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SVM with Custom Kernel in Scikit-learn

Simple usage of Support Vector Machines to classify a sample. It will plot the decision surface and the support vectors.

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Version

In [1]:
import sklearn
sklearn.__version__
Out[1]:
'0.18.1'

Imports

In [2]:
print(__doc__)

import plotly.plotly as py
import plotly.graph_objs as go

import numpy as np
import matplotlib.pyplot as plt
from sklearn import svm, datasets
Automatically created module for IPython interactive environment

Calculations

In [3]:
# import some data to play with
iris = datasets.load_iris()
X = iris.data[:, :2]  # we only take the first two features. We could
                      # avoid this ugly slicing by using a two-dim dataset
Y = iris.target


def my_kernel(X, Y):
    """
    We create a custom kernel:

                 (2  0)
    k(X, Y) = X  (    ) Y.T
                 (0  1)
    """
    M = np.array([[2, 0], [0, 1.0]])
    return np.dot(np.dot(X, M), Y.T)


h = .02  # step size in the mesh

# we create an instance of SVM and fit out data.
clf = svm.SVC(kernel=my_kernel)
clf.fit(X, Y)
Out[3]:
SVC(C=1.0, cache_size=200, class_weight=None, coef0=0.0,
  decision_function_shape=None, degree=3, gamma='auto',
  kernel=<function my_kernel at 0x7fb4606bfed8>, max_iter=-1,
  probability=False, random_state=None, shrinking=True, tol=0.001,
  verbose=False)
In [4]:
def matplotlib_to_plotly(cmap, pl_entries):
    h = 1.0/(pl_entries-1)
    pl_colorscale = []
    
    for k in range(pl_entries):
        C = map(np.uint8, np.array(cmap(k*h)[:3])*255)
        pl_colorscale.append([k*h, 'rgb'+str((C[0], C[1], C[2]))])
        
    return pl_colorscale

cmap = matplotlib_to_plotly(plt.cm.Paired, 4)

Plot Results

Plot the decision boundary. For that, we will assign a color to each point in the mesh [x_min, x_max]x[y_min, y_max].

In [5]:
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
x_ = np.arange(x_min, x_max, h)
y_ =  np.arange(y_min, y_max, h)
xx, yy = np.meshgrid(x_, y_)
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])

# Put the result into a color plot
Z = Z.reshape(xx.shape)
In [6]:
trace1 = go.Heatmap(x=x_, y=y_, z=Z,
                    colorscale=cmap,
                    showscale=False)

trace2 = go.Scatter(x=X[:, 0], y=X[:, 1], 
                    mode='markers',
                    marker=dict(color=Y, 
                                colorscale=cmap, 
                                showscale=False,
                                line=dict(color='black', width=1)))

layout = go.Layout(title="3-Class classification using Support Vector Machine with custom kernel")
fig = go.Figure(data= [trace1, trace2], layout=layout)
In [7]:
py.iplot(fig)
Out[7]:
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