notes_estom/Python/scipy/14cluster.md

聚类

cluster.vq

Provides routines for k-means clustering, generating code books from k-means models and quantizing vectors by comparing them with centroids in a code book.

function	introduction
whiten(obs[, check_finite])	Normalize a group of observations on a per feature basis.每行元素除以该行的标准差。
vq(obs, code_book[, check_finite])	Assign codes from a code book to observations.
kmeans(obs, k_or_guess[, iter, thresh, …])	Performs k-means on a set of observation vectors forming k clusters.
kmeans2(data, k[, iter, thresh, minit, …])	Classify a set of observations into k clusters using the k-means algorithm.

cluster.hierarchy

Hierarchical clustering (scipy.cluster.hierarchy)

• These functions cut hierarchical clusterings into flat clusterings or find the roots of the forest formed by a cut by providing the flat cluster ids of each observation.

functions	introduction
fcluster(Z, t[, criterion, depth, R, monocrit])	Form flat clusters from the hierarchical clustering defined by the given linkage matrix.
fclusterdata(X, t[, criterion, metric, …])	Cluster observation data using a given metric.
leaders(Z, T)	Return the root nodes in a hierarchical clustering.

• These are routines for agglomerative clustering.

functions	introduction
linkage(y[, method, metric, optimal_ordering])	Perform hierarchical/agglomerative clustering.
single(y)	Perform single/min/nearest linkage on the condensed distance matrix y.
complete(y)	Perform complete/max/farthest point linkage on a condensed distance matrix.
average(y)	Perform average/UPGMA linkage on a condensed distance matrix.
weighted(y)	Perform weighted/WPGMA linkage on the condensed distance matrix.
centroid(y)	Perform centroid/UPGMC linkage.
median(y)	Perform median/WPGMC linkage.
ward(y)	Perform Ward’s linkage on a condensed distance matrix.

• These routines compute statistics on hierarchies.

functions	introduction
cophenet(Z[, Y])	Calculate the cophenetic distances between each observation in the hierarchical clustering defined by the linkage Z.
from_mlab_linkage(Z)	Convert a linkage matrix generated by MATLAB(TM) to a new linkage matrix compatible with this module.
inconsistent(Z[, d])	Calculate inconsistency statistics on a linkage matrix.
maxinconsts(Z, R)	Return the maximum inconsistency coefficient for each non-singleton cluster and its children.
maxdists(Z)	Return the maximum distance between any non-singleton cluster.
maxRstat(Z, R, i)	Return the maximum statistic for each non-singleton cluster and its children.

to_mlab_linkage(Z) | Convert a linkage matrix to a MATLAB(TM) compatible one.

• Routines for visualizing flat clusters.

functions	introduction
dendrogram(Z[, p, truncate_mode, …])	Plot the hierarchical clustering as a dendrogram.

• These are data structures and routines for representing hierarchies as tree objects.

functions	introduction
ClusterNode(id[, left, right, dist, count])	A tree node class for representing a cluster.
leaves_list(Z)	Return a list of leaf node ids.
to_tree(Z[, rd])	Convert a linkage matrix into an easy-to-use tree object.
cut_tree(Z[, n_clusters, height])	Given a linkage matrix Z, return the cut tree.
optimal_leaf_ordering(Z, y[, metric])	Given a linkage matrix Z and distance, reorder the cut tree.

• These are predicates for checking the validity of linkage and inconsistency matrices as well as for checking isomorphism of two flat cluster assignments.

functions	introduction
is_valid_im(R[, warning, throw, name])	Return True if the inconsistency matrix passed is valid.
is_valid_linkage(Z[, warning, throw, name])	Check the validity of a linkage matrix.
is_isomorphic(T1, T2)	Determine if two different cluster assignments are equivalent.
is_monotonic(Z)	Return True if the linkage passed is monotonic.
correspond(Z, Y)	Check for correspondence between linkage and condensed distance matrices.
num_obs_linkage(Z)	Return the number of original observations of the linkage matrix passed.

• Utility routines for plotting:

functions	introduction
set_link_color_palette(palette)	Set list of matplotlib color codes for use by dendrogram.

原理

K均值聚类是一种在一组未标记数据中查找聚类和聚类中心的方法。 直觉上，我们可以将一个群集(簇聚)看作 - 包含一组数据点，其点间距离与群集外点的距离相比较小。 给定一个K中心的初始集合，K均值算法重复以下两个步骤 -

• 对于每个中心，比其他中心更接近它的训练点的子集(其聚类)被识别出来。
• 计算每个聚类中数据点的每个要素的平均值，并且此平均向量将成为该聚类的新中心。

重复这两个步骤，直到中心不再移动或分配不再改变。 然后，可以将新点x分配给最接近的原型的群集。 SciPy库通过集群包提供了K-Means算法的良好实现。 下面来了解如何使用它。

实现

• 导入K-Means

from SciPy.cluster.vq import kmeans,vq,whiten
Python

• 数据生成

from numpy import vstack,array
from numpy.random import rand

# data generation with three features
data = vstack((rand(100,3) + array([.5,.5,.5]),rand(100,3)))

• 根据每个要素标准化一组观察值。 在运行K-Means之前，使用白化重新缩放观察集的每个特征维度是有好处的。 每个特征除以所有观测值的标准偏差以给出其单位差异。美化数据

# whitening of data
data = whiten(data)
print (data)

• 用三个集群计算K均值现在使用以下代码计算三个群集的K均值。

# computing K-Means with K = 3 (2 clusters)
centroids,_ = kmeans(data,3)

• 上述代码对形成K个簇的一组观测向量执行K均值。 K-Means算法调整质心直到不能获得足够的进展，即失真的变化，因为最后一次迭代小于某个阈值。 在这里，可以通过使用下面给出的代码打印centroids变量来观察簇。

print(centroids)

• 使用下面给出的代码将每个值分配给一个集群。

# assign each sample to a cluster
clx,_ = vq(data,centroids)

• vq函数将'M'中的每个观察向量与'N' obs数组与centroids进行比较，并将观察值分配给最近的聚类。 它返回每个观察和失真的聚类。 我们也可以检查失真。使用下面的代码检查每个观察的聚类。