def test_pca_on_uncentered_data():
pca1 = PCA(solver='svd')
pca1.fit(X)
pca2 = PCA(solver='eigen')
pca2.fit(X)
assert_almost_equal(pca1.e_vals_normalized_, pca2.e_vals_normalized_)
def test_pca_on_uncentered_data():
pca1 = PCA(solver='svd')
pca1.fit(X)
pca2 = PCA(solver='eigen')
pca2.fit(X)
assert_almost_equal(pca1.e_vals_normalized_, pca2.e_vals_normalized_)
def test_evals():
pca = PCA(n_components=2, solver='eigen')
pca.fit(X_std)
assert_almost_equal(pca.e_vals_, [2.9, 0.9, 0.2, 0.02], decimal=1)
pca = PCA(n_components=2, solver='svd')
pca.fit(X_std)
assert_almost_equal(pca.e_vals_, [2.9, 0.9, 0.2, 0.02], decimal=1)
def test_evals():
pca = PCA(n_components=2, solver='eigen')
pca.fit(X_std)
assert_almost_equal(pca.e_vals_, [2.9, 0.9, 0.2, 0.02], decimal=1)
pca = PCA(n_components=2, solver='svd')
pca.fit(X_std)
assert_almost_equal(pca.e_vals_, [2.9, 0.9, 0.2, 0.02], decimal=1)
def test_whitening():
pca = PCA(n_components=2)
res = pca.fit(X_std).transform(X_std)
diagonals_sum = np.sum(np.diagonal(np.cov(res.T)))
assert round(diagonals_sum, 1) == 3.9, diagonals_sum
pca = PCA(n_components=2, whitening=True)
res = pca.fit(X_std).transform(X_std)
diagonals_sum = np.sum(np.diagonal(np.cov(res.T)))
assert round(diagonals_sum, 1) == 2.0, diagonals_sum
def test_whitening():
pca = PCA(n_components=2)
res = pca.fit(X_std).transform(X_std)
diagonals_sum = np.sum(np.diagonal(np.cov(res.T)))
assert round(diagonals_sum, 1) == 3.9, diagonals_sum
pca = PCA(n_components=2, whitening=True)
res = pca.fit(X_std).transform(X_std)
diagonals_sum = np.sum(np.diagonal(np.cov(res.T)))
assert round(diagonals_sum, 1) == 2.0, diagonals_sum
def test_evals():
pca = PCA(n_components=2, solver='eigen')
pca.fit(X_std)
expected = [2.93035378, 0.92740362, 0.14834223, 0.02074601]
assert_almost_equal(pca.e_vals_, expected, decimal=5)
pca = PCA(n_components=2, solver='svd')
pca.fit(X_std)
assert_almost_equal(pca.e_vals_, expected, decimal=5)
def test_loadings():
expect = np.array([[0.9, -0.4, -0.3, 0.], [-0.5, -0.9, 0.1, -0.],
[1., -0., 0.1, -0.1], [1., -0.1, 0.2, 0.1]])
pca = PCA(solver='eigen')
pca.fit(X_std)
assert_almost_equal(pca.loadings_, expect, decimal=1)
expect = np.array([[-0.9, -0.4, 0.3, 0.], [0.4, -0.9, -0.1, -0.],
[-1., -0., -0.1, -0.1], [-1., -0.1, -0.2, 0.1]])
pca = PCA(solver='svd')
pca.fit(X_std)
assert_almost_equal(pca.loadings_, expect, decimal=1)
def test_loadings():
expect = np.array([[0.9, -0.4, -0.3, 0.],
[-0.5, -0.9, 0.1, -0.],
[1., -0., 0.1, -0.1],
[1., -0.1, 0.2, 0.1]])
pca = PCA(solver='eigen')
pca.fit(X_std)
assert_almost_equal(pca.loadings_, expect, decimal=1)
expect = np.array([[-0.9, -0.4, 0.3, 0.],
[0.4, -0.9, -0.1, -0.],
[-1., -0., -0.1, -0.1],
[-1., -0.1, -0.2, 0.1]])
pca = PCA(solver='svd')
pca.fit(X_std)
assert_almost_equal(pca.loadings_, expect, decimal=1)
from sklearn.ensemble import ExtraTreesClassifier
from mlxtend.feature_extraction import PrincipalComponentAnalysis as PCA
from sklearn.model_selection import cross_val_score
import numpy as np
import matplotlib.pyplot as plt
