? 使用神经网络来为散点作分类
● 单层感知机，代码
1 import numpy as np
2 import matplotlib.pyplot as plt
3 from mpl_toolkits.mplot3d import Axes3D
4 from mpl_toolkits.mplot3d.art3d import Poly3DCollection
5 from matplotlib.patches import Rectangle
6
7 dataSize = 2000
8 trainRatio = 0.3
9 ita = 0.3
10 epsilon = 0.001
11 maxTurn = 300
12
13 colors = [[0.5,0.25,0],[1,0,0],[0,0.5,0],[0,0,1],[1,0.5,0]] # 棕红绿蓝橙
14 trans = 0.5
15
16 def dataSplit(data, part): # 将数据集分割为训练集和测试集
17 return data[0:part,:],data[part:,:]
18
19 def mySign(x): # 区分 np.sign()
20 return (1 + np.sign(x))/2
21
22 def function(x,para): # 连续回归函数，用于画图
23 return np.sum(x * para[0]) - para[1] # 注意是减号
24
25 def judge(x, para): # 分类函数，由乘加部分和阈值部分组成
26 return mySign(function(x, para))
27
28 def createData(dim, len): # 生成测试数据
29 np.random.seed(103)
30 output=np.zeros([len,dim+1])
31 for i in range(dim):
32 output[:,i] = np.random.rand(len)
33 output[:,dim] = list(map(lambda x : int(x > 0.5), (3 - 2 * dim)*output[:,0] + 2 * np.sum(output[:,1:dim], 1)))
34 #print(output, "\n", np.sum(output[:,-1])/len)
35 return output
36
37 def perceptron(data): # 单层感知机
38 len = np.shape(data)[0]
39 dim = np.shape(data)[1] - 1
40 xE = np.concatenate((data[:, 0:-1], -np.ones(len)[:,np.newaxis]), axis = 1)
41 w = np.zeros(dim + 1)
42 finishFlag = False
43 count = 0
44 while finishFlag == False and count < maxTurn:
45 error = 0.0
46 for i in range(len):
47 delta = ita * (data[i,-1] - mySign(np.sum(xE[i] * w))) * xE[i] # 注意 np.sign 的定义
48 error += np.sum(delta * delta)
49 w += delta
50 count += 1
51 print("count = ",count,", w = ", w, ", error = ", error)
52 if error < epsilon:
53 finishFlag = True
54 break
55 return (w[:-1],w[-1])
56
57 def test(dim): # 测试函数
58 allData = createData(dim, dataSize)
59 trainData, testData = dataSplit(allData, int(dataSize * trainRatio))
60
61 para = perceptron(trainData)
62
63 myResult = [ judge(i[0:dim], para) for i in testData ]
64 errorRatio = np.sum((np.array(myResult) - testData[:,-1].astype(int))**2) / (dataSize*(1-trainRatio))
65 print("dim = "+ str(dim) + ", errorRatio = " + str(round(errorRatio,4)))
66 if dim >= 4: # 4维以上不画图，只输出测试错误率
67 return
68
69 errorP = [] # 画图部分，测试数据集分为错误类，1 类和 0 类
70 class1 = []
71 class0 = []
72 for i in range(np.shape(testData)[0]):
73 if myResult[i] != testData[i,-1]:
74 errorP.append(testData[i])
75 elif myResult[i] == 1:
76 class1.append(testData[i])
77 else:
78 class0.append(testData[i])
79 errorP = np.array(errorP)
80 class1 = np.array(class1)
81 class0 = np.array(class0)
82
83 fig = plt.figure(figsize=(10, 8))
84
85 if dim == 1:
86 plt.xlim(0.0,1.0)
87 plt.ylim(-0.25,1.25)
88 plt.plot([0.5, 0.5], [-0.5, 1.25], color = colors[0],label = "realBoundary")
89 plt.plot([0, 1], [ function(i, para) for i in [0,1] ],color = colors[4], label = "myF")
90 plt.scatter(class1[:,0], class1[:,1],color = colors[1], s = 2,label = "class1Data")
91 plt.scatter(class0[:,0], class0[:,1],color = colors[2], s = 2,label = "class0Data")
92 if len(errorP) != 0:
93 plt.scatter(errorP[:,0], errorP[:,1],color = colors[3], s = 16,label = "errorData")
94 plt.text(0.2, 1.12, "realBoundary: 2x = 1\nmyF(x) = " + str(round(para[0][0],2)) + " x - " + str(round(para[1],2)) + "\n errorRatio = " + str(round(errorRatio,4)), 95 size=15, ha="center", va="center", bbox=dict(boxstyle="round", ec=(1., 0.5, 0.5), fc=(1., 1., 1.)))
