? 使用线性回归来为散点作分类
● 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 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
10 trans = 0.5
11
12 def dataSplit(data, part): # 将数据集分割为训练集和测试集
13 return data[0:part,:],data[part:,:]
14
15 def function(x,para): # 连续回归函数
16 return np.sum(x * para[0]) + para[1]
17
18 def judge(x, para): # 分类函数，用 0.5 作突跃点
19 return int(function(x, para) > 0.5)
20
21 def createData(dim, len): # 生成测试数据
22 np.random.seed(103)
23 output=np.zeros([len,dim+1])
24
25 if dim == 1:
26 temp = 2 * np.random.rand(len)
27 output[:,0] = temp
28 output[:,1] = list(map(lambda x : int(x > 1), temp))
29 #print(output, "\n", np.sum(output[:,-1])/len)
30 return output
31 if dim == 2:
32 output[:,0] = 2 * np.random.rand(len)
33 output[:,1] = 2 * np.random.rand(len)
34 output[:,2] = list(map(lambda x,y : int(y > 0.5 * (x + 1)), output[:,0], output[:,1]))
35 #print(output, "\n", np.sum(output[:,-1])/len)
36 return output
37 if dim == 3:
38 output[:,0] = 2 * np.random.rand(len)
39 output[:,1] = 2 * np.random.rand(len)
40 output[:,2] = 2 * np.random.rand(len)
41 output[:,3] = list(map(lambda x,y,z : int(-3 * x + 2 * y + 2 * z > 0), output[:,0], output[:,1], output[:,2]))
42 #print(output, "\n", np.sum(output[:,-1])/len)
43 return output
44 else:
45 for i in range(dim):
46 output[:,i] = 2 * np.random.rand(len)
47 output[:,dim] = list(map(lambda x : int(x > 1), (3 - 2 * dim)*output[:,0] + 2 * np.sum(output[:,1:dim], 1)))
48 #print(output, "\n", np.sum(output[:,-1])/len)
49 return output
50
51 def linearRegression(data): # 线性回归
52 len = np.shape(data)[0]
53 dim = np.shape(data)[1] - 1
54 if(dim) == 1: # 一元
55 sumX = np.sum(data[:,0])
56 sumY = np.sum(data[:,1])
57 sumXY = np.sum([x*y for x,y in data])
58 sumXX = np.sum([x*x for x in data[:,0]])
59 w = (sumXY * len - sumX * sumY) / (sumXX * len - sumX * sumX)
60 b = (sumY - w * sumX) / len
61 return (w , b)
62 else: # 二元及以上，暂不考虑降秩的问题
63 dataE = np.concatenate((data[:, 0:-1], np.ones(len)[:,np.newaxis]), axis = 1)
64 w = np.matmul(np.matmul(np.linalg.inv(np.matmul(dataE.T, dataE)),dataE.T),data[:,-1]) # w = (X^T * X)^(-1) * X^T * y
65 return (w[0:-1],w[-1])
66
67 def test(dim): # 测试函数
68 allData = createData(dim, dataSize)
69 trainData, testData = dataSplit(allData, int(dataSize * trainRatio))
70
71 para = linearRegression(trainData)
72
73 myResult = [ judge(i[0:dim], para) for i in testData ]
74 errorRatio = np.sum((np.array(myResult) - testData[:,-1].astype(int))**2) / (dataSize*(1-trainRatio))
75 print("dim = "+ str(dim) + ", errorRatio = " + str(round(errorRatio,4)))
76 if dim >= 4: # 4维以上不画图，只输出测试错误率
77 return
78
79 errorP = [] # 画图部分，测试数据集分为错误类，1 类和 0 类
80 class1 = []
81 class0 = []
82 for i in range(np.shape(testData)[0]):
83 if myResult[i] != testData[i,-1]:
84 errorP.append(testData[i])
85 elif myResult[i] == 1:
86 class1.append(testData[i])
87 else:
88 class0.append(testData[i])
89 errorP = np.array(errorP)
90 class1 = np.array(class1)
91 class0 = np.array(class0)
92
93 fig = plt.figure(figsize=(10, 8))
94
95 if dim == 1:
96 plt.xlim(0.0,2.0)
97 plt.ylim(-0.5,1.25)
98 plt.plot([1, 1], [-0.5, 1.25], color = colors[0],label = "realBoundary")
99 xx = np.arange(0,2,0.2)
100 plt.plot(xx, [function(i, para) for i in xx],color = colors[4], label = "myF")
101 plt.scatter(class1[:,0], class1[:,1],color = colors[1], s = 2,label = "class1Data")
102 plt.scatter(class0[:,0], class0[:,1],color = colors[2], s = 2,label = "class0Data")
103 plt.scatter(errorP[:,0], errorP[:,1],color = colors[3], s = 16,label = "errorData")
104 plt.text(0.4, 1.12, "realBoundary: 2x = 1\nmyF(x) = " + str(round(para[0],2)) + " x + " + str(round(para[1],2)) + "\n errorRatio = " + str(round(errorRatio,4)),105 size=15, ha="center", va="center", bbox=dict(boxstyle="round", ec=(1., 0.5, 0.5), fc=(1., 1., 1.)))