X = np.genfromtxt('../../contest_data/xtrain_linear_imputed.csv', delimiter=',')
y = np.genfromtxt('../../contest_data/train.csv', delimiter=',')[1:,-1]
pca = PCA(n_components=1000)
X_pca = pca.fit(X).transform(X)
et = ExtraTreesClassifier(n_estimators=1000, max_depth=None, random_state=0,verbose=0)
scores = cross_val_score(et, X_pca, y,scoring='f1_micro',cv=5,verbose=5)
print scores.mean()
et = ExtraTreesClassifier(n_estimators=300, max_depth=None, random_state=0,verbose=1)
scores = cross_val_score(et, X, y,scoring='f1_micro',cv=5,verbose=5)
print scores.mean()
'''
components=1000,estimators=1000 gives 32.6% f1
'''
pca = PCA(n_components=1000)
def test_fail_array_transform():
pca = PCA(n_components=2)
pca.fit(X)
exp = pca.transform(X[1])
def test_default_components():
pca = PCA()
res = pca.fit(X_std).transform(X_std)
assert res.shape[1] == 4
def test_variance_explained_ratio():
pca = PCA()
pca.fit(X_std)
assert np.sum(pca.e_vals_normalized_) == 1.
assert np.sum(pca.e_vals_normalized_ < 0.) == 0
def test_fail_array_fit():
pca = PCA(n_components=2)
pca.fit(X[1])
def test_evals():
pca = PCA(n_components=2, solver='eigen')
pca.fit(X)
res = pca.fit(X).transform(X)
assert_almost_equal(pca.e_vals_, [2.93, 0.93, 0.15, 0.02], decimal=2)
def test_default_2components():
pca = PCA(n_components=2)
res = pca.fit(X).transform(X)
assert res.shape[1] == 2
def test_eigen_vs_svd():
pca = PCA(n_components=2, solver='eigen')
eigen_res = pca.fit(X).transform(X)
pca = PCA(n_components=2, solver='svd')
svd_res = pca.fit(X).transform(X)
assert_allclose(np.absolute(eigen_res), np.absolute(svd_res), atol=0.0001)
color='blue', marker='^', alpha=0.5)
plt.xlabel('x coordinate')
plt.ylabel('y coordinate')
#plt.show()
plt.savefig('../figs/tutorial/mlxtendex1_1.png')
plt.close()
# Moons are linearly inseperable so standard linear PCA will fail to accurately represent data in 1D space.
#Use PCA for dimensionality reduction
#specify number of components in PCA
pca = PCA(n_components=2)
#Transform X in accordance with 2-component PCA
X_pca = pca.fit(X).transform(X)
# Red half moon
plt.scatter(X_pca[y==0, 0], X_pca[y==0, 1], # Start and peak/troughof each 'moon'.
color ='red', marker='o', alpha=0.5)
#Blue half moon
plt.scatter(X_pca[y==1, 0], X_pca[y==1, 1], # Start and peak/troughof each 'moon'.
color='blue', marker='^', alpha=0.5)
plt.xlabel('PC1')
plt.ylabel('PC2')
#plt.show()
plt.savefig('../figs/tutorial/mlxtendex1_2.png')
plt.close()
def plot_pca_correlation_graph(X,
variables_names,
dimensions=(1, 2),
figure_axis_size=6,
X_pca=None,
explained_variance=None):
"""
Compute the PCA for X and plots the Correlation graph
Parameters
----------
X : 2d array like.
The columns represent the different variables and the rows are the
samples of thos variables
variables_names : array like
Name of the columns (the variables) of X
dimensions: tuple with two elements.
dimensions to be plotted (x,y)
figure_axis_size :
size of the final frame. The figure created is a square with length
and width equal to figure_axis_size.
X_pca : np.ndarray, shape = [n_samples, n_components].
