Implementation of K-means algorithm in Python

K-means is a commonly used algorithm in machine learning. It is an unsupervised learning algorithm. It is often used for data clustering. You only need to specify the number of clusters for it to automatically aggregate data into multiple categories. , the data similarity in the same cluster is high, and the data similarity in different clusters is low.

The K-MEANS algorithm is an algorithm that inputs the number of clusters k and a database containing n data objects, and outputs k clusters that meet the minimum variance criterion. The k-means algorithm accepts an input quantity k; then divides n data objects into k clusters so that the obtained clusters satisfy: the similarity of objects in the same cluster is higher; and the similarity of objects in different clusters is smaller. This article will introduce to you the implementation of the K-means algorithm in Python.

Core idea

Iteratively find a partitioning scheme for k clusters, so that the mean value of these k clusters is used to represent the corresponding types of samples. The overall error is the smallest.

k clusters have the following characteristics: each cluster itself is as compact as possible, and each cluster is as separated as possible.

The basis of the k-means algorithm is the minimum error sum of squares criterion. The advantages and disadvantages of K-menas:

Advantages:

Simple principle
Fast speed
Good scalability for large data sets

Disadvantages:

Need to specify The number of clusters K
is sensitive to outliers
is sensitive to initial values

The clustering process of K-means

its The clustering process is similar to the gradient descent algorithm. A cost function is established and the value of the cost function becomes smaller and smaller through iteration.

Appropriately select the initial centers of c classes;
In the k-th iteration, for any For a sample, find the distance to c centers, and classify the sample into the class of the center with the shortest distance;
Use methods such as mean to update the center value of the class;
For all c cluster centers , if the value remains unchanged after updating using the iteration method of (2) (3), the iteration ends, otherwise the iteration continues.

The biggest advantage of this algorithm is its simplicity and speed. The key to the algorithm lies in the selection of the initial center and the distance formula.

K-means example shows

Some parameters of km in python:

sklearn.cluster.KMeans(
  n_clusters=8,
  init='k-means++', 
  n_init=10, 
  max_iter=300, 
  tol=0.0001, 
  precompute_distances='auto', 
  verbose=0, 
  random_state=None, 
  copy_x=True, 
  n_jobs=1, 
  algorithm='auto'
  )
n_clusters: 簇的个数，即你想聚成几类
init: 初始簇中心的获取方法
n_init: 获取初始簇中心的更迭次数，为了弥补初始质心的影响，算法默认会初始10个质心，实现算法，然后返回最好的结果。
max_iter: 最大迭代次数（因为kmeans算法的实现需要迭代）
tol: 容忍度，即kmeans运行准则收敛的条件
precompute_distances:是否需要提前计算距离，这个参数会在空间和时间之间做权衡，如果是True 会把整个距离矩阵都放到内存中，auto 会默认在数据样本大于featurs*samples 的数量大于12e6 的时候False,False 时核心实现的方法是利用Cpython 来实现的
verbose: 冗长模式（不太懂是啥意思，反正一般不去改默认值）
random_state: 随机生成簇中心的状态条件。
copy_x: 对是否修改数据的一个标记，如果True，即复制了就不会修改数据。bool 在scikit-learn 很多接口中都会有这个参数的，就是是否对输入数据继续copy 操作，以便不修改用户的输入数据。这个要理解Python 的内存机制才会比较清楚。
n_jobs: 并行设置
algorithm: kmeans的实现算法，有：'auto', ‘full', ‘elkan', 其中 ‘full'表示用EM方式实现
虽然有很多参数，但是都已经给出了默认值。所以我们一般不需要去传入这些参数,参数的。可以根据实际需要来调用。

The following shows a code example

from sklearn.cluster import KMeans
from sklearn.externals import joblib
from sklearn import cluster
import numpy as np

# 生成10*3的矩阵
data = np.random.rand(10,3)
print data
# 聚类为4类
estimator=KMeans(n_clusters=4)
# fit_predict表示拟合+预测，也可以分开写
res=estimator.fit_predict(data)
# 预测类别标签结果
lable_pred=estimator.labels_
# 各个类别的聚类中心值
centroids=estimator.cluster_centers_
# 聚类中心均值向量的总和
inertia=estimator.inertia_

print lable_pred
print centroids
print inertia

代码执行结果
[0 2 1 0 2 2 0 3 2 0]

[[ 0.3028348  0.25183096 0.62493622]
 [ 0.88481287 0.70891813 0.79463764]
 [ 0.66821961 0.54817207 0.30197415]
 [ 0.11629904 0.85684903 0.7088385 ]]
 
0.570794546829

For a more intuitive description, this time it is done on the picture A demonstration. Since it is more intuitive to draw two dimensions on the image, the data was adjusted to two dimensions. 100 points were selected to draw. The clustering category was 3 categories

from sklearn.cluster import KMeans
from sklearn.externals import joblib
from sklearn import cluster
import numpy as np
import matplotlib.pyplot as plt

data = np.random.rand(100,2)
estimator=KMeans(n_clusters=3)
res=estimator.fit_predict(data)
lable_pred=estimator.labels_
centroids=estimator.cluster_centers_
inertia=estimator.inertia_
#print res
print lable_pred
print centroids
print inertia

for i in range(len(data)):
  if int(lable_pred[i])==0:
    plt.scatter(data[i][0],data[i][1],color='red')
  if int(lable_pred[i])==1:
    plt.scatter(data[i][0],data[i][1],color='black')
  if int(lable_pred[i])==2:
    plt.scatter(data[i][0],data[i][1],color='blue')
plt.show()

It can be seen that the clustering effect is still good. We conducted a test on the clustering efficiency of k-means and expanded the dimension to 50 dimensions

from sklearn.externals import joblib
joblib.dump(km,"model/km_model.m")

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