96 R = [Rectangle((0,0),0,0, color = colors[k]) for k in range(5)]
97 plt.legend(R, ["realBoundary", "class1Data", "class0Data", "errorData", "myF"], loc=[0.81, 0.2], ncol=1, numpoints=1, framealpha = 1)
98
99 if dim == 2:
100 plt.xlim(0.0,1.0)
101 plt.ylim(0.0,1.0)
102 plt.plot([0,1], [0.25,0.75], color = colors[0],label = "realBoundary")
103 xx = np.arange(0, 1 + 0.1, 0.1)
104 X,Y = np.meshgrid(xx, xx)
105 contour = plt.contour(X, Y, [ [ function((X[i,j],Y[i,j]), para) for j in range(11)] for i in range(11) ])
106 plt.clabel(contour, fontsize = 10,colors=‘k‘)
107 plt.scatter(class1[:,0], class1[:,1],color = colors[1], s = 2,label = "class1Data")
108 plt.scatter(class0[:,0], class0[:,1],color = colors[2], s = 2,label = "class0Data")
109 if len(errorP) != 0:
110 plt.scatter(errorP[:,0], errorP[:,1],color = colors[3], s = 8,label = "errorData")
111 plt.text(0.75, 0.92, "realBoundary: -x + 2y = 1\nmyF(x,y) = " + str(round(para[0][0],2)) + " x + " + str(round(para[0][1],2)) + " y - " + str(round(para[1],2)) + "\n errorRatio = " + str(round(errorRatio,4)), 112 size = 15, ha="center", va="center", bbox=dict(boxstyle="round", ec=(1., 0.5, 0.5), fc=(1., 1., 1.)))
113 R = [Rectangle((0,0),0,0, color = colors[k]) for k in range(4)]
114 plt.legend(R, ["realBoundary", "class1Data", "class0Data", "errorData"], loc=[0.81, 0.2], ncol=1, numpoints=1, framealpha = 1)
115
116 if dim == 3:
117 ax = Axes3D(fig)
118 ax.set_xlim3d(0.0, 1.0)
119 ax.set_ylim3d(0.0, 1.0)
120 ax.set_zlim3d(0.0, 1.0)
121 ax.set_xlabel(‘X‘, fontdict={‘size‘: 15, ‘color‘: ‘k‘})
122 ax.set_ylabel(‘Y‘, fontdict={‘size‘: 15, ‘color‘: ‘k‘})
123 ax.set_zlabel(‘W‘, fontdict={‘size‘: 15, ‘color‘: ‘k‘})
124 v = [(0, 0, 0.25), (0, 0.25, 0), (0.5, 1, 0), (1, 1, 0.75), (1, 0.75, 1), (0.5, 0, 1)]
125 f = [[0,1,2,3,4,5]]
126 poly3d = [[v[i] for i in j] for j in f]
127 ax.add_collection3d(Poly3DCollection(poly3d, edgecolor = ‘k‘, facecolors = colors[0]+[trans], linewidths=1))
128 ax.scatter(class1[:,0], class1[:,1],class1[:,2], color = colors[1], s = 2, label = "class1")
129 ax.scatter(class0[:,0], class0[:,1],class0[:,2], color = colors[2], s = 2, label = "class0")
130 if len(errorP) != 0:
131 ax.scatter(errorP[:,0], errorP[:,1],errorP[:,2], color = colors[3], s = 8, label = "errorData")
132 ax.text3D(0.8, 1, 1.15, "realBoundary: -3x + 2y +2z = 1\nmyF(x,y,z) = " + str(round(para[0][0],2)) + " x + " + 133 str(round(para[0][1],2)) + " y + " + str(round(para[0][2],2)) + " z - " + str(round(para[1],2)) + "\n errorRatio = " + str(round(errorRatio,4)), 134 size = 12, ha="center", va="center", bbox=dict(boxstyle="round", ec=(1, 0.5, 0.5), fc=(1, 1, 1)))
