? 使用逻辑地模型来进行分类，可以算出每个测试样本分属于每个类别的概率
● 二分类代码
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 = 10000
8 trainRatio = 0.3
9 ita = 0.03
10 epsilon = 0.01
11 defaultTurn = 500
12 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
13 trans = 0.5
14
15 def sigmoid(x):
16 return 1.0 / (1 + np.exp(-x))
17
18 def function(x, para): # 回归函数
19 return sigmoid(np.sum(x * para[0]) + para[1])
20
21 def judge(x, para): # 分类函数，由乘加部分和阈值部分组成
22 return int(function(x, para) > 0.5)
23
24 def dataSplit(x, y, part):
25 return x[:part], y[:part],x[part:],y[part:]
26
27 def createData(dim, count = dataSize): # 创建数据集
28 np.random.seed(103)
29 X = np.random.rand(count, dim)
30 Y = ((3 - 2 * dim)*X[:,0] + 2 * np.sum(X[:,1:], 1) > 0.5).astype(int) # 只考虑 {0，1} 的二分类
31 class1Count = 0
32 for i in range(count):
33 class1Count += (Y[i] + 1)>>1
34 print("dim = %d, dataSize = %d, class 1 ratio -> %4f"%(dim, count, class1Count / count))
35 return X, Y
36
37 def stochasticGradientDescent(dataX, dataY, turn = defaultTurn):
38 count, dim = np.shape(dataX)
39 xE = np.concatenate((dataX, np.ones(count)[:,np.newaxis]), axis = 1)
40 w = np.ones(dim + 1)
41
42 for t in range(turn):
43 y = sigmoid(np.dot(xE, w).T)
44 error = dataY - y
45 w += ita * np.dot(error, xE)
46 if np.sum(error * error) < count * epsilon:
47 break
48 return (w[:-1], w[-1])
49
50 def test(dim):
51 allX, allY = createData(dim)
52 trainX, trainY, testX, testY = dataSplit(allX, allY, int(dataSize * trainRatio)) # 分离训练集
53
54 para = stochasticGradientDescent(testX, testY) # 训练
55
56 myResult = [ judge(x, para) for x in testX] # 测试结果
57 errorRatio = np.sum((np.array(myResult) - testY)**2) / (dataSize * (1 - trainRatio))
58 print("dim = %d, errorRatio = %4f\n"%(dim, errorRatio))
59
60 if dim >= 4: # 4维以上不画图，只输出测试错误率
61 return
62 errorPX = [] # 测试数据集分为错误类，1 类和 0 类
63 errorPY = []
64 class1 = []
65 class0 = []
66 for i in range(len(testX)):
67 if myResult[i] != testY[i]:
68 errorPX.append(testX[i])
69 errorPY.append(testY[i])
70 elif myResult[i] == 1:
71 class1.append(testX[i])
72 else:
73 class0.append(testX[i])
74 errorPX = np.array(errorPX)
75 errorPY = np.array(errorPY)
76 class1 = np.array(class1)
77 class0 = np.array(class0)
78
79 fig = plt.figure(figsize=(10, 8))
80
81 if dim == 1:
82 plt.xlim(0.0,1.0)
83 plt.ylim(-0.25,1.25)
84 plt.plot([0.5, 0.5], [-0.5, 1.25], color = colors[0],label = "realBoundary")
85 plt.plot([0, 1], [ function(i, para) for i in [0,1] ],color = colors[4], label = "myF")
86 plt.scatter(class1, np.ones(len(class1)), color = colors[1], s = 2,label = "class1Data")
87 plt.scatter(class0, np.zeros(len(class0)), color = colors[2], s = 2,label = "class0Data")
88 if len(errorPX) != 0:
89 plt.scatter(errorPX, errorPY,color = colors[3], s = 16,label = "errorData")
90 plt.text(0.21, 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)), 91 size=15, ha="center", va="center", bbox=dict(boxstyle="round", ec=(1., 0.5, 0.5), fc=(1., 1., 1.)))
