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fuzzycmeans.py
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fuzzycmeans.py
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#!/usr/bin/env python
# -*- encoding: utf-8 -*-
'''
@File : fuzzycmeans.py
@Time : 2019/10/24 10:52:31
@Author : Qi Yang
@Version : 1.0
@Describtion: None
'''
# here put the import lib
import numpy as np
from numpy import random
import matplotlib.pyplot as plt
from sklearn.datasets import make_blobs
from scipy.linalg import norm
import kmeans
from matplotlib.pyplot import scatter,plot
from scipy.spatial.distance import cdist
class fuzzy_cmeans(object):
def __init__(self,m,clusters):
self.m=m
self.k=clusters
self.epsilon=1
self.episode=1000
self.centers=[]
self.u= None
def new_center(self,point,u):
um = u ** self.m
return (point.T @ um / np.sum(um, axis=0)).T
def update_u(self,point,centers):
power = float(2 / (self.m - 1))
temp = cdist(point, centers) ** power
denominator_ = temp.reshape((point.shape[0], 1, -1)).repeat(temp.shape[-1], axis=1)
denominator_ = temp[:, :, np.newaxis] / denominator_
return 1 / denominator_.sum(2)
@staticmethod
def dist(p1,p2):
return np.sqrt(np.power(p1[0]-p2[0],2)+np.power(p1[1]-p2[1],2))
def Jfunc(self,point,center,u):
dist_sum=0
for j,cj in enumerate(center):
for i,si in enumerate(point):
dist_sum += np.power(u[i][j],self.m) * np.power(self.dist(si,cj),2)
return dist_sum
def fit(self,point):
n=len(point)
# initilize centers
for i in range(self.k):
self.centers.append(point[random.randint(0,n)])
# initialize u matrix of membership grade
self.u = np.zeros((n,self.k),dtype = float)
for i in range(n):
self.u[i][random.randint(0,self.k)] = 1 # set one in every column
assert np.sum(self.u,axis=1).all() == 1.
u=self.u.copy()
centers=self.centers.copy()
iter_times = 0
dist_sum=[]
dist_sum.append(self.Jfunc(point,centers,u))
while iter_times < self.episode:
centers=self.new_center(point,u)
u=self.update_u(point,centers)
iter_times += 1
dist_sum.append(self.Jfunc(point,centers,u))
if (norm(u - self.u) < self.epsilon) or (dist_sum[iter_times-1]-dist_sum[iter_times]<self.epsilon) :
break
if iter_times%100==0:
print("is running",str(iter_times),"times")
self.centers=centers
self.u=u
return dist_sum
def run(m,point):
fcm = fuzzy_cmeans(clusters=2,m=m)
fcm_distance = fcm.fit(point)
fcm_centers = fcm.centers
x=[]
for i in range(len(fcm_distance)-1):
x.append(i)
y1=point.copy()
y2=point.copy()
for i in range(len(point)):
y1[i][1]=fcm.u[i][0]
y2[i][1]=fcm.u[i][1]
line1=0.01
line3=0.05
plt.figure(figsize=(25,5))
plt.subplot(131)
plt.scatter(point[:,0], point[:,1],linewidths=line1,c='black')
plt.scatter(fcm_centers[:1,0], fcm_centers[:1,1],marker='^',c='#F4A460')
plt.scatter(y1[:,0],y1[:,1],c='#F4A460',linewidths=line3)
plt.legend(('points','centers','membership grade'))
plt.title('u of No.1 center')
plt.subplot(132)
plt.scatter(point[:,0], point[:,1],linewidths=line1,c='black')
plt.scatter(fcm_centers[1:,0], fcm_centers[1:,1],marker='^',c='#00CED1')
plt.scatter(y2[:,0],y2[:,1],c='#00CED1',linewidths=line3)
plt.legend(('points','centers','membership grade'))
plt.title('u of No.2 center')
plt.subplot(133)
plt.plot(x,fcm_distance[1:],c='black')
plt.title('Cumulative distance')
name='fig'+str(m)
plt.savefig(name)
plt.show()
n_samples = 50
#centerbox= [(-5,0),(5,0)]
#point,_ = make_blobs(n_samples=100, n_features=2, cluster_std=1.6,center_box=centerbox, shuffle=False, random_state=42)
point=np.zeros((n_samples,2))
for i in range(25):
point[i][0]=random.randint(0,45)
point[-i][0]=random.randint(55,100)
run(2,point)
run(3,point)
run(4,point)
run(5,point)
run(10,point)
run(100,point)
kmeans.run(2,point)