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import time
for n_components in (2, 10, 154):
print("n_components =", n_components)
regular_pca = PCA(n_components=n_components)
inc_pca = IncrementalPCA(n_components=n_components, batch_size=500)
rnd_pca = PCA(n_components=n_components, random_state=42, svd_solver="randomized")
for pca in (regular_pca, inc_pca, rnd_pca):
t1 = time.time()
pca.fit(X_train)
t2 = time.time()
print(" {}: {:.1f} seconds".format(pca.__class__.__name__, t2 - t1))
n_components = 2
PCA: 1.1 seconds
IncrementalPCA: 7.2 seconds
PCA: 1.0 seconds
n_components = 10
PCA: 1.5 seconds
IncrementalPCA: 7.5 seconds
PCA: 1.5 seconds
n_components = 154
PCA: 2.7 seconds
IncrementalPCA: 9.5 seconds
PCA: 2.8 seconds
times_rpca = []
times_pca = []
sizes = [1000, 10000, 20000, 30000, 40000, 50000, 70000, 100000, 200000, 500000]
for n_samples in sizes:
X = np.random.randn(n_samples, 5)
pca = PCA(n_components = 2, svd_solver="randomized", random_state=42)
t1 = time.time()
pca.fit(X)
t2 = time.time()
times_rpca.append(t2 - t1)
pca = PCA(n_components = 2)
t1 = time.time()
pca.fit(X)
t2 = time.time()
times_pca.append(t2 - t1)
plt.plot(sizes, times_rpca, "b-o", label="RPCA")
plt.plot(sizes, times_pca, "r-s", label="PCA")
plt.xlabel("n_samples")
plt.ylabel("Training time")
plt.legend(loc="upper left")
plt.title("PCA and Randomized PCA time complexity ")
Out[53]: Text(0.5, 1.0, 'PCA and Randomized PCA time complexity ')
times_rpca = []
times_pca = []
sizes = [1000, 2000, 3000, 4000, 5000, 6000]
for n_features in sizes:
X = np.random.randn(2000, n_features)
pca = PCA(n_components = 2, random_state=42, svd_solver="randomized")
t1 = time.time()
pca.fit(X)
t2 = time.time()
times_rpca.append(t2 - t1)
pca = PCA(n_components = 2)
t1 = time.time()
pca.fit(X)
t2 = time.time()
times_pca.append(t2 - t1)
plt.plot(sizes, times_rpca, "b-o", label="RPCA")
plt.plot(sizes, times_pca, "r-s", label="PCA")
plt.xlabel("n_features")
plt.ylabel("Training time")
plt.legend(loc="upper left")
plt.title("PCA and Randomized PCA time complexity ")
Out[54]: Text(0.5, 1.0, 'PCA and Randomized PCA time complexity ')
X, t = make_swiss_roll(n_samples=1000, noise=0.2, random_state=42)
from sklearn.decomposition import KernelPCA
rbf_pca = KernelPCA(n_components = 2, kernel="rbf", gamma=0.04)
X_reduced = rbf_pca.fit_transform(X)
from sklearn.decomposition import KernelPCA
lin_pca = KernelPCA(n_components = 2, kernel="linear", fit_inverse_transform=True)
rbf_pca = KernelPCA(n_components = 2, kernel="rbf", gamma=0.0433, fit_inverse_transform=True)
sig_pca = KernelPCA(n_components = 2, kernel="sigmoid", gamma=0.001, coef0=1, fit_inverse_transform=True)
y = t > 6.9
plt.figure(figsize=(11, 4))
for subplot, pca, title in ((131, lin_pca, "Linear kernel"), (132, rbf_pca, "RBF kernel, $\gamma=0.04$"), (133, sig_pca, "Sigmoid kernel, $\gamma=10^{-3}, r=1$")):
X_reduced = pca.fit_transform(X)
if subplot == 132:
X_reduced_rbf = X_reduced
plt.subplot(subplot)
#plt.plot(X_reduced[y, 0], X_reduced[y, 1], "gs")
#plt.plot(X_reduced[~y, 0], X_reduced[~y, 1], "y^")
plt.title(title, fontsize=14)
plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=t, cmap=plt.cm.hot)
plt.xlabel("$z_1$", fontsize=18)
if subplot == 131:
plt.ylabel("$z_2$", fontsize=18, rotation=0)
plt.grid(True)
save_fig("kernel_pca_plot")
plt.show()
Saving figure kernel_pca_plot
Traceback (most recent call last):
plt.figure(figsize=(6, 5))
X_inverse = rbf_pca.inverse_transform(X_reduced_rbf)
ax = plt.subplot(111, projection='3d')
ax.view_init(10, -70)
ax.scatter(X_inverse[:, 0], X_inverse[:, 1], X_inverse[:, 2], c=t, cmap=plt.cm.hot, marker="x")
ax.set_xlabel("")
ax.set_ylabel("")
ax.set_zlabel("")
ax.set_xticklabels([])
ax.set_yticklabels([])
ax.set_zticklabels([])
save_fig("preimage_plot", tight_layout=False)
plt.show()
Saving figure preimage_plot
plt.figure(figsize=(6, 5))
X_inverse = rbf_pca.inverse_transform(X_reduced_rbf)