Optional.
`X_pca` is the matrix of the transformed components from X.
If not provided, the function computes PCA automatically using
mlxtend.feature_extraction.PrincipalComponentAnalysis
Expected `n_componentes >= max(dimensions)`
explained_variance : 1 dimension np.ndarray, length = n_components
Optional.
`explained_variance` are the eigenvalues from the diagonalized
covariance matrix on the PCA transformatiopn.
If not provided, the function computes PCA independently
Expected `n_componentes == X.shape[1]`
Returns
----------
matplotlib_figure, correlation_matrix
Examples
-----------
For usage examples, please see
http://rasbt.github.io/mlxtend/user_guide/plotting/plot_pca_correlation_graph/
"""
X = np.array(X)
X = X - X.mean(axis=0)
n_comp = max(dimensions)
if (X_pca is None) and (explained_variance is None):
pca = PrincipalComponentAnalysis(n_components=n_comp)
pca.fit(X)
X_pca = pca.transform(X)
explained_variance = pca.e_vals_
elif (X_pca is not None) and (explained_variance is None):
raise ValueError("If `X_pca` is not None, the `explained variance`"
" values should not be `None`.")
elif (X_pca is None) and (explained_variance is not None):
raise ValueError("If `explained variance` is not None, the `X_pca`"
" values should not be `None`.")
elif (X_pca is not None) and (explained_variance is not None):
if X_pca.shape[1] != len(explained_variance):
raise ValueError(f"Number of principal components must "
f"match the number "
f"of eigenvalues. Got "
f"{X_pca.shape[1]} "
f"!= "
f"{len(explained_variance)}")
if X_pca.shape[1] < n_comp:
raise ValueError(f"Input array `X_pca` contains fewer principal"
f" components than expected based on `dimensions`."
f" Got {X_pca.shape[1]} components in X_pca, expected"
f" at least `max(dimensions)={n_comp}`.")
if len(explained_variance) < n_comp:
raise ValueError(f"Input array `explained_variance` contains fewer"
f" elements than expected. Got"
f" {len(explained_variance)} elements, expected"
f"`X.shape[1]={X.shape[1]}`.")
corrs = create_correlation_table(
X_pca, X, ['Dim ' + str(i + 1) for i in range(n_comp)],
variables_names)
tot = sum(X.var(0)) * X.shape[0] / (X.shape[0] - 1)
explained_var_ratio = [(i / tot) * 100 for i in explained_variance]
# Plotting circle
fig_res = plt.figure(figsize=(figure_axis_size, figure_axis_size))
plt.Circle((0, 0), radius=1, color='k', fill=False)
circle1 = plt.Circle((0, 0), radius=1, color='k', fill=False)
fig = plt.gcf()
fig.gca().add_artist(circle1)
# Plotting arrows
texts = []
for name, row in corrs.iterrows():
x = row['Dim ' + str(dimensions[0])]
y = row['Dim ' + str(dimensions[1])]
plt.arrow(0.0,
0.0,
x,
y,
color='k',
length_includes_head=True,
head_width=.05)
plt.plot([0.0, x], [0.0, y], 'k-')
texts.append(plt.text(x, y, name, fontsize=2 * figure_axis_size))
# Plotting vertical lines
plt.plot([-1.1, 1.1], [0, 0], 'k--')
plt.plot([0, 0], [-1.1, 1.1], 'k--')
# Adjusting text
adjust_text(texts)
# Setting limits and title
plt.xlim((-1.1, 1.1))
plt.ylim((-1.1, 1.1))
plt.title("Correlation Circle", fontsize=figure_axis_size * 3)
plt.xlabel("Dim " + str(dimensions[0]) +
" (%s%%)" % str(explained_var_ratio[dimensions[0] - 1])[:4],
fontsize=figure_axis_size * 2)
plt.ylabel("Dim " + str(dimensions[1]) +
" (%s%%)" % str(explained_var_ratio[dimensions[1] - 1])[:4],
fontsize=figure_axis_size * 2)
return fig_res, corrs
def test_default_components():
pca = PCA()
res = pca.fit(X_std).transform(X_std)
assert res.shape[1] == 4
def test_variance_explained_ratio():
pca = PCA()
pca.fit(X_std)
assert np.sum(pca.e_vals_normalized_) == 1.
