，神经网络
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? 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
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