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
ell = mpl.patches.Ellipse(mean, 2 * v[0] ** 0.5, 2 * v[1] ** 0.5,
180 + angle, color=color)
ell.set_clip_box(splot.bbox)
ell.set_alpha(0.5)
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()
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
ell = mpl.patches.Ellipse(mean,
2 * v[0]**0.5,
2 * v[1]**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()