135 R = [Rectangle((0,0),0,0, color = colors[k]) for k in range(4)]
136 plt.legend(R, ["realBoundary", "class1Data", "class0Data", "errorData"], loc=[0.83, 0.1], ncol=1, numpoints=1, framealpha = 1)
137
138 fig.savefig("R:\\dim" + str(dim) + ".png")
139 plt.close()
140
141 if __name__ == ‘__main__‘:
142 test(1)
143 test(2)
144 test(3)
145 test(4)
● 输出结果，一维 6 遍收敛，二维 39 遍，三维 87 遍，四维 89 遍
count = 1 , w = [1.39770297 0.45 ] , error = 5.222155402906847 count = 2 , w = [1.52702391 0.75 ] , error = 1.6525212964325524 count = 3 , w = [1.99396967 0.75 ] , error = 3.8768795270185015 count = 4 , w = [2.0734924 1.05 ] , error = 2.1108010510371176 count = 5 , w = [2.08542138 1.05 ] , error = 0.2226526876961404 count = 6 , w = [2.08542138 1.05 ] , error = 0.0 dim = 1, errorRatio = 0.0043 count = 1 , w = [-0.86290479 1.73543324 0.45 ] , error = 10.072859142827403 count = 2 , w = [-1.13927193 2.04084504 0.45 ] , error = 4.4609363561371165 count = 3 , w = [-1.15553275 2.73079122 0.75 ] , error = 7.930218436293679 ... count = 37 , w = [-3.24442847 6.45406089 1.65 ] , error = 0.5427638905658313 count = 38 , w = [-3.25333719 6.53959919 1.65 ] , error = 2.6670168284877542 count = 39 , w = [-3.25333719 6.53959919 1.65 ] , error = 0.0 dim = 2, errorRatio = 0.0 count = 1 , w = [-1.83648172 1.13115561 1.48731853 0.15 ] , error = 15.299397796880317 count = 2 , w = [-2.21432213 1.4718464 1.61271137 0.45 ] , error = 5.514265592439243 count = 3 , w = [-2.65894841 1.73243095 1.7833203 0.45 ] , error = 5.782491180281051 ... count = 84 , w = [-8.76231537 5.53262355 5.91015865 1.35 ] , error = 2.3909384841900865 count = 85 , w = [-8.80616091 5.60771114 5.82973106 1.35 ] , error = 1.9246305102403725 count = 86 , w = [-8.77906986 5.58426138 5.92865995 1.35 ] , error = 0.4663079739497135 count = 87 , w = [-8.77906986 5.58426138 5.92865995 1.35 ] , error = 0.0 dim = 3, errorRatio = 0.0121 count = 1 , w = [-2.55073743 0.77544673 0.79572989 1.11402485 0.15 ] , error = 21.2911454497099 count = 2 , w = [-3.17104932 1.33820515 1.13266849 1.11805123 0.15 ] , error = 11.542535217905032 count = 3 , w = [-3.56132108 1.37329683 1.34578486 1.58997522 0.45 ] , error = 9.590714392019622 ... count = 87 , w = [-10.13469991 4.36826988 4.06767039 4.25598478 0.75 ] , error = 1.9723755293196636 count = 88 , w = [-10.27022167 4.12906605 4.11467555 4.10943389 1.05 ] , error = 1.5046863818100382 count = 89 , w = [-10.27022167 4.12906605 4.11467555 4.10943389 1.05 ] , error = 0.0 dim = 4, errorRatio = 0.0014
● 画图
原文地址：https://www.cnblogs.com/cuancuancuanhao/p/11128493.html
时间： 2024-10-30 00:50:19