分类：感知机
简单判断图片是纵向还是横向
训练数据：images1.csv
x1,x2,y 153,432,-1 220,262,-1 118,214,-1 474,384,1 485,411,1 233,430,-1 396,361,1 484,349,1 429,259,1 286,220,1 399,433,-1 403,340,1 252,34,1 497,472,1 379,416,-1 76,163,-1 263,112,1 26,193,-1 61,473,-1 420,253,1import numpy as np import matplotlib.pyplot as plt train = np.loadtxt('images1.csv',delimiter=',',skiprows=1) #取第一列和第二列 train_x = train[:,0:2] #取第三列 train_y = train[:,2] #plt.plot(train_x[train_y == 1,0],train_x[train_y == 1,1],'o') #plt.plot(train_x[train_y==-1,0],train_x[train_y==-1,1],'x') #plt.axis('scaled') #plt.show() #权重初始化 #w·x = w1x1 + w2x2 = 0 w = np.random.rand(2) #判别函数 def f(x): if np.dot(w,x)>=0: return 1 else: return -1; #迭代次数 epoch = 10 #更新次数 count = 0 #学习权重 for _ in range(epoch): for x,y in zip(train_x,train_y): if f(x) != y: w = w + y*x #输出日志 count += 1 print('第{}次：w={}'.format(count,w)) #w·x = w1x1 + w2x2 = 0 #x2 = -w1/w2*x1 x1 = np.arange(0,500) plt.plot(train_x[train_y == 1,0],train_x[train_y==1,1],'o') plt.plot(train_x[train_y==-1,0],train_x[train_y==-1,1],'x') plt.plot(x1,-w[0]/w[1]*x1,linestyle = 'dashed') plt.show() #预测 #200x100 横向 print(f([200,100])) #100x200 纵向 print(f([100,200]))
分类：逻辑回归
训练数据：images2.csv
x1,x2,y 153,432,0 220,262,0 118,214,0 474,384,1 485,411,1 233,430,0 396,361,1 484,349,1 429,259,1 286,220,1 399,433,0 403,340,1 252,34,1 497,472,1 379,416,0 76,163,0 263,112,1 26,193,0 61,473,0 420,253,1import numpy as np import matplotlib.pyplot as plt #读入 train = np.loadtxt('images2.csv',delimiter=',',skiprows=1) train_x = train[:,0:2] train_y = train[:,2] #初始化参数 theta = np.random.rand(3) #标准化 #axis=0会计算每列的平均值和标准差 mu = train_x.mean(axis=0) sigma = train_x.std(axis=0) def standardize(x): return (x-mu)/sigma train_z = standardize(train_x) #增加x0 def to_matrix(x): #创建和x1一样的行一列的矩阵 x0 = np.ones([x.shape[0],1]) #参数合并成一个矩阵 return np.hstack([x0,x]) X = to_matrix(train_z) #可视化 ''' plt.plot(train_z[train_y==1,0],train_z[train_y==1,1],'o') plt.plot(train_z[train_y==0,0],train_z[train_y==0,1],'x') plt.show() ''' #sigmoid函数 def f(x): return 1/(1+np.exp(-np.dot(x,theta))) #学习率 ETA = 1e-3 #迭代次数 epoch = 5000 #重复学习 for _ in range(epoch): theta = theta - ETA*np.dot(f(X)-train_y,X) #theta.Tx = 0 #theta.Tx = theta0x0 + theta1x1 + theta2x2 = 0 #x2 = -(theta0 + theta1*x1)/theta2 x0 = np.linspace(-2,2,100) plt.plot(train_z[train_y==1,0],train_z[train_y==1,0],'o') plt.plot(train_z[train_y==0,0],train_z[train_y==0,0],'x') plt.plot(x0,-(theta[0]+theta[1]*x0)/theta[2],linestyle='dashed') plt.show() #预测 #astype(np.int_)：将布尔值转为整数（True→1，False→0），最终输出0或1的分类结果。 def classify1(x): return (f(x)>=0.5).astype(np.int_) array = classify1(to_matrix(standardize([ [200,100], [100,200] ]))) print(array)分类：线性不可分分类问题
训练数据：