assert np.sum(pca.e_vals_normalized_ < 0.) == 0
#print scores
np.savetxt('../../contest_data/xtest_tree_imputed.csv', xtrain, delimiter=',')
from sklearn.naive_bayes import MultinomialNB
gnb = MultinomialNB()
scores = cross_val_score(gnb,
xtrain,
ytrain,
scoring='f1_micro',
cv=5,
verbose=5)
print scores.mean()
pca = PCA(n_components=300)
xtrain_pca = pca.fit(xtrain[:, 500:]).transform(xtrain[:, 500:])
xtest_pca = pca.fit(xtrain[:, 500:]).transform(xtest[:, 500:])
#imputing test data
for i in range(500):
print i
train_missings = np.isnan(xtrain[:, i])
train_nonmissings = ~train_missings
test_missings = np.isnan(xtest[:, i])
test_nonmissings = ~test_missings
xtest[test_missings,
i] = lin.fit(xtrain_pca[train_nonmissings, :],
xtrain[train_nonmissings,
i]).predict(xtest_pca[test_missings, :])
np.savetxt('../../contest_data/xtest_linear_imputed.csv', xtest, delimiter=',')
'''
def test_default_2components():
pca = PCA(n_components=2)
res = pca.fit(X).transform(X)
assert res.shape[1] == 2
def test_variance_explained_ratio():
pca = PCA()
pca.fit(X_std)
assert math.isclose(np.sum(pca.e_vals_normalized_), 1.)
assert math.isclose(np.sum(pca.e_vals_normalized_ < 0.), 0, abs_tol=1e-10)
def test_evals():
pca = PCA(n_components=2, solver='eigen')
pca.fit(X)
res = pca.fit(X).transform(X)
assert_almost_equal(pca.e_vals_, [2.93, 0.93, 0.15, 0.02], decimal=2)
def plot_pca_correlation_graph(X,
variables_names,
dimensions=(1, 2),
figure_axis_size=6,
X_pca=None):
"""
Compute the PCA for X and plots the Correlation graph
Parameters
----------
X : 2d array like.
The columns represent the different variables and the rows are the
samples of thos variables
variables_names : array like
Name of the columns (the variables) of X
dimensions: tuple with two elements.
dimensions to be plot (x,y)
X_pca : optional. if not provided, compute PCA independently
figure_axis_size :
size of the final frame. The figure created is a square with length
and width equal to figure_axis_size.
Returns
----------
matplotlib_figure , correlation_matrix
"""
X = np.array(X)
X = X - X.mean(axis=0)
n_comp = max(dimensions)
if X_pca is None:
pca = PrincipalComponentAnalysis(n_components=n_comp)
pca.fit(X)
X_pca = pca.transform(X)
corrs = create_correlation_table(
X_pca, X, ['Dim ' + str(i + 1) for i in range(n_comp)],
variables_names)
tot = sum(pca.e_vals_)
explained_var_ratio = [(i / tot) * 100 for i in pca.e_vals_]
# Plotting circle
fig_res = plt.figure(figsize=(figure_axis_size, figure_axis_size))
plt.Circle((0, 0), radius=1, color='k', fill=False)
circle1 = plt.Circle((0, 0), radius=1, color='k', fill=False)
fig = plt.gcf()
fig.gca().add_artist(circle1)
# Plotting arrows
texts = []
for name, row in corrs.iterrows():
x = row['Dim ' + str(dimensions[0])]
y = row['Dim ' + str(dimensions[1])]
plt.arrow(0.0,
0.0,
x,
y,
color='k',
length_includes_head=True,
head_width=.05)
plt.plot([0.0, x], [0.0, y], 'k-')
texts.append(plt.text(x, y, name, fontsize=2 * figure_axis_size))
# Plotting vertical lines
plt.plot([-1.1, 1.1], [0, 0], 'k--')
plt.plot([0, 0], [-1.1, 1.1], 'k--')
# Adjusting text
adjust_text(texts)
# Setting limits and title
plt.xlim((-1.1, 1.1))
plt.ylim((-1.1, 1.1))
plt.title("Correlation Circle", fontsize=figure_axis_size * 3)
plt.xlabel("Dim " + str(dimensions[0]) + " (%s%%)" %
str(explained_var_ratio[dimensions[0] - 1])[:4].lstrip("0."),
fontsize=figure_axis_size * 2)
plt.ylabel("Dim " + str(dimensions[1]) + " (%s%%)" %
str(explained_var_ratio[dimensions[1] - 1])[:4].lstrip("0."),
fontsize=figure_axis_size * 2)
return fig_res, corrs
def test_eigen_vs_svd():
pca = PCA(n_components=2, solver='eigen')
eigen_res = pca.fit(X).transform(X)
pca = PCA(n_components=2, solver='svd')
svd_res = pca.fit(X).transform(X)
assert_allclose(np.absolute(eigen_res), np.absolute(svd_res), atol=0.0001)
def test_variance_explained_ratio():
pca = PCA()
pca.fit(X_std)
assert_almost_equal(np.sum(pca.e_vals_normalized_), 1.)
