ML | Non-Linear SVM

Prerequisite: Classifying data using SVM

In Linear SVM, the two classes were linearly separable, i.e a single straight line is able to classify both the classes. But imagine if you have three classes, obviously they will not be linearly separable. Therefore, Non-linear SVM’s come handy while handling these kinds of data where classes are not linearly separable.

We will be discussing a Non-Linear Kernel, the RBF kernel, (Radial Basis Function Kernel). So, what this kernel basically does is that it tries to transform the given data into almost linearly separable data.

Let’s consider the example of the IRIS dataset plotted with only 2 of the 4 features (Petal length and Petal Width).

Following is the scatter plot of the same:

It’s quite obvious that these classes are not linearly separable. Following is the contour plot of the non-linear SVM which has successfully classified the IRIS dataset using RBF kernel.

The above figure shows the classification of the three classes of the IRIS dataset.

1. From sklearn, we imported the SVM library.
2. We created 3 non-linear SVM’s (RBF kernel based).
3. Each SVM was fed with 1 class kept positive and other 2 as negative. Say, SVM1 had labels corresponding to class 1 only else all were made 0. Same for SVM2 and SVM3 respectively.
4. Plot the contour plot of each SVM.
5. Plot the data points.

Below is the Python implementation for the same.

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib import style
from sklearn.svm import SVC

style.use('fivethirtyeight')

# create mesh grids
def make_meshgrid(x, y, h =.02):
    x_min, x_max = x.min() - 1, x.max() + 1
    y_min, y_max = y.min() - 1, y.max() + 1
    xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
    return xx, yy

# plot the contours
def plot_contours(ax, clf, xx, yy, **params):
    Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
    Z = Z.reshape(xx.shape)
    out = ax.contourf(xx, yy, Z, **params)
    return out

color = ['r', 'b', 'g', 'k']

iris = pd.read_csv("iris-data.txt").values


features = iris[0:150, 2:4]
level1 = np.zeros(150)
level2 = np.zeros(150)
level3 = np.zeros(150)

# level1 contains 1 for class1 and 0 for all others.
# level2 contains 1 for class2 and 0 for all others.
# level3 contains 1 for class3 and 0 for all others.
for i in range(150):
    if i>= 0 and i<50:
        level1[i] = 1
    elif i>= 50 and i<100:
        level2[i] = 1
    elif i>= 100 and i<150:
        level3[i]= 1

# create 3 svm with rbf kernels
svm1 = SVC(kernel ='rbf')
svm2 = SVC(kernel ='rbf')
svm3 = SVC(kernel ='rbf')

# fit each svm's
svm1.fit(features, level1)
svm2.fit(features, level2)
svm3.fit(features, level3)

fig, ax = plt.subplots()
X0, X1 = iris[:, 2], iris[:, 3]
xx, yy = make_meshgrid(X0, X1)

# plot the contours
plot_contours(ax, svm1, xx, yy, cmap = plt.get_cmap('hot'), alpha = 0.8)
plot_contours(ax, svm2, xx, yy, cmap = plt.get_cmap('hot'), alpha = 0.3)
plot_contours(ax, svm3, xx, yy, cmap = plt.get_cmap('hot'), alpha = 0.5)

color = ['r', 'b', 'g', 'k']

for i in range(len(iris)):
    plt.scatter(iris[i][2], iris[i][3], s = 30, c = color[int(iris[i][4])])
plt.show()