.fit(data[['X1', 'X2']], data['y'])
svc2.score(data[['X1', 'X2']], data['y'])
# Plot the classify line and figure
x1, x2 = find_decision_boundary(svc, 0, 4, 1.5, 5, 2 * 10**-3)
fig, ax = plt.subplots(figsize=(12,8))
ax.scatter(x1, x2, s=10, c='r',label='Boundary')
plot_init_data(data, fig, ax)
ax.set_title('SVM (C=100) Decision Boundary')
ax.legend()
plt.show()
#gaussian kernel (高斯核函數)
def gaussian_kernel(x1, x2, sigma):
return np.exp(-(np.sum((x1 - x2) ** 2) / (2 * (sigma ** 2))))
# test gaussian kernel
x1 = np.array([1.0, 2.0, 1.0])
x2 = np.array([0.0, 4.0, -1.0])
sigma = 2
gaussian_kernel(x1, x2, sigma)
# test another data as the unlinear data and plot the figure
raw_data = loadmat('/home/kesci/input/andrew_ml_ex67101/ex6data2.mat')
data = pd.DataFrame(raw_data['X'], columns=['X1', 'X2'])
data['y'] = raw_data['y']
fig, ax = plt.subplots(figsize=(12,8))
plot_init_data(data, fig, ax)
ax.legend()
plt.show()
# show the feature of SVM
svc = svm.SVC(C=100, gamma=10, probability=True)
svc
svc.fit(data[['X1', 'X2']], data['y'])
svc.score(data[['X1', 'X2']], data['y'])
x1, x2 = find_decision_boundary(svc, 0, 1, 0.4, 1, 0.01)
fig, ax = plt.subplots(figsize=(12,8))
plot_init_data(data, fig, ax)
ax.scatter(x1, x2, s=10)
plt.show()
# CA+B set the C and B(gamma) [0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30, 100] to find the best solution
raw_data = loadmat('/home/kesci/input/andrew_ml_ex67101/ex6data3.mat')
X = raw_data['X']
Xval = raw_data['Xval']
y = raw_data['y'].ravel()
yval = raw_data['yval'].ravel()
fig, ax = plt.subplots(figsize=(12,8))
data = pd.DataFrame(raw_data.get('X'), columns=['X1', 'X2'])
data['y'] = raw_data.get('y')
plot_init_data(data, fig, ax)
plt.show()
C_values = [0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30, 100]
gamma_values = [0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30, 100]
best_score = 0
best_params = {'C': None, 'gamma': None}
for C in C_values:
for gamma in gamma_values:
svc = svm.SVC(C=C, gamma=gamma)
svc.fit(X, y)
score = svc.score(Xval, yval)
if score > best_score:
best_score = score
best_params['C'] = C
best_params['gamma'] = gamma
best_score, best_params
# plot the figure
svc = svm.SVC(C=best_params['C'], gamma=best_params['gamma'])
svc.fit(X, y)
x1, x2 = find_decision_boundary(svc, -0.6, 0.3, -0.7, 0.6, 0.005)
fig, ax = plt.subplots(figsize=(12,8))
plot_init_data(data, fig, ax)
ax.scatter(x1, x2, s=10)
plt.show()