3、手写数字上的流形学习
from time import time
import numpy as np
import matplotlib.pyplot as plt
from matplotlib import offsetbox
from sklearn import (manifold, datasets, decomposition, ensemble,
discriminant_analysis, random_projection, neighbors)
print(__doc__)
plt.rcParams['font.sans-serif'] = ['SimHei']
plt.rcParams['axes.unicode_minus'] = False
digits = datasets.load_digits(n_class=6)
X = digits.data
y = digits.target
n_samples, n_features = X.shape
n_neighbors = 30
# 嵌入向量的缩放和可视化
def plot_embedding(X, title=None):
x_min, x_max = np.min(X, 0), np.max(X, 0)
X = (X - x_min) / (x_max - x_min)
plt.figure()
ax = plt.subplot(111)
for i in range(X.shape[0]):
plt.text(X[i, 0], X[i, 1], str(y[i]),
color=plt.cm.Set1(y[i] / 10.),
fontdict={'weight': 'bold', 'size': 9})
if hasattr(offsetbox, 'AnnotationBbox'):
# 仅使用matplotlib>1.0打印缩略图
shown_images = np.array([[1., 1.]]) # just something big
for i in range(X.shape[0]):
dist = np.sum((X[i] - shown_images) ** 2, 1)
if np.min(dist) < 4e-3:
# 不要显示太接近的点
continue
shown_images = np.r_[shown_images, [X[i]]]
imagebox = offsetbox.AnnotationBbox(
offsetbox.OffsetImage(digits.images[i], cmap=plt.cm.gray_r),
X[i])
ax.add_artist(imagebox)
plt.xticks([]), plt.yticks([])
if title is not None:
plt.title(title)
#绘制数字图像
n_img_per_row = 20
img = np.zeros((10 * n_img_per_row, 10 * n_img_per_row))
for i in range(n_img_per_row):
ix = 10 * i + 1
for j in range(n_img_per_row):
iy = 10 * j + 1
img[ix:ix + 8, iy:iy + 8] = X[i * n_img_per_row + j].reshape((8, 8))
plt.imshow(img, cmap=plt.cm.binary)
plt.xticks([])
plt.yticks([])
plt.title('64维数字数据集中的选择')
# 利用随机酉矩阵的随机二维投影
print("Computing random projection")
rp = random_projection.SparseRandomProjection(n_components=2, random_state=42)
X_projected = rp.fit_transform(X)
plot_embedding(X_projected, "数字的随机投影")
# 对前2个主成分的投影
print("Computing PCA projection")
t0 = time()
X_pca = decomposition.TruncatedSVD(n_components=2).fit_transform(X)
plot_embedding(X_pca,
"数字的主成分投影 (time %.2fs)" %
(time() - t0))
#关于前2个线性判别分量的投影
print("Computing Linear Discriminant Analysis projection")
X2 = X.copy()
X2.flat[::X.shape[1] + 1] += 0.01 # 使X可逆
t0 = time()
X_lda = discriminant_analysis.LinearDiscriminantAnalysis(n_components=2
).fit_transform(X2, y)
plot_embedding(X_lda,
"数字的线性判别投影 (time %.2fs)" %
(time() - t0))
# 数字数据集的Isomap投影
print("Computing Isomap projection")
t0 = time()
X_iso = manifold.Isomap(n_neighbors=n_neighbors, n_components=2
).fit_transform(X)
print("Done.")
plot_embedding(X_iso,
"数字的Isomap投影 (time %.2fs)" %
(time() - t0))
# 数字数据集的局部线性嵌入
print("Computing LLE embedding")
clf = manifold.LocallyLinearEmbedding(n_neighbors=n_neighbors, n_components=2,
method='standard')
t0 = time()
X_lle = clf.fit_transform(X)
print("Done. Reconstruction error: %g" % clf.reconstruction_error_)
plot_embedding(X_lle,
"数字的局部线性嵌入 (time %.2fs)" %
(time() - t0))
# 数字数据集的改进局部线性嵌入
print("Computing modified LLE embedding")
clf = manifold.LocallyLinearEmbedding(n_neighbors=n_neighbors, n_components=2,
method='modified')
t0 = time()
X_mlle = clf.fit_transform(X)
print("Done. Reconstruction error: %g" % clf.reconstruction_error_)
plot_embedding(X_mlle,
"修正的数字局部线性嵌入 (time %.2fs)" %
(time() - t0))
# 数字数据集的HLLE嵌入
print("Computing Hessian LLE embedding")
clf = manifold.LocallyLinearEmbedding(n_neighbors=n_neighbors, n_components=2,
method='hessian')
t0 = time()
X_hlle = clf.fit_transform(X)
print("Done. Reconstruction error: %g" % clf.reconstruction_error_)
plot_embedding(X_hlle,
"数字的Hessian局部线性嵌入 (time %.2fs)" %
(time() - t0))
# 数字数据集的LTSA嵌入
print("Computing LTSA embedding")
clf = manifold.LocallyLinearEmbedding(n_neighbors=n_neighbors, n_components=2,
method='ltsa')
t0 = time()
X_ltsa = clf.fit_transform(X)
print("Done. Reconstruction error: %g" % clf.reconstruction_error_)
plot_embedding(X_ltsa,
"数字的局部切空间对齐 (time %.2fs)" %
(time() - t0))
# 数字数据集的MDS嵌入
print("Computing MDS embedding")
clf = manifold.MDS(n_components=2, n_init=1, max_iter=100)
t0 = time()
X_mds = clf.fit_transform(X)
print("Done. Stress: %f" % clf.stress_)
plot_embedding(X_mds,
"数字的MDS嵌入 (time %.2fs)" %
(time() - t0))
# 数字数据集的随机树嵌入
print("Computing Totally Random Trees embedding")
hasher = ensemble.RandomTreesEmbedding(n_estimators=200, random_state=0,
max_depth=5)
t0 = time()
X_transformed = hasher.fit_transform(X)
pca = decomposition.TruncatedSVD(n_components=2)
X_reduced = pca.fit_transform(X_transformed)
plot_embedding(X_reduced,
"数字的随机森林嵌入 (time %.2fs)" %
(time() - t0))
# 数字数据集的谱嵌入
print("Computing Spectral embedding")
embedder = manifold.SpectralEmbedding(n_components=2, random_state=0,
eigen_solver="arpack")
t0 = time()
X_se = embedder.fit_transform(X)
plot_embedding(X_se,
"数字的谱嵌入 (time %.2fs)" %
(time() - t0))
# 数字数据集的t-SNE嵌入
print("Computing t-SNE embedding")
tsne = manifold.TSNE(n_components=2, init='pca', random_state=0)
t0 = time()
X_tsne = tsne.fit_transform(X)
plot_embedding(X_tsne,
"数字的t-SNE嵌入 (time %.2fs)" %
(time() - t0))
# 数字数据集的NCA投影
print("Computing NCA projection")
nca = neighbors.NeighborhoodComponentsAnalysis(init='random',
n_components=2, random_state=0)
t0 = time()
X_nca = nca.fit_transform(X, y)
plot_embedding(X_nca,
"数字的NCA嵌入 (time %.2fs)" %
(time() - t0))
plt.show()
