def figure_4_4_and_4_8(i, j):
"""Reproduces figure 4.4 and 4_8 in ESLii displaying canonical coordinates
for the vowel data. Here i and j specify which canonical coordinates to show
where i and j range from 1 to 10.
"""
assert(1 <= i and 1 <= j and i < j and i <= 9 and j <= 10)
vowels = eslii.read_vowel_data()
X = vowels[vowels.columns[1:]]
y = vowels['y']
rr_x = LDA().fit_transform(X, y)
plt.scatter(rr_x[:, i - 1], rr_x[:, j - 1], c=y)
def table_4_1():
"""Reproduces table 4.1 in ESLii showing the training and test error rates
for classifying vowels using different classification techniques. The
sklearn implementation of logistic regression uses OvA instead of a true
multinomial which likely accounts for the worse results
"""
vowels_train = eslii.read_vowel_data()
train_X = vowels_train[vowels_train.columns[1:]]
train_y = vowels_train['y']
vowels_test = eslii.read_vowel_data(train=False)
test_X = vowels_test[vowels_test.columns[1:]]
test_y = vowels_test['y']
lda = LDA().fit(train_X, train_y)
print "Linear discriminant analysis: {:.2f} {:.2f}".format(
1 - lda.score(train_X, train_y), 1 - lda.score(test_X, test_y))
qda = QDA().fit(train_X, train_y)
print "Quadratic discriminant analysis: {:.2f} {:.2f}".format(
1 - qda.score(train_X, train_y), 1 - qda.score(test_X, test_y))
lr = LogisticRegression(C=1e30).fit(train_X, train_y)
print "Logistic regression: {:.2f} {:.2f}".format(
1 - lr.score(train_X, train_y), 1 - lr.score(test_X, test_y))