x1,x2,y 0.54508775,2.34541183,0 0.32769134,13.43066561,0 4.42748117,14.74150395,0 2.98189041,-1.81818172,1 4.02286274,8.90695686,1 2.26722613,-6.61287392,1 -2.66447221,5.05453871,1 -1.03482441,-1.95643469,1 4.06331548,1.70892541,1 2.89053966,6.07174283,0 2.26929206,10.59789814,0 4.68096051,13.01153161,1 1.27884366,-9.83826738,1 -0.1485496,12.99605136,0 -0.65113893,10.59417745,0 3.69145079,3.25209182,1 -0.63429623,11.6135625,0 0.17589959,5.84139826,0 0.98204409,-9.41271559,1 -0.11094911,6.27900499,0import numpy as np import matplotlib.pyplot as plt #读入 train = np.loadtxt('data3.csv',delimiter=',',skiprows=1) train_x = train[:,0:2] train_y = train[:,2] ''' plt.plot(train_x[train_y==1,0],train_x[train_y==1,1],'o') plt.plot(train_x[train_y==0,0],train_x[train_y==0,1],'x') plt.show() ''' #参数初始化 theta = np.random.rand(4) #精度历史记录 accuracies = [] #标准化 mu = train_x.mean(axis=0) sigma = train_x.std(axis=0) def standardize(x): return (x-mu)/sigma train_z = standardize(train_x) #增加x0和x3 def to_matrix(x): x0 = np.ones([x.shape[0],1]) x3 = x[:,0,np.newaxis]**2 return np.hstack([x0,x,x3]) X = to_matrix(train_z) #sigmoid函数 def f(x): return 1/(1+np.exp(-np.dot(x,theta))) #学习率 ETA = 1e-3 #迭代次数 epoch = 5000 def classify1(x): return (f(x)>=0.5).astype(np.int_) #重复学习 for _ in range(epoch): theta = theta - ETA*np.dot(f(X)-train_y,X) #计算现在精度 result = classify1(X) == train_y accuracy = len(result[result==True])/len(result) accuracies.append(accuracy) #theta.Tx = theta0x0 + theta1x1 + theta2x2 + theta3x3^2 # = theta0 + theta1x1 + theta2x2 + theta3x1^2 = 0 #x2 = -(theta0+theta1x1+theta3x1^2)/theta2 x1 = np.linspace(-2,2,100) x2 = -(theta[0]+theta[1]*x1+theta[3]*x1**2)/theta[2] plt.plot(train_z[train_y==1,0],train_z[train_y==1,1],'o') plt.plot(train_z[train_y==0,0],train_z[train_y==0,1],'x') plt.plot(x1,x2,linestyle='dashed') plt.show() #绘制acc曲线 # x = np.arange(len(accuracies)) # plt.plot(x,accuracies) # plt.show()
因为训练数据过少只有20个 精度值只能为0.05的整数倍 所以acc曲线有棱有角：
分类：线性不可分分类问题 随机梯度下降法的实现
训练数据：同上
import numpy as np import matplotlib.pyplot as plt #读入 train = np.loadtxt('data3.csv',delimiter=',',skiprows=1) train_x = train[:,0:2] train_y = train[:,2] ''' plt.plot(train_x[train_y==1,0],train_x[train_y==1,1],'o') plt.plot(train_x[train_y==0,0],train_x[train_y==0,1],'x') plt.show() ''' #参数初始化 theta = np.random.rand(4) #精度历史记录 accuracies = [] #标准化 mu = train_x.mean(axis=0) sigma = train_x.std(axis=0) def standardize(x): return (x-mu)/sigma train_z = standardize(train_x) #增加x0和x3 def to_matrix(x): x0 = np.ones([x.shape[0],1]) x3 = x[:,0,np.newaxis]**2 return np.hstack([x0,x,x3]) X = to_matrix(train_z) #sigmoid函数 def f(x): return 1/(1+np.exp(-np.dot(x,theta))) #学习率 ETA = 1e-3 #迭代次数 epoch = 5000 def classify1(x): return (f(x)>=0.5).astype(np.int_) #重复学习 for _ in range(epoch): #使用随机梯度下降法更新参数 p = np.random.permutation(X.shape[0]) for x,y in zip(X[p,:],train_y[p]): theta = theta - ETA*(f(x)-y)*x #theta.Tx = theta0x0 + theta1x1 + theta2x2 + theta3x3^2 # = theta0 + theta1x1 + theta2x2 + theta3x1^2 = 0 #x2 = -(theta0+theta1x1+theta3x1^2)/theta2 x1 = np.linspace(-2,2,100) x2 = -(theta[0]+theta[1]*x1+theta[3]*x1**2)/theta[2] plt.plot(train_z[train_y==1,0],train_z[train_y==1,1],'o') plt.plot(train_z[train_y==0,0],train_z[train_y==0,1],'x') plt.plot(x1,x2,linestyle='dashed') plt.show()