在K-Means算法中使用肘部法寻找最佳聚类数_肘部法确定最佳聚类中心

1.from scipy.cluster.vq import kmeans包的介绍：

输入 数据集和簇的数量 

返回 聚类中心坐标（codebook）、观测值与生成的质心之间的平均（非平方）欧氏距离（distortion）

例1：

import numpy as np
from scipy.cluster.vq import vq, kmeans, whiten
import matplotlib.pyplot as plt
 
features = np.array([[1,1],
                     [2,2],
                     [3,3],
                     [4,4],
                     [5,5]])
 
wf = whiten(features)
print("whiten features: \n", wf)
 
book = np.array((wf[0], wf[1]))
 
codebook, distortion = kmeans(wf, book)
# 可以写kmeans(wf,2)， 2表示两个质心，同时启用iter参数
print("codebook:", codebook)
print("distortion: ", distortion)
 
plt.scatter(wf[:,0], wf[:,1])
plt.scatter(codebook[:, 0], codebook[:, 1], c='r')
plt.show()

结果：

whiten features: 
 [[0.70710678 0.70710678]
 [1.41421356 1.41421356]
 [2.12132034 2.12132034]
 [2.82842712 2.82842712]
 [3.53553391 3.53553391]]
codebook: [[1.06066017 1.06066017]
 [2.82842712 2.82842712]]
distortion:  0.5999999999999999

例2：

import numpy as np
from scipy.cluster.vq import vq, kmeans, whiten
import matplotlib.pyplot as plt
pts = 5
a = np.random.multivariate_normal([0, 0], [[4, 1], [1, 4]], size=pts)
b = np.random.multivariate_normal([30, 10],
                             [[10, 2], [2, 10]],
                                  size=pts)#np.random.multivariate_normal这个官方解释说从多元正态分布中抽取随机样本
features = np.concatenate((a, b))
#print(features)
print(features.shape)
whitened = whiten(features)
print(whitened)
codebook, distortion = kmeans(whitened, 2)  #这个Kmeans好像只返回聚类中心、观测值和聚类中心之间的失真
plt.scatter(whitened[:, 0], whitened[:, 1],c = 'g')
plt.scatter(codebook[:, 0], codebook[:, 1], c='r')
plt.show()

结果：

(10, 2)
[[-0.01741221 -0.49577372]
 [-0.08524789 -0.17768591]
 [ 0.0657376   0.47027214]
 [ 0.27825025 -0.37835465]
 [-0.0079966   0.50196071]
 [ 1.824303    2.55040188]
 [ 2.05886112  2.08174181]
 [ 2.13775252  1.69008105]
 [ 2.26411531  1.2035603 ]
 [ 1.83463368  0.45632992]]

2.针对鸢尾花数据集的k-means的肘部法优化的聚类

"""Find optimal number of clustres from a Dataset."""
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from scipy.cluster.vq import kmeans
from sklearn.datasets import load_iris
from scipy.spatial.distance import cdist
from scipy.spatial.distance import pdist
 
 
def load_dataset():
    """Load dataset."""
    # Loading dataset.
    return load_iris().data
 
 
def find_clusters(dataset):
    """Function to find optimal number of clusters in dataset."""
    # cluster data into K=1..10 clusters
    num_clusters = range(1, 50)
    #从1到50个分别进行聚类，得到50种kmeans的质点坐标和欧式距离
    k_means = [kmeans(dataset, k) for k in num_clusters]
    # cluster's centroids，得到k_means的质点坐标
    centroids = [cent for (cent, var) in k_means]
    #计算[ [每个数据点到每个质点的距离] (<-中括号为一个点到每个质点的距离)....] <-指当质心数为某时，所有点到质点距离的集合
    clusters_dist = [cdist(dataset, cent, 'euclidean') for cent in centroids]
    #argmin：返回每组距离矩阵最小的值的下标。这里每组的意思是一个点到每个质点的距离集合。
    # #所以这里用来判断该数据属于哪一类（哪一个质点），并且argmin会将多重数组平铺成一重数组，即每组clusters_dist都会放到同一个数组中，即最后只有50组数组
    cidx = [np.argmin(_dist, axis=1) for _dist in clusters_dist]
    #返回最短的距离
    dist = [np.min(_dist, axis=1) for _dist in clusters_dist]
    # Mean within-cluster (sum of squares)
    avg_within_sum_sqrd = [sum(d) / dataset.shape[0] for d in dist]
    return {'cidx': cidx, 'avg_within_sum_sqrd': avg_within_sum_sqrd,
            'K': num_clusters}
 
 
def plot_elbow_curv(details):
    """Function to plot elbo curv."""
    kidx = 2
    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.plot(details['K'], details['avg_within_sum_sqrd'], 'b*-')
    ax.plot(details['K'][kidx], details['avg_within_sum_sqrd'][kidx],
            marker='o', markersize=12, markeredgewidth=2,
            markeredgecolor='r', markerfacecolor='None')
    plt.grid(True)
    plt.xlabel('Number of clusters')
    plt.ylabel('Average within-cluster sum of squares')
    plt.title('Elbow for KMeans clustering')
 
 
def scatter_plot(dataset, details):
    """Function to plot scatter plot of clusters."""
    kidx = 2
    fig = plt.figure()
    ax = fig.add_subplot(111)
    clr = ['b', 'g', 'r', 'c', 'm', 'y', 'k']
    #这个循环为质点个数，每次循环代表一个聚落
    for i in range(details['K'][kidx]):
        #返回Ture或False
        #其实就是当前聚落设为True,其余为False。数组读取的只能为True的值
        ind = (details['cidx'][kidx] == i)
        #数组[Ture,0]指取[0]值，数组[False,0]指不取[0]值
        #dataset[ind[index],2]指：取dataset的第二列的每行，其中ind对应行为False时dataset数组不取
        ax.scatter(dataset[ind, 2], dataset[ind, 1],
                   s=30, c=clr[i], label='Cluster %d' % i)
    plt.xlabel('Petal Length')
    plt.ylabel('Sepal Width')
    plt.title('Iris Dataset, KMeans clustering with K=%d' % details['K'][kidx])
    plt.legend()
    plt.show()
 
#判断肘点，需肉眼观察，上述kidx的值基于这个函数。n代表聚类个数
def eblow(n):
    """Elbow testing."""
    #测试集的属性
    cols = ['sepal_length', 'sepal_width', 'petal_length', 'petal_width']
    df = pd.read_csv('data.csv', usecols=cols).values
    #聚类数从1到n-1的模型
    kmeans_var = [KMeans(n_clusters=k).fit(df) for k in range(1, n)]
    #得到中心点坐标，每个属性看作一维，所以每个中心点坐标有4个值
    centroids = [x.cluster_centers_ for x in kmeans_var]
    #得到每个数据点到每个中心点的距离
    k_euclid = [cdist(df, cent) for cent in centroids]
    #得到k_euclid每组最小的值
    dist = [np.min(ke, axis=1) for ke in k_euclid]
    #每种聚类数对应的最小距离平方和
    wcss = [sum(d**2) for d in dist]
    #原数据集距离平方和的均值
    tss = sum(pdist(df)**2) / df.shape[0]
    bss = tss - wcss
    plt.plot(bss)
    plt.show()
 
dataset = load_dataset()
details = find_clusters(dataset)
plot_elbow_curv(details)
scatter_plot(dataset, details)
#可以观察到肘点
eblow(10)

结果：