################################################################################
# load sample dataset
from scikits.learn.datasets import load_iris
iris = load_iris()
X = iris.data[:,:2] # Take only 2 dimensions
y = iris.target
X = X[y > 0]
y = y[y > 0]
y -= 1
target_names = iris.target_names[1:]
################################################################################
# LDA
lda = LDA()
y_pred = lda.fit(X, y, store_covariance=True).predict(X)
# QDA
qda = QDA()
y_pred = qda.fit(X, y, store_covariances=True).predict(X)
###############################################################################
# Plot results
def plot_ellipse(splot, mean, cov, color):
v, w = linalg.eigh(cov)
u = w[0] / linalg.norm(w[0])
angle = np.arctan(u[1]/u[0])
angle = 180 * angle / np.pi # convert to degrees
# filled gaussian at 2 standard deviation
import pylab as pl
from scikits.learn import datasets
from scikits.learn.pca import PCA
from scikits.learn.lda import LDA
iris = datasets.load_iris()
X = iris.data
y = iris.target
target_names = iris.target_names
pca = PCA(n_components=2)
X_r = pca.fit(X).transform(X)
lda = LDA(n_components=2)
X_r2 = lda.fit(X, y).transform(X)
# Percentage of variance explained for each components
print 'explained variance ratio (first two components):', \
pca.explained_variance_ratio_
pl.figure()
pl.subplot(2, 1, 1)
for c, i, target_name in zip("rgb", [0, 1, 2], target_names):
pl.scatter(X_r[y == i, 0], X_r[y == i, 1], c=c, label=target_name)
pl.legend()
pl.title('PCA of IRIS dataset')
pl.subplot(2, 1, 2)
for c, i, target_name in zip("rgb", [0, 1, 2], target_names):
################################################################################
# load sample dataset
from scikits.learn.datasets import load_iris
iris = load_iris()
X = iris.data[:, :2] # Take only 2 dimensions
y = iris.target
X = X[y > 0]
y = y[y > 0]
y -= 1
target_names = iris.target_names[1:]
################################################################################
# LDA
lda = LDA()
y_pred = lda.fit(X, y, store_covariance=True).predict(X)
# QDA
qda = QDA()
y_pred = qda.fit(X, y, store_covariances=True).predict(X)
###############################################################################
# Plot results
def plot_ellipse(splot, mean, cov, color):
v, w = linalg.eigh(cov)
u = w[0] / linalg.norm(w[0])
angle = np.arctan(u[1] / u[0])
angle = 180 * angle / np.pi # convert to degrees
from scikits.learn import datasets
from scikits.learn.decomposition import PCA
from scikits.learn.lda import LDA
iris = datasets.load_iris()
X = iris.data
y = iris.target
target_names = iris.target_names
print target_names
pca = PCA(n_components=2)
X_r = pca.fit(X).transform(X)
lda = LDA(n_components=2)
X_r2 = lda.fit(X, y).transform(X)
# Percentage of variance explained for each components
print 'explained variance ratio (first two components):', \
pca.explained_variance_ratio_
pl.figure()
for c, i, target_name in zip("rgb", [0, 1, 2], target_names):
pl.scatter(X_r[y == i, 0], X_r[y == i, 1], c=c, label=target_name)
pl.legend()
pl.title('PCA of IRIS dataset')
pl.figure()
for c, i, target_name in zip("rgb", [0, 1, 2], target_names):
pl.scatter(X_r2[y == i, 0], X_r2[y == i, 1], c=c, label=target_name)
============================ A classification example using Linear Discriminant Analysis (LDA). """ import numpy as np ################################################################################ # import some data to play with # The IRIS dataset from scikits.learn import datasets iris = datasets.load_iris() # Some noisy data not correlated E = np.random.normal(size=(len(iris.data), 35)) # Add the noisy data to the informative features X = np.hstack((iris.data, E)) y = iris.target ################################################################################ # LDA from scikits.learn.lda import LDA lda = LDA() y_pred = lda.fit(X, y).predict(X) print "Number of mislabeled points : %d"%(y != y_pred).sum()
180 + angle, color=color)
ell.set_clip_box(splot.bbox)
ell.set_alpha(0.5)
splot.add_artist(ell)
def plot_lda_cov(lda, splot):
plot_ellipse(splot, lda.means_[0], lda.covariance_, 'red')
plot_ellipse(splot, lda.means_[1], lda.covariance_, 'blue')
def plot_qda_cov(qda, splot):
plot_ellipse(splot, qda.means_[0], qda.covariances_[0], 'red')
plot_ellipse(splot, qda.means_[1], qda.covariances_[1], 'blue')
###############################################################################
for i, (X, y) in enumerate([dataset_fixed_cov(), dataset_cov()]):
# LDA
lda = LDA()
y_pred = lda.fit(X, y, store_covariance=True).predict(X)
splot = plot_data(lda, X, y, y_pred, fig_index=2 * i + 1)
plot_lda_cov(lda, splot)
pl.axis('tight')
# QDA
qda = QDA()
y_pred = qda.fit(X, y, store_covariances=True).predict(X)
splot = plot_data(qda, X, y, y_pred, fig_index=2 * i + 2)
plot_qda_cov(qda, splot)
pl.axis('tight')
pl.suptitle('LDA vs QDA')
pl.show()
splot.add_artist(ell)
def plot_lda_cov(lda, splot):
plot_ellipse(splot, lda.means_[0], lda.covariance_, 'red')
plot_ellipse(splot, lda.means_[1], lda.covariance_, 'blue')
def plot_qda_cov(qda, splot):
plot_ellipse(splot, qda.means_[0], qda.covariances_[0], 'red')
plot_ellipse(splot, qda.means_[1], qda.covariances_[1], 'blue')
###############################################################################
for i, (X, y) in enumerate([dataset_fixed_cov(), dataset_cov()]):
# LDA
lda = LDA()
y_pred = lda.fit(X, y, store_covariance=True).predict(X)
splot = plot_data(lda, X, y, y_pred, fig_index=2 * i + 1)
plot_lda_cov(lda, splot)
pl.axis('tight')
# QDA
qda = QDA()
y_pred = qda.fit(X, y, store_covariances=True).predict(X)
splot = plot_data(qda, X, y, y_pred, fig_index=2 * i + 2)
plot_qda_cov(qda, splot)
pl.axis('tight')
pl.suptitle('LDA vs QDA')
pl.show()
