Support vector machines (SVM) is a supervised machine learning. Application areas include:
- classification
- regression
Its biggest advantage is that it can define both a linear or a non-linear decision boundary by using kernel functions.
support vector machines also draws a margin around the decision boundary to increase prediction confidence.
Support vector machines allow some misclassification during the learning process. So they can do a better job at classifying most vectors in the testing set.
usage
import random
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
def generate_random_dataset(size):
""" Generate a random dataset and that follows a quadratic distribution
"""
x = []
y = []
target = []
for i in range(size):
# class zero
x.append(np.round(random.uniform(0, 2.5), 1))
y.append(np.round(random.uniform(0, 20), 1))
target.append(0)
# class one
x.append(np.round(random.uniform(1, 5), 2))
y.append(np.round(random.uniform(20, 25), 2))
target.append(1)
x.append(np.round(random.uniform(3, 5), 2))
y.append(np.round(random.uniform(5, 25), 2))
target.append(1)
df_x = pd.DataFrame(data=x)
df_y = pd.DataFrame(data=y)
df_target = pd.DataFrame(data=target)
data_frame = pd.concat([df_x, df_y], ignore_index=True, axis=1)
data_frame = pd.concat([data_frame, df_target], ignore_index=True, axis=1)
data_frame.columns = ['x', 'y', 'target']
return data_frame
# Generate dataset
size = 100
dataset = generate_random_dataset(size)
features = dataset[['x', 'y']]
label = dataset['target']
# Hold out 20% of the dataset for training
test_size = int(np.round(size * 0.2, 0))
# Split dataset into training and testing sets
x_train = features[:-test_size].values
y_train = label[:-test_size].values
x_test = features[-test_size:].values
y_test = label[-test_size:].values
# Plotting the training set
fig, ax = plt.subplots(figsize=(12, 7))
# removing to and right border
ax.spines['top'].set_visible(False)
ax.spines['left'].set_visible(False)
ax.spines['right'].set_visible(False)
# adding major gridlines
ax.grid(color='grey', linestyle='-', linewidth=0.25, alpha=0.5)
ax.scatter(features[:-test_size]['x'], features[:-test_size]['y'], color="#8C7298")
plt.show()
#train model
from sklearn import svm
model = svm.SVC(kernel='poly', degree=2)
model.fit(x_train, y_train)
#plot decision boundary
fig, ax = plt.subplots(figsize=(12, 7))
# Removing to and right border
ax.spines['top'].set_visible(False)
ax.spines['left'].set_visible(False)
ax.spines['right'].set_visible(False)
# Create grid to evaluate model
xx = np.linspace(-1, max(features['x']) + 1, len(x_train))
yy = np.linspace(0, max(features['y']) + 1, len(y_train))
YY, XX = np.meshgrid(yy, xx)
xy = np.vstack([XX.ravel(), YY.ravel()]).T
train_size = len(features[:-test_size]['x'])
# Assigning different colors to the classes
colors = y_train
colors = np.where(colors == 1, '#8C7298', '#4786D1')
# Plot the dataset
ax.scatter(features[:-test_size]['x'], features[:-test_size]['y'], c=colors)
# Get the separating hyperplane
Z = model.decision_function(xy).reshape(XX.shape)
# Draw the decision boundary and margins
ax.contour(XX, YY, Z, colors='k', levels=[-1, 0, 1], alpha=0.5, linestyles=['--', '-', '--'])
# Highlight support vectors with a circle around them
ax.scatter(model.support_vectors_[:, 0], model.support_vectors_[:, 1], s=100, linewidth=1, facecolors='none', edgecolors='k')
plt.show()
#run test
from sklearn.metrics import accuracy_score
predictions_poly = model.predict(x_test)
accuracy_poly = accuracy_score(y_test, predictions_poly)
print("2nd degree polynomial Kernel\nAccuracy (normalized): " + str(accuracy_poly))