106 R = [Rectangle((0,0),0,0, color = colors[k]) for k in range(5)]
107 plt.legend(R, ["realBoundary", "class1Data", "class0Data", "errorData", "myF"], loc=[0.81, 0.2], ncol=1, numpoints=1, framealpha = 1)
108
109 if dim == 2:
110 plt.xlim(0.0,2.0)
111 plt.ylim(0.0,2.0)
112 xx = np.arange(0, 2 + 0.2, 0.2)
113 plt.plot(xx, [function(i,(0.5,0.5)) for i in xx], color = colors[0],label = "realBoundary")
114 X,Y = np.meshgrid(xx, xx)
115 contour = plt.contour(X, Y, [ [ function((X[i,j],Y[i,j]), para) for j in range(11)] for i in range(11) ])
116 plt.clabel(contour, fontsize = 10,colors=‘k‘)
117 plt.scatter(class1[:,0], class1[:,1],color = colors[1], s = 2,label = "class1Data")
118 plt.scatter(class0[:,0], class0[:,1],color = colors[2], s = 2,label = "class0Data")
119 plt.scatter(errorP[:,0], errorP[:,1],color = colors[3], s = 8,label = "errorData")
120 plt.text(1.48, 1.85, "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)), 121 size = 15, ha="center", va="center", bbox=dict(boxstyle="round", ec=(1., 0.5, 0.5), fc=(1., 1., 1.)))
122 R = [Rectangle((0,0),0,0, color = colors[k]) for k in range(4)]
123 plt.legend(R, ["realBoundary", "class1Data", "class0Data", "errorData"], loc=[0.81, 0.2], ncol=1, numpoints=1, framealpha = 1)
124
125 if dim == 3:
126 ax = Axes3D(fig)
127 ax.set_xlim3d(0.0, 2.0)
128 ax.set_ylim3d(0.0, 2.0)
129 ax.set_zlim3d(0.0, 2.0)
130 ax.set_xlabel(‘X‘, fontdict={‘size‘: 15, ‘color‘: ‘k‘})
131 ax.set_ylabel(‘Y‘, fontdict={‘size‘: 15, ‘color‘: ‘k‘})
132 ax.set_zlabel(‘W‘, fontdict={‘size‘: 15, ‘color‘: ‘k‘})
133 v = [(0, 0, 0.5), (0, 0.5, 0), (1, 2, 0), (2, 2, 1.5), (2, 1.5, 2), (1, 0, 2)]
134 f = [[0,1,2,3,4,5]]
135 poly3d = [[v[i] for i in j] for j in f]
136 ax.add_collection3d(Poly3DCollection(poly3d, edgecolor = ‘k‘, facecolors = colors[0]+[trans], linewidths=1))
137 ax.scatter(class1[:,0], class1[:,1],class1[:,2], color = colors[1], s = 2, label = "class1")
138 ax.scatter(class0[:,0], class0[:,1],class0[:,2], color = colors[2], s = 2, label = "class0")
139 ax.scatter(errorP[:,0], errorP[:,1],errorP[:,2], color = colors[3], s = 8, label = "errorData")
140 ax.text3D(1.62, 2, 2.35, "realBoundary: -3x + 2y +2z = 1\nmyF(x,y,z) = " + str(round(para[0][0],2)) + " x + " + 141 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)), 142 size = 12, ha="center", va="center", bbox=dict(boxstyle="round", ec=(1, 0.5, 0.5), fc=(1, 1, 1)))
143 R = [Rectangle((0,0),0,0, color = colors[k]) for k in range(4)]
144 plt.legend(R, ["realBoundary", "class1Data", "class0Data", "errorData"], loc=[0.83, 0.1], ncol=1, numpoints=1, framealpha = 1)
145
146 fig.savefig("R:\\dim" + str(dim) + ".png")
147 plt.close()
148
149 if __name__ == ‘__main__‘:
150 test(1)
151 test(2)
152 test(3)
153 test(4)
● 输出结果
dim = 1, errorRatio = 0.003 dim = 2, errorRatio = 0.0307 dim = 3, errorRatio = 0.0186 dim = 4, errorRatio = 0.0349
原文地址：https://www.cnblogs.com/cuancuancuanhao/p/11111014.html
时间： 2024-07-29 13:42:20