K-means演算法：

關於步驟：參考之前的部落格
關於程式碼與資料：暫時整理程式碼如下：後期會附上github地址，上傳原始資料與程式碼完整版，

各種聚類演算法的對比：參考連線

Kmeans演算法的缺陷

1.聚類中心的個數K 需要事先給定，但在實際中這個 K 值的選定是非常難以估計的，很多時候，事先並不知道給定的資料集應該分成多少個類別才最合適
2.Kmeans需要人為地確定初始聚類中心，不同的初始聚類中心可能導致完全不同的聚類結果。

#!usr/bin/env python
#_*_ coding:utf-8 _*_
import random
import math
'''
kMeans:2列資料對比，帶有head
'''
 

#1.load data
def importData():
   f = lambda name,b,d: [name, float(b), float(d)]

   with open('birth-death-rates.csv', 'r') as inputFile:
          return [f(*line.strip().split('\t')) for line in inputFile]

寫入檔案型別

#2. calculate Distance

def euclideanDistance(x,y):
    return math.sqrt(sum([(a-b)**2
 
 for (a,b) in zip(x,y)]))

#L=points,
def partition(points, k, means, d=euclideanDistance):
   # print('means={}'.format(means))
   thePartition = [[] for _ in means]  # list of k empty lists

   indices = range(k)
   # print('indices={}'.format(indices))

   for x in points:

      #index為indices索引，呼叫d函式，計算每個值與聚類中心的距離，將其分類
 

      closestIndex = min(indices, key=lambda index: d(x, means[index]))#實現X與每個Y直接的求解：key=lambda index: d(x, means[index])

      thePartition[closestIndex].append(x)

   return thePartition

#3.尋找收斂點
def mean(points):
   ''' assume the entries of the list of points are tuples;
       e.g. (3,4) or (6,3,1). '''

   n = len(points)
   # print(tuple(float(sum(x)) / n for x in zip(*points)))   #*points將【[1，2]，[2，3]】分割出來【1，2】
   return tuple(float(sum(x)) / n for x in zip(*points))  #將最開始的[[4, 1], [1, 5]] 經過處理變成[（4, 1）,（1, 5）]


def kMeans(points, k, initialMeans, d=euclideanDistance):
   oldPartition = []
   newPartition = partition(points, k, initialMeans, d)

   while oldPartition != newPartition:
      oldPartition = newPartition
      newMeans = [mean(S) for S in oldPartition]
      newPartition = partition(points, k, newMeans, d)

   return newPartition

#0.函式呼叫初始中心點

if __name__ == "__main__":
   L = [x[1:] for x in importData()] # remove names
   # print (str(L).replace('[','{').replace(']', '}'))
   import matplotlib.pyplot as plt
   '''
   plt.scatter(*zip(*L))
   plt.show()
   '''
   import random
   k = 3
   partition = kMeans(L, k, random.sample(L, k))  #L是集合，K分類個數，random.sample(L, k)中心點
   plt.scatter(*zip(*partition[0]), c='b')#[[],[],[]]
   plt.scatter(*zip(*partition[1]), c='r')
   plt.scatter(*zip(*partition[2]), c='g')
   plt.show()