在数据的多变量统计和聚类里，谱聚类技术使用数据的相似矩阵的谱（即，相似矩阵的特征值）降低特征的维度。然后，在降维后的空间使用k-means聚类。其中的相似矩阵度量了数据集的任何两点的相似性。

这个例子产生一个带有连接的圆圈区域的图像，使用谱聚类法(spectral clustering)分隔出这些区域。在这种情况下，谱聚类法解决了标准的图像分割问题：图像被当作一个由三维像素连接的图，谱聚类算法等于是选择图分割的区域，最小化沿着分割的梯度改变率。因为该算法试图平衡区域的大小，如果我们分隔的圆圈大小不同，分割就等于失败了。

实例详解

首先，从scikit-learn的feature_extraction导入image, 从clusters导入谱聚类函数spectral_clustering. 在image里定义4个圆圈区域。

import numpy as np
import matplotlib.pyplot as plt

from sklearn.feature_extraction import image
from sklearn.cluster import spectral_clustering

l = 100
x, y = np.indices((l, l))

center1 = (28, 24)
center2 = (40, 50)
center3 = (67, 58)
center4 = (24, 70)

radius1, radius2, radius3, radius4 = 16, 14, 15, 14

circle1 = (x - center1[0]) ** 2 + (y - center1[1]) ** 2 < radius1 ** 2
circle2 = (x - center2[0]) ** 2 + (y - center2[1]) ** 2 < radius2 ** 2
circle3 = (x - center3[0]) ** 2 + (y - center3[1]) ** 2 < radius3 ** 2
circle4 = (x - center4[0]) ** 2 + (y - center4[1]) ** 2 < radius4 ** 2
在这里，我们想要分隔出定义的4个区域，而不是把它们从背景里分隔出来。因此，我们使用一个mask限制背景。

# 4 circles
img = circle1 + circle2 + circle3 + circle4

# We use a mask that limits to the foreground: the problem that we are
# interested in here is not separating the objects from the background,
# but separating them one from the other.
mask = img.astype(bool)

img = img.astype(float)
img += 1 + 0.2 * np.random.randn(*img.shape)

# Convert the image into a graph with the value of the gradient on the
# edges.
graph = image.img_to_graph(img, mask=mask)

# Take a decreasing function of the gradient: we take it weakly
# dependent from the gradient the segmentation is close to a voronoi
graph.data = np.exp(-graph.data / graph.data.std())

# Force the solver to be arpack, since amg is numerically
# unstable on this example
labels = spectral_clustering(graph, n_clusters=4, eigen_solver='arpack')
label_im = np.full(mask.shape, -1.)
label_im[mask] = labels

plt.matshow(img)
plt.matshow(label_im)

plt.show()


下面的程序分隔出2个圆圈区域。

# 2 circles
img = circle1 + circle2
mask = img.astype(bool)
img = img.astype(float)

img += 1 + 0.2 * np.random.randn(*img.shape)

graph = image.img_to_graph(img, mask=mask)
graph.data = np.exp(-graph.data / graph.data.std())

labels = spectral_clustering(graph, n_clusters=2, eigen_solver='arpack')
label_im = np.full(mask.shape, -1.)
label_im[mask] = labels

plt.matshow(img)
plt.matshow(label_im)

plt.show()


---------------------
【转载】
作者：Goodsta
原文：https://blog.csdn.net/wong2016/article/details/84501627