流形学习（sklearn调包的demo）

• 导入数据
• 可视化数字
• 可视化的函数
• 流形学习的算法
• 对图像数据进行非线性降维（降至2维）
• 可视化降维情况

from sklearn.datasets import load_digits

digits = load_digits(n_class=6)
X, y = digits.data, digits.target
n_samples, n_features = X.shape
n_neighbors = 30

import matplotlib.pyplot as plt

fig, axs = plt.subplots(nrows=10, ncols=10, figsize=(6, 6))
for idx, ax in enumerate(axs.ravel()):
    ax.imshow(X[idx].reshape((8, 8)), cmap=plt.cm.binary)
    ax.axis("off")
    fig.suptitle("A selection from the 64-dimensional digits dataset", fontsize=16)

import numpy as np
from matplotlib import offsetbox
from sklearn.preprocessing import MinMaxScaler


def plot_embedding(X, title, ax):
    # 标准化数据
    X = MinMaxScaler().fit_transform(X)

    shown_images = np.array([[1.0, 1.0]])  # 一个二维点，值较大
    for i in range(X.shape[0]):
        # 打印一个数字
        ax.text(
            X[i, 0],
            X[i, 1],
            str(y[i]),
            color=plt.cm.Dark2(y[i]),
            fontdict={"weight": "bold", "size": 9},
        )
        dist = np.sum((X[i] - shown_images) ** 2, 1)
        if np.min(dist) < 4e-3:
            # 太近的点不打印
            continue
        # 上下叠在一起
        shown_images = np.concatenate([shown_images, [X[i]]], axis=0)
        # 注释框
        imagebox = offsetbox.AnnotationBbox(
            offsetbox.OffsetImage(digits.images[i], cmap=plt.cm.gray_r), X[i]
        )
        ax.add_artist(imagebox)

    ax.set_title(title)
    ax.axis("off")

from sklearn.decomposition import TruncatedSVD
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis
from sklearn.ensemble import RandomTreesEmbedding
from sklearn.manifold import (
    Isomap,
    LocallyLinearEmbedding,
    MDS,
    SpectralEmbedding,
    TSNE,
)
from sklearn.neighbors import NeighborhoodComponentsAnalysis
from sklearn.pipeline import make_pipeline
from sklearn.random_projection import SparseRandomProjection

embeddings = {
    "Random projection embedding": SparseRandomProjection(
        n_components=2, random_state=42
    ),
    "Truncated SVD embedding": TruncatedSVD(n_components=2),
    "Linear Discriminant Analysis embedding": LinearDiscriminantAnalysis(
        n_components=2
    ),
    "Isomap embedding": Isomap(n_neighbors=n_neighbors, n_components=2),
    "Standard LLE embedding": LocallyLinearEmbedding(
        n_neighbors=n_neighbors, n_components=2, method="standard"
    ),
    "Modified LLE embedding": LocallyLinearEmbedding(
        n_neighbors=n_neighbors, n_components=2, method="modified"
    ),
    "Hessian LLE embedding": LocallyLinearEmbedding(
        n_neighbors=n_neighbors, n_components=2, method="hessian"
    ),
    "LTSA LLE embedding": LocallyLinearEmbedding(
        n_neighbors=n_neighbors, n_components=2, method="ltsa"
    ),
    "MDS embedding": MDS(n_components=2, n_init=1, max_iter=100),
    "Random Trees embedding": make_pipeline(
        RandomTreesEmbedding(n_estimators=200, max_depth=5, random_state=0),
        TruncatedSVD(n_components=2),
    ),
    "Spectral embedding": SpectralEmbedding(
        n_components=2, random_state=0, eigen_solver="arpack"
    ),
    "t-SNE embeedding": TSNE(
        n_components=2, init="pca", learning_rate="auto", random_state=0
    ),
    "NCA embedding": NeighborhoodComponentsAnalysis(
        n_components=2, init="random", random_state=0
    ),
}

from time import time

projections, timing = {}, {}
for name, transformer in embeddings.items():
    if name.startswith("Linear Discriminant Analysis"):
        data = X.copy()
        data.flat[:: X.shape[1] + 1] += 0.01  # 矩阵对角线上添加扰动，使X可逆
    else:
        data = X
    try:
        print(f"Computing {name}...")
        start_time = time()
        # 非线性降维至二维
        projections[name] = transformer.fit_transform(data, y)
        timing[name] = time() - start_time
    except :
        continue

from itertools import zip_longest

fig, axs = plt.subplots(nrows=7, ncols=2, figsize=(17, 24))

for name, ax in zip_longest(timing, axs.ravel()):
    if name is None:
        ax.axis("off")
        continue
    title = f"{name} (time {timing[name]:.3f}s)"
    plot_embedding(projections[name], title, ax)

plt.show()