03.03 - SVMs

!wget --no-cache -O init.py -q https://raw.githubusercontent.com/rramosp/ai4eng.v1/main/content/init.py
import init; init.init(force_download=False); init.get_weblink()

from sklearn.datasets import *
import numpy as np
from local.lib import mlutils
from sklearn.tree import DecisionTreeClassifier
import matplotlib.pyplot as plt
%matplotlib inline
from IPython.display import Image
from mpl_toolkits.mplot3d import Axes3D

from sklearn.linear_model import LogisticRegression
from sklearn.datasets import make_circles
X,y = make_circles(200, noise=.05)

Feature transformation

A linear classifier on higher dimensions

lr = LogisticRegression()
lr.fit(X,y)
print ("SCORE %.2f"%lr.score(X,y))
mlutils.plot_2Ddata(X, y, dots_alpha=.3)
mlutils.plot_2D_boundary(lr.predict, np.min(X, axis=0), np.max(X, axis=0),
                 line_width=3, line_alpha=.7, label=None)

SCORE 0.51

/opt/anaconda2/envs/p36/lib/python3.6/site-packages/sklearn/linear_model/logistic.py:433: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.
  FutureWarning)

(0.514125, 0.485875)

X,y = make_circles(300, noise=.05)
X = np.vstack((X.T,X[:,0]**2+X[:,1]**2)).T
X.shape

(300, 3)

fig = plt.figure(figsize=(8,6))
ax = fig.add_subplot(111, projection='3d')
ax.scatter(X[:,0][y==0], X[:,1][y==0],X[:,2][y==0], color="blue")
ax.scatter(X[:,0][y==1], X[:,1][y==1],X[:,2][y==1], color="red")

<mpl_toolkits.mplot3d.art3d.Path3DCollection at 0x7fa8b2663fd0>

lr = LogisticRegression()
lr.fit(X,y)
print ("SCORE %.2f"%lr.score(X,y))

SCORE 0.98

/opt/anaconda2/envs/p36/lib/python3.6/site-packages/sklearn/linear_model/logistic.py:433: FutureWarning: Default solver will be changed to 'lbfgs' in 0.22. Specify a solver to silence this warning.
  FutureWarning)

Support vector machines

observa que \(\gamma\) representa cuanto de cercanos han de estar dos puntos para considerarlos similares

## KEEPOUTPUT
from sklearn.svm import SVC
X,y = make_blobs(300, centers=2, cluster_std=1)
sv = SVC(gamma=1e-2)
sv.fit(X,y)
print (sv.score(X,y))
mlutils.plot_2Ddata(X, y, dots_alpha=.3)
mlutils.plot_2D_boundary(sv.predict, np.min(X, axis=0), np.max(X, axis=0),
                 line_width=3, line_alpha=.7, label=None)

plt.scatter(sv.support_vectors_[:,0], sv.support_vectors_[:,1], s=100, alpha=.8, color="gray")
print ("number of support vectors", len(sv.support_vectors_))

0.99
number of support vectors 50

## KEEPOUTPUT
from sklearn.svm import SVC
X,y = make_moons(200, noise=0.2)
sv = SVC(gamma=.1)
sv.fit(X,y)
print (sv.score(X,y))
mlutils.plot_2Ddata(X, y, dots_alpha=.3)
mlutils.plot_2D_boundary(sv.predict, np.min(X, axis=0), np.max(X, axis=0),
                 line_width=3, line_alpha=.7, label=None)

plt.scatter(sv.support_vectors_[:,0], sv.support_vectors_[:,1], s=100, alpha=.8, color="gray")

0.88

<matplotlib.collections.PathCollection at 0x7ff51a2d75c0>

## KEEPOUTPUT
sv.support_vectors_.shape

(86, 2)

## KEEPOUTPUT
sv = SVC(gamma=1)
sv.fit(X,y)
print (sv.score(X,y))
mlutils.plot_2Ddata(X, y, dots_alpha=.3)
mlutils.plot_2D_boundary(sv.predict, np.min(X, axis=0), np.max(X, axis=0),
                 line_width=3, line_alpha=.7, label=None)

plt.scatter(sv.support_vectors_[:,0], sv.support_vectors_[:,1], s=100, alpha=.5, color="gray")

0.955

<matplotlib.collections.PathCollection at 0x7ff51a244630>

## KEEPOUTPUT
sv = SVC(gamma=1e-4)
sv.fit(X,y)
print (sv.score(X,y))
mlutils.plot_2Ddata(X, y, dots_alpha=.3)
mlutils.plot_2D_boundary(sv.predict, np.min(X, axis=0), np.max(X, axis=0),
                 line_width=3, line_alpha=.7, label=None)

plt.scatter(sv.support_vectors_[:,0], sv.support_vectors_[:,1], s=100, alpha=.7, color="gray")

0.79

<matplotlib.collections.PathCollection at 0x7ff51a2400b8>