assert np.sum(pca.e_vals_normalized_ < 0.) == 0
def plot_pca_correlation_graph(X, variables_names, dimensions=(1, 2),
figure_axis_size=6, X_pca=None):
"""
Compute the PCA for X and plots the Correlation graph
Parameters
----------
X : 2d array like.
The columns represent the different variables and the rows are the
samples of thos variables
variables_names : array like
Name of the columns (the variables) of X
dimensions: tuple with two elements.
dimensions to be plot (x,y)
X_pca : optional. if not provided, compute PCA independently
figure_axis_size :
size of the final frame. The figure created is a square with length
and width equal to figure_axis_size.
Returns
----------
matplotlib_figure , correlation_matrix
"""
X = np.array(X)
X = X - X.mean(axis=0)
n_comp = max(dimensions)
if X_pca is None:
pca = PrincipalComponentAnalysis(n_components=n_comp)
pca.fit(X)
X_pca = pca.transform(X)
corrs = create_correlation_table(X_pca, X, ['Dim ' + str(i + 1) for i in
range(n_comp)],
variables_names)
tot = sum(pca.e_vals_)
explained_var_ratio = [(i / tot) * 100 for i in pca.e_vals_]
# Plotting circle
fig_res = plt.figure(figsize=(figure_axis_size, figure_axis_size))
plt.Circle((0, 0), radius=1, color='k', fill=False)
circle1 = plt.Circle((0, 0), radius=1, color='k', fill=False)
fig = plt.gcf()
fig.gca().add_artist(circle1)
# Plotting arrows
texts = []
for name, row in corrs.iterrows():
x = row['Dim ' + str(dimensions[0])]
y = row['Dim ' + str(dimensions[1])]
plt.arrow(0.0, 0.0, x, y, color='k', length_includes_head=True,
head_width=.05)
plt.plot([0.0, x], [0.0, y], 'k-')
texts.append(plt.text(x, y, name, fontsize=2 * figure_axis_size))
# Plotting vertical lines
plt.plot([-1.1, 1.1], [0, 0], 'k--')
plt.plot([0, 0], [-1.1, 1.1], 'k--')
# Adjusting text
adjust_text(texts)
# Setting limits and title
plt.xlim((-1.1, 1.1))
plt.ylim((-1.1, 1.1))
plt.title("Correlation Circle", fontsize=figure_axis_size * 3)
plt.xlabel("Dim " + str(dimensions[0]) + " (%s%%)" %
str(explained_var_ratio[dimensions[0] - 1])[:4].lstrip("0."),
fontsize=figure_axis_size * 2)
plt.ylabel("Dim " + str(dimensions[1]) + " (%s%%)" %
str(explained_var_ratio[dimensions[1] - 1])[:4].lstrip("0."),
fontsize=figure_axis_size * 2)
return fig_res, corrs
def test_default_components():
pca = PCA(n_components=0)
pca.fit(X)
res = pca.fit(X).transform(X)
