python實現徑向基核函式
阿新 • • 發佈：2018-12-16
1、生成資料集（雙月資料集）
class moon_data_class(object):
def __init__(self,N,d,r,w):
self.N=N
self.w=w
self.d=d
self.r=r
def sgn(self,x):
if(x>0):
return 1;
else:
return -1;
def sig(self,x):
return 1.0/(1+np.exp( 2、k均值聚類
def k_means(input_cells, k_count):
count = len(input_cells) #點的個數
x = input_cells[0:count, 0]
y = input_cells[0:count, 1]
#隨機選擇K個點
k = rd.sample(range(count), k_count)
k_point = [[x[i], [y[i]]] for i in k] #保證有序
k_point.sort()
global frames
#global step
while True:
km = [[] for i in range(k_count)] #儲存每個簇的索引
#遍歷所有點
for i in range(count):
cp = [x[i], y[i]] #當前點
#計算cp點到所有質心的距離
_sse = [distance(k_point[j], cp) for j in range(k_count)]
#cp點到那個質心最近
min_index = _sse.index(min(_sse))
#把cp點併入第i簇
km[min_index].append(i)
#更換質心
k_new = []
for i in range(k_count):
_x = sum([x[j] for j in km[i]]) / len(km[i])
_y = sum([y[j] for j in km[i]]) / len(km[i])
k_new.append([_x, _y])
k_new.sort() #排序
if (k_new != k_point):#一直迴圈直到聚類中心沒有變化
k_point = k_new
else:
return k_point,km
3、高斯核函式
def gaussian (a,b, sigma):
return np.exp(-norm(a-b)**2 / (2 * sigma**2))
4、求高斯核函式的方差
Sigma_Array = []
for j in range(k_count):
Sigma = []
for i in range(len(center_array[j][0])):
temp = Phi(np.array([center_array[j][0][i],center_array[j][1][i]]),np.array(center[j]))
Sigma.append(temp)
Sigma = np.array(Sigma)
Sigma_Array.append(np.cov(Sigma))
5、顯示高斯核函式計算結果
gaussian_kernel_array = []
fig = plt.figure()
ax = Axes3D(fig)
for j in range(k_count):
gaussian_kernel = []
for i in range(len(center_array[j][0])):
temp = Phi(np.array([center_array[j][0][i],center_array[j][1][i]]),np.array(center[j]))
temp1 = gaussian(temp,Sigma_Array[0])
gaussian_kernel.append(temp1)
gaussian_kernel_array.append(gaussian_kernel)
ax.scatter(center_array[j][0], center_array[j][1], gaussian_kernel_array[j],s=20)
plt.show()
6、執行結果
7、完整程式碼
# coding:utf-8
import numpy as np
import pylab as pl
import random as rd
import imageio
import math
import random
import matplotlib.pyplot as plt
import numpy as np
import mpl_toolkits.mplot3d
from mpl_toolkits.mplot3d import Axes3D
from scipy import *
from scipy.linalg import norm, pinv
from matplotlib import pyplot as plt
random.seed(0)
#定義sigmoid函式和它的導數
def sigmoid(x):
return 1.0/(1.0+np.exp(-x))
def sigmoid_derivate(x):
return x*(1-x) #sigmoid函式的導數
class moon_data_class(object):
def __init__(self,N,d,r,w):
self.N=N
self.w=w
self.d=d
self.r=r
def sgn(self,x):
if(x>0):
return 1;
else:
return -1;
def sig(self,x):
return 1.0/(1+np.exp(x))
def dbmoon(self):
N1 = 10*self.N
N = self.N
r = self.r
w2 = self.w/2
d = self.d
done = True
data = np.empty(0)
while done:
#generate Rectangular data
tmp_x = 2*(r+w2)*(np.random.random([N1, 1])-0.5)
tmp_y = (r+w2)*np.random.random([N1, 1])
tmp = np.concatenate((tmp_x, tmp_y), axis=1)
tmp_ds = np.sqrt(tmp_x*tmp_x + tmp_y*tmp_y)
#generate double moon data ---upper
idx = np.logical_and(tmp_ds > (r-w2), tmp_ds < (r+w2))
idx = (idx.nonzero())[0]
if data.shape[0] == 0:
data = tmp.take(idx, axis=0)
else:
data = np.concatenate((data, tmp.take(idx, axis=0)), axis=0)
if data.shape[0] >= N:
done = False
#print (data)
db_moon = data[0:N, :]
#print (db_moon)
#generate double moon data ----down
data_t = np.empty([N, 2])
data_t[:, 0] = data[0:N, 0] + r
data_t[:, 1] = -data[0:N, 1] - d
db_moon = np.concatenate((db_moon, data_t), axis=0)
return db_moon
def distance(a, b):
return (a[0]- b[0]) ** 2 + (a[1] - b[1]) ** 2
#K均值演算法
def k_means(input_cells, k_count):
count = len(input_cells) #點的個數
x = input_cells[0:count, 0]
y = input_cells[0:count, 1]
#隨機選擇K個點
k = rd.sample(range(count), k_count)
k_point = [[x[i], [y[i]]] for i in k] #保證有序
k_point.sort()
global frames
#global step
while True:
km = [[] for i in range(k_count)] #儲存每個簇的索引
#遍歷所有點
for i in range(count):
cp = [x[i], y[i]] #當前點
#計算cp點到所有質心的距離
_sse = [distance(k_point[j], cp) for j in range(k_count)]
#cp點到那個質心最近
min_index = _sse.index(min(_sse))
#把cp點併入第i簇
km[min_index].append(i)
#更換質心
k_new = []
for i in range(k_count):
_x = sum([x[j] for j in km[i]]) / len(km[i])
_y = sum([y[j] for j in km[i]]) / len(km[i])
k_new.append([_x, _y])
k_new.sort() #排序
if (k_new != k_point):#一直迴圈直到聚類中心沒有變化
k_point = k_new
else:
pl.figure()
pl.title("N=%d,k=%d iteration"%(count,k_count))
for j in range(k_count):
pl.plot([x[i] for i in km[j]], [y[i] for i in km[j]], color[j%4])
pl.plot(k_point[j][0], k_point[j][1], dcolor[j%4])
return k_point,km
def Phi(a,b):
return norm(a-b)
def gaussian (x, sigma):
return np.exp(-x**2 / (2 * sigma**2))
if __name__ == '__main__':
#計算平面兩點的歐氏距離
step=0
color=['.r','.g','.b','.y']#顏色種類
dcolor=['*r','*g','*b','*y']#顏色種類
frames = []
N = 200
d = -4
r = 10
width = 6
data_source = moon_data_class(N, d, r, width)
data = data_source.dbmoon()
# x0 = [1 for x in range(1,401)]
input_cells = np.array([np.reshape(data[0:2*N, 0], len(data)), np.reshape(data[0:2*N, 1], len(data))]).transpose()
labels_pre = [[1] for y in range(1, 201)]
labels_pos = [[0] for y in range(1, 201)]
labels=labels_pre+labels_pos
k_count = 2
center,km = k_means(input_cells, k_count)
test = Phi(input_cells[1],np.array(center[0]))
print(test)
test = distance(input_cells[1],np.array(center[0]))
print(np.sqrt(test))
count = len(input_cells)
x = input_cells[0:count, 0]
y = input_cells[0:count, 1]
center_array = []
for j in range(k_count):
center_array.append([[x[i] for i in km[j]], [y[i] for i in km[j]]])
Sigma_Array = []
for j in range(k_count):
Sigma = []
for i in range(len(center_array[j][0])):
temp = Phi(np.array(