ax = plt.subplot(111, projection='3d')
ax.view_init(10, -70)
ax.scatter(X_inverse[:, 0], X_inverse[:, 1], X_inverse[:, 2], c=t, cmap=plt.cm.hot, marker="x")
ax.set_xlabel("")
ax.set_ylabel("")
ax.set_zlabel("")
ax.set_xticklabels([])
ax.set_yticklabels([])
ax.set_zticklabels([])
save_fig("preimage_plot", tight_layout=False)
plt.show()
Saving figure preimage_plot
X_reduced = rbf_pca.fit_transform(X)
plt.figure(figsize=(11, 4))
plt.subplot(132)
plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=t, cmap=plt.cm.hot, marker="x")
plt.xlabel("$z_1$", fontsize=18)
plt.ylabel("$z_2$", fontsize=18, rotation=0)
plt.grid(True)
from sklearn.model_selection import GridSearchCV
from sklearn.linear_model import LogisticRegression
from sklearn.pipeline import Pipeline
clf = Pipeline([
("kpca", KernelPCA(n_components=2)),
("log_reg", LogisticRegression(solver="liblinear"))
])
param_grid = [{
"kpca__gamma": np.linspace(0.03, 0.05, 10),
"kpca__kernel": ["rbf", "sigmoid"]
}]
grid_search = GridSearchCV(clf, param_grid, cv=3)
grid_search.fit(X, y)
Out[61]:
GridSearchCV(cv=3, error_score=nan,
estimator=Pipeline(memory=None,
steps=[('kpca',
KernelPCA(alpha=1.0, coef0=1,
copy_X=True, degree=3,
eigen_solver='auto',
fit_inverse_transform=False,
gamma=None, kernel='linear',
kernel_params=None,
max_iter=None, n_components=2,
n_jobs=None,
random_state=None,
remove_zero_eig=False,
tol=0)),
('log_reg',
LogisticRegression(C=1.0,
cl...
solver='liblinear',
tol=0.0001,
verbose=0,
warm_start=False))],
verbose=False),
iid='deprecated', n_jobs=None,
param_grid=[{'kpca__gamma': array([0.03 , 0.03222222, 0.03444444, 0.03666667, 0.03888889,
0.04111111, 0.04333333, 0.04555556, 0.04777778, 0.05 ]),
'kpca__kernel': ['rbf', 'sigmoid']}],
pre_dispatch='2*n_jobs', refit=True, return_train_score=False,
scoring=None, verbose=0)
print(grid_search.best_params_)
{'kpca__gamma': 0.043333333333333335, 'kpca__kernel': 'rbf'}
rbf_pca = KernelPCA(n_components = 2, kernel="rbf", gamma=0.0433,
fit_inverse_transform=True)
X_reduced = rbf_pca.fit_transform(X)
X_preimage = rbf_pca.inverse_transform(X_reduced)
from sklearn.metrics import mean_squared_error
mean_squared_error(X, X_preimage)
Out[64]: 32.78630879576615
#################### 局部线性嵌入 ########################
X, t = make_swiss_roll(n_samples=1000, noise=0.2, random_state=41)
from sklearn.manifold import LocallyLinearEmbedding
lle = LocallyLinearEmbedding(n_components=2, n_neighbors=10, random_state=42)
X_reduced = lle.fit_transform(X)
plt.title("Unrolled swiss roll using LLE", fontsize=14)
plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=t, cmap=plt.cm.hot)
plt.xlabel("$z_1$", fontsize=18)
plt.ylabel("$z_2$", fontsize=18)
plt.axis([-0.065, 0.055, -0.1, 0.12])
plt.grid(True)
save_fig("lle_unrolling_plot")
plt.show()
#####################其他降维技巧 #########################
from sklearn.manifold import MDS
mds = MDS(n_components=2, random_state=42)
X_reduced_mds = mds.fit_transform(X)
from sklearn.manifold import Isomap
isomap = Isomap(n_components=2)
X_reduced_isomap = isomap.fit_transform(X)
from sklearn.manifold import TSNE
tsne = TSNE(n_components=2, random_state=42)
X_reduced_tsne = tsne.fit_transform(X)
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
lda = LinearDiscriminantAnalysis(n_components=2)
X_mnist = mnist["data"]
y_mnist = mnist["target"]
lda.fit(X_mnist, y_mnist)
X_reduced_lda = lda.transform(X_mnist)
titles = ["MDS", "Isomap", "t-SNE"]
plt.figure(figsize=(11,4))
for subplot, title, X_reduced in zip((131, 132, 133), titles,
(X_reduced_mds, X_reduced_isomap, X_reduced_tsne)):
plt.subplot(subplot)
plt.title(title, fontsize=14)
plt.scatter(X_reduced[:, 0], X_reduced[:, 1], c=t, cmap=plt.cm.hot)
plt.xlabel("$z_1$", fontsize=18)
if subplot == 131:
plt.ylabel("$z_2$", fontsize=18, rotation=0)
plt.grid(True)
save_fig("other_dim_reduction_plot")
plt.show()
Saving figure other_dim_reduction_plot
