Affinity Propagation

Affinity propagation
其中两点相似度s(i, j)的度量默认采用负欧氏距离。
sklearn.cluster.AffinityPropagation
有参数preference（设定每一个点的偏好，将偏好于跟其他节点的相似性进行比较，选择
高的作为exmplar,未设定则使用所有相似性的中位数）、damping （阻尼系数，
利用阻尼系数与1-阻尼系数对r 及 a进行有关迭代步数的凸组合，使得算法收敛
default 0.5 可以取值与[0.5, 1)）

cluster_centers_indices_:中心样本的指标。

利用条件熵定义的同质性度量：
sklearn.metrics.homogeneity_score:每一个聚出的类仅包含一个类别的程度度量。
sklearn.metrics.completeness:每一个类别被指向相同聚出的类的程度度量。
sklearn.metrics.v_measure_score:上面两者的一种折衷：
 v = 2 * (homogeneity * completeness) / (homogeneity + completeness)
 可以作为聚类结果的一种度量。
sklearn.metrics.adjusted_rand_score:调整兰德系数。
sklearn.metrics.adjusted_mutual_info_score:调整互信息。
sklearn.metrics.silhouette_score:
 对于一个样本点(b - a)/max(a, b)
 a平均类内距离，b样本点到与其最近的非此类的距离。
 silihouette_score返回的是所有样本的该值。
这些度量均是越大越好（类似于判别）

下面是例子：

from sklearn.cluster import AffinityPropagation from sklearn import metrics from sklearn.datasets.samples_generator import make_blobs centers = [[1, 1], [-1, -1], [1, -1]]X, labels_true = make_blobs(n_samples = 300, centers = centers, cluster_std = 0.5, random_state = 0)af = AffinityPropagation(preference = -50).fit(X)cluster_centers_indices = af.cluster_centers_indices_labels = af.labels_ n_clusters_ = len(cluster_centers_indices)print "Estimated number of clusters: %d" % n_clusters_ print "Homogeneity: %0.3f" % metrics.homogeneity_score(labels_true, labels)print "Completeness: %0.3f" % metrics.completeness_score(labels_true, labels)print "V-measure: %0.3f" % metrics.v_measure_score(labels_true, labels)print "Adjusted Rand Index: %0.3f" % metrics.adjusted_rand_score(labels_true, labels)print "Adjusted Mutual Information: %0.3f" % metrics.adjusted_mutual_info_score(labels_true, labels)print "Silhouette Coefficiet: %0.3f" % metrics.silhouette_score(X, labels, metric = 'sqeuclidean')import matplotlib.pyplot as plt from itertools import cycle plt.close('all')plt.figure(1)plt.clf()colors = cycle('bgrcmyk')for k, col in zip(range(n_clusters_), colors): class_members = labels == k cluster_center = X[cluster_centers_indices[k]] plt.plot(X[class_members, 0], X[class_members, 1], col + '.') plt.plot(cluster_center[0], cluster_center[1], 'o', markerfacecolor = col, \   markeredgecolor = 'k', markersize = 14) for x in X[class_members]:  plt.plot([cluster_center[0], x[0]], [cluster_center[1], x[1]], col)plt.title('Estimated number of clusters: %d' % n_clusters_)plt.show()