跟着Leo机器学习：sklearn之Support Vector Machines

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sklearn框架

函数导图

1. Classification

from sklearn import svm
X = [[0, 0], [1, 1]]
y = [0, 1]
clf = svm.SVC()
clf.fit(X, y)
clf.predict([[2., 2.]])

内部参数

# get support vectors
clf.support_vectors_
# get indices of support vectors

clf.support_
# get number of support vectors for each class

clf.n_support_

1.1. Multi-class classification

SVC

X = [[0], [1], [2], [3]]
Y = [0, 1, 2, 3]
clf = svm.SVC(decision_function_shape='ovo')
clf.fit(X, Y)
dec = clf.decision_function([[1]])

dec.shape[1] # 4 classes: 4*3/2 = 6
clf.decision_function_shape = "ovr"

dec = clf.decision_function([[1]])

dec.shape[1] # 4 classes

LinearSVC

lin_clf = svm.LinearSVC()
lin_clf.fit(X, Y)
dec = lin_clf.decision_function([[1]])

dec.shape[1]

1.3. Unbalanced problems

Plot different SVM classifiers in the iris dataset

print(__doc__)
import numpy as np

import matplotlib.pyplot as plt

from sklearn import svm, datasets
def make_meshgrid(x, y, h=.02):

"""Create a mesh of points to plot in
Parameters
----------
x: data to base x-axis meshgrid on
y: data to base y-axis meshgrid on
h: stepsize for meshgrid, optional

Returns
-------
xx, yy : ndarray
"""</span>
x_min<span class="token punctuation">,</span> x_max <span class="token operator">=</span> x<span class="token punctuation">.</span><span class="token builtin">min</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">,</span> x<span class="token punctuation">.</span><span class="token builtin">max</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">+</span> <span class="token number">1</span>
y_min<span class="token punctuation">,</span> y_max <span class="token operator">=</span> y<span class="token punctuation">.</span><span class="token builtin">min</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">-</span> <span class="token number">1</span><span class="token punctuation">,</span> y<span class="token punctuation">.</span><span class="token builtin">max</span><span class="token punctuation">(</span><span class="token punctuation">)</span> <span class="token operator">+</span> <span class="token number">1</span>
xx<span class="token punctuation">,</span> yy <span class="token operator">=</span> np<span class="token punctuation">.</span>meshgrid<span class="token punctuation">(</span>np<span class="token punctuation">.</span>arange<span class="token punctuation">(</span>x_min<span class="token punctuation">,</span> x_max<span class="token punctuation">,</span> h<span class="token punctuation">)</span><span class="token punctuation">,</span>
                     np<span class="token punctuation">.</span>arange<span class="token punctuation">(</span>y_min<span class="token punctuation">,</span> y_max<span class="token punctuation">,</span> h<span class="token punctuation">)</span><span class="token punctuation">)</span>
<span class="token keyword">return</span> xx<span class="token punctuation">,</span> yy

def plot_contours(ax, clf, xx, yy, **params):

"""Plot the decision boundaries for a classifier.
Parameters
----------
ax: matplotlib axes object
clf: a classifier
xx: meshgrid ndarray
yy: meshgrid ndarray
params: dictionary of params to pass to contourf, optional
"""</span>
Z <span class="token operator">=</span> clf<span class="token punctuation">.</span>predict<span class="token punctuation">(</span>np<span class="token punctuation">.</span>c_<span class="token punctuation">[</span>xx<span class="token punctuation">.</span>ravel<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">,</span> yy<span class="token punctuation">.</span>ravel<span class="token punctuation">(</span><span class="token punctuation">)</span><span class="token punctuation">]</span><span class="token punctuation">)</span>
Z <span class="token operator">=</span> Z<span class="token punctuation">.</span>reshape<span class="token punctuation">(</span>xx<span class="token punctuation">.</span>shape<span class="token punctuation">)</span>
out <span class="token operator">=</span> ax<span class="token punctuation">.</span>contourf<span class="token punctuation">(</span>xx<span class="token punctuation">,</span> yy<span class="token punctuation">,</span> Z<span class="token punctuation">,</span> <span class="token operator">**</span>params<span class="token punctuation">)</span>
<span class="token keyword">return</span> out

# import some data to play with

iris = datasets.load_iris()

# Take the first two features. We could avoid this by using a two-dim dataset

X = iris.data[:, :2]

y = iris.target
# we create an instance of SVM and fit out data. We do not scale our

# data since we want to plot the support vectors

C = 1.0  # SVM regularization parameter

models = (svm.SVC(kernel='linear', C=C),

svm.LinearSVC(C=C, max_iter=10000),

svm.SVC(kernel='rbf', gamma=0.7, C=C),

svm.SVC(kernel='poly', degree=3, gamma='auto', C=C))

models = (clf.fit(X, y) for clf in models)
# title for the plots

titles = ('SVC with linear kernel',

'LinearSVC (linear kernel)',

'SVC with RBF kernel',

'SVC with polynomial (degree 3) kernel')
# Set-up 2x2 grid for plotting.

fig, sub = plt.subplots(2, 2)

plt.subplots_adjust(wspace=0.4, hspace=0.4)
X0, X1 = X[:, 0], X[:, 1]

xx, yy = make_meshgrid(X0, X1)
for clf, title, ax in zip(models, titles, sub.flatten()):

plot_contours(ax, clf, xx, yy,

cmap=plt.cm.coolwarm, alpha=0.8)

ax.scatter(X0, X1, c=y, cmap=plt.cm.coolwarm, s=20, edgecolors='k')

ax.set_xlim(xx.min(), xx.max())

ax.set_ylim(yy.min(), yy.max())

ax.set_xlabel('Sepal length')

ax.set_ylabel('Sepal width')

ax.set_xticks(())

ax.set_yticks(())

ax.set_title(title)
plt.show()

2. Regression

from sklearn import svm
X = [[0, 0], [2, 2]]
y = [0.5, 2.5]
clf = svm.SVR()
clf.fit(X, y)
clf.predict([[1, 1]])

3. Density estimation, novelty detection

The class OneClassSVM implements a One-Class SVM which is used in outlier detection.

from sklearn.svm import OneClassSVM
X = [[0], [0.44], [0.45], [0.46], [1]]
clf = OneClassSVM(gamma='auto').fit(X)
clf.predict(X)
clf.score_samples(X)  # doctest: +ELLIPSIS

6. Kernel functions

6.1. Custom Kernels

6.1.1. Using Python functions as kernels

import numpy as np
from sklearn import svm
def my_kernel(X, Y):
    return np.dot(X, Y.T)
clf = svm.SVC(kernel=my_kernel)

6.1.2. Using the Gram matrix

import numpy as np
from sklearn import svm
X = np.array([[0, 0], [1, 1]])
y = [0, 1]
clf = svm.SVC(kernel='precomputed')
# linear kernel computation
gram = np.dot(X, X.T)
clf.fit(gram, y)
# predict on training examples

clf.predict(gram)