92 R = [Rectangle((0,0),0,0, color = colors[k]) for k in range(5)]
93 plt.legend(R, ["realBoundary", "class1Data", "class0Data", "errorData", "myF"], loc=[0.81, 0.2], ncol=1, numpoints=1, framealpha = 1)
94
95 if dim == 2:
96 plt.xlim(0.0,1.0)
97 plt.ylim(0.0,1.0)
98 plt.plot([0,1], [0.25,0.75], color = colors[0],label = "realBoundary")
99 xx = np.arange(0, 1 + 0.1, 0.1)
100 X,Y = np.meshgrid(xx, xx)
101 contour = plt.contour(X, Y, [ [ function((X[i,j],Y[i,j]), para) for j in range(11)] for i in range(11) ])
102 plt.clabel(contour, fontsize = 10,colors=‘k‘)
103 plt.scatter(class1[:,0], class1[:,1], color = colors[1], s = 2,label = "class1Data")
104 plt.scatter(class0[:,0], class0[:,1], color = colors[2], s = 2,label = "class0Data")
105 if len(errorPX) != 0:
106 plt.scatter(errorPX[:,0], errorPX[:,1], color = colors[3], s = 8,label = "errorData")
107 plt.text(0.71, 0.92, "realBoundary: -x + 2y = 1/2\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)), 108 size = 15, ha="center", va="center", bbox=dict(boxstyle="round", ec=(1., 0.5, 0.5), fc=(1., 1., 1.)))
109 R = [Rectangle((0,0),0,0, color = colors[k]) for k in range(4)]
110 plt.legend(R, ["realBoundary", "class1Data", "class0Data", "errorData"], loc=[0.81, 0.2], ncol=1, numpoints=1, framealpha = 1)
111
112 if dim == 3:
113 ax = Axes3D(fig)
114 ax.set_xlim3d(0.0, 1.0)
115 ax.set_ylim3d(0.0, 1.0)
116 ax.set_zlim3d(0.0, 1.0)
117 ax.set_xlabel(‘X‘, fontdict={‘size‘: 15, ‘color‘: ‘k‘})
118 ax.set_ylabel(‘Y‘, fontdict={‘size‘: 15, ‘color‘: ‘k‘})
119 ax.set_zlabel(‘W‘, fontdict={‘size‘: 15, ‘color‘: ‘k‘})
120 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)]
121 f = [[0,1,2,3,4,5]]
122 poly3d = [[v[i] for i in j] for j in f]
123 ax.add_collection3d(Poly3DCollection(poly3d, edgecolor = ‘k‘, facecolors = colors[0]+[trans], linewidths=1))
124 ax.scatter(class1[:,0], class1[:,1],class1[:,2], color = colors[1], s = 2, label = "class1")
125 ax.scatter(class0[:,0], class0[:,1],class0[:,2], color = colors[2], s = 2, label = "class0")
126 if len(errorPX) != 0:
127 ax.scatter(errorPX[:,0], errorPX[:,1],errorPX[:,2], color = colors[3], s = 8, label = "errorData")
128 ax.text3D(0.74, 0.95, 1.15, "realBoundary: -3x + 2y +2z = 1/2\nmyF(x,y,z) = " + str(round(para[0][0],2)) + " x + " + 129 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)), 130 size = 12, ha="center", va="center", bbox=dict(boxstyle="round", ec=(1, 0.5, 0.5), fc=(1, 1, 1)))
131 R = [Rectangle((0,0),0,0, color = colors[k]) for k in range(4)]
132 plt.legend(R, ["realBoundary", "class1Data", "class0Data", "errorData"], loc=[0.83, 0.1], ncol=1, numpoints=1, framealpha = 1)
133
134 fig.savefig("R:\\dim" + str(dim) + ".png")
135 plt.close()
136
137 if __name__==‘__main__‘:
138 test(1)
139 test(2)
140 test(3)
141 test(4)
142 test(5)
● 输出结果
dim = 1, dataSize = 10000, class 1 ratio -> 0.509000 dim = 1, errorRatio = 0.015000 dim = 2, dataSize = 10000, class 1 ratio -> 0.496000 dim = 2, errorRatio = 0.008429 dim = 3, dataSize = 10000, class 1 ratio -> 0.498200 dim = 3, errorRatio = 0.012429 dim = 4, dataSize = 10000, class 1 ratio -> 0.496900 dim = 4, errorRatio = 0.012857 dim = 5, dataSize = 10000, class 1 ratio -> 0.500000 dim = 5, errorRatio = 0.012143
● 画图
● 多分类代码（坑）
原文地址：https://www.cnblogs.com/cuancuancuanhao/p/11251632.html
时间： 2024-10-08 08:24:18