logistic 回归(线性和非线性)
Posted qiang-wei
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一:线性logistic 回归
代码如下:
import numpy as np import pandas as pd import matplotlib.pyplot as plt import scipy.optimize as opt import seaborn as sns #读取数据集 path = ‘ex2data1.txt‘ data = pd.read_csv(path, header=None, names=[‘Exam 1‘, ‘Exam 2‘, ‘Admitted‘]) #将正负数据集分开 positive = data[data[‘Admitted‘].isin([1])] negative = data[data[‘Admitted‘].isin([0])] ‘‘‘ #查看分布 fig, ax = plt.subplots(figsize=(12, 8)) ax.scatter(positive[‘Exam 1‘], positive[‘Exam 2‘], s=60, c=‘b‘, marker=‘o‘, label=‘Admitted‘) ax.scatter(negative[‘Exam 1‘], negative[‘Exam 2‘], s=50, c=‘r‘, marker=‘x‘, label=‘UnAdmitted‘) ax.legend() ax.set_xlabel(‘Exam 1 Score‘) ax.set_ylabel(‘Exam 2 Score‘) plt.show() ‘‘‘ #sigmoid函数实现 def sigmoid(h): return 1 / (1 + np.exp(-h)) ‘‘‘ #测试sigmoid函数 nums = np.arange(-10, 11, step=1) fig, ax = plt.subplots(figsize=(12, 8)) ax.plot(nums, sigmoid(nums), ‘k‘) plt.show() ‘‘‘ #计算损失函数值 def cost(theta, X, y): theta = np.matrix(theta) X = np.matrix(X) y = np.matrix(y) part1 = np.multiply(-y, np.log(sigmoid(X * theta.T))) part2 = np.multiply((1-y), np.log(1-sigmoid(X * theta.T))) return np.sum(part1-part2) / len(X) #在原矩阵第1列前加一列全1 data.insert(0, ‘ones‘, 1) cols = data.shape[1] X = data.iloc[:, 0:cols-1] y = data.iloc[:, cols-1:cols] X = np.array(X.values) y = np.array(y.values) theta = np.zeros(3) #这里是一个行向量 #返回梯度向量,注意是向量 def gradient(theta, X, y): theta = np.matrix(theta) X = np.matrix(X) y = np.matrix(y) parameters = theta.ravel().shape[1] grad = np.zeros(parameters) error = sigmoid(X * theta.T) - y grad = error.T.dot(X) grad = grad / len(X) return grad #通过高级算法计算出最好的theta值 result = opt.fmin_tnc(func=cost, x0=theta, fprime=gradient, args=(X, y)) #print(cost(result[0], X, y)) #测试所得theta的性能 #计算原数据集的预测情况 def predict(theta, X): theta = np.matrix(theta) X = np.matrix(X) probability = sigmoid(X * theta.T) return [1 if i > 0.5 else 0 for i in probability] theta_min = result[0] predictions = predict(theta_min, X) correct = [1 if((a == 1 and b == 1) or(a == 0 and b == 0)) else 0 for(a, b) in zip(predictions, y)] accuracy = (sum(map(int, correct)) % len(correct)) print(‘accuracy = {0}%‘.format(accuracy))#训练集测试准确度89% # 作图 theta_temp = theta_min theta_temp = theta_temp / theta_temp[2] x = np.arange(130, step=0.1) y = -(theta_temp[0] + theta_temp[1] * x) #画出原点 sns.set(context=‘notebook‘, style=‘ticks‘, font_scale=1.5) sns.lmplot(‘Exam 1‘, ‘Exam 2‘, hue=‘Admitted‘, data=data, size=6, fit_reg=False, scatter_kws={"s": 25} ) #画出分界线 plt.plot(x, y, ‘grey‘) plt.xlim(0, 130) plt.ylim(0, 130) plt.title(‘Decision Boundary‘) plt.show()
二:非线性logistic 回归(正则化)
代码如下:
import pandas as pd import numpy as np import scipy.optimize as opt import matplotlib.pyplot as plt path = ‘ex2data2.txt‘ data = pd.read_csv(path, header=None, names=[‘Test 1‘, ‘Test 2‘, ‘Accepted‘]) positive = data[data[‘Accepted‘].isin([1])] negative = data[data[‘Accepted‘].isin([0])] ‘‘‘ #显示原始数据的分布 fig, ax = plt.subplots(figsize=(12, 8)) ax.scatter(positive[‘Test 1‘], positive[‘Test 2‘], s=50, c=‘b‘, marker=‘o‘, label=‘Accepted‘) ax.scatter(negative[‘Test 1‘], negative[‘Test 2‘], s=50, c=‘r‘, marker=‘x‘, label=‘Unaccepted‘) ax.legend() #显示右上角的Accepted 和 Unaccepted标签 ax.set_xlabel(‘Test 1 Score‘) ax.set_ylabel(‘Test 2 Score‘) plt.show() ‘‘‘ degree = 5 x1 = data[‘Test 1‘] x2 = data[‘Test 2‘] #在data的第三列插入一列全1 data.insert(3, ‘Ones‘, 1) #创建多项式特征值,最高阶为4 for i in range(1, degree): for j in range(0, i): data[‘F‘ + str(i) + str(j)] = np.power(x1, i-j) * np.power(x2, j) #删除原数据中的test 1和test 2两列 data.drop(‘Test 1‘, axis=1, inplace=True) data.drop(‘Test 2‘, axis=1, inplace=True) #sigmoid函数实现 def sigmoid(h): return 1 / (1 + np.exp(-h)) def cost(theta, X, y, learnRate): theta = np.matrix(theta) X = np.matrix(X) y = np.matrix(y) first = np.multiply(-y, np.log(sigmoid(X * theta.T))) second = np.multiply((1 - y), np.log(1 - sigmoid(X * theta.T))) reg = (learnRate / (2 * len(X))) * np.sum(np.power(theta[:, 1:theta.shape[1]], 2)) return np.sum(first - second) / len(X) + reg learnRate = 1 cols = data.shape[1] X = data.iloc[:, 1:cols] y = data.iloc[:, 0:1] X = np.array(X) y = np.array(y) theta = np.zeros(X.shape[1]) #计算原数据集的预测情况 def predict(theta, X): theta = np.matrix(theta) X = np.matrix(X) probability = sigmoid(X * theta.T) return [1 if i > 0.5 else 0 for i in probability] def gradientReg(theta, X, y, learnRate): theta = np.matrix(theta) X = np.matrix(X) y = np.matrix(y) paramates = int(theta.ravel().shape[1]) grad = np.zeros(paramates) grad = (sigmoid(X * theta.T) - y).T * X / len(X) + (learnRate / len(X)) * theta[:, i] grad[0] = grad[0] - (learnRate / len(X)) * theta[:, i] return grad result = opt.fmin_tnc(func=cost, x0=theta, fprime=gradientReg, args=(X, y, learnRate)) print(result) theta_min = np.matrix(result[0]) predictions = predict(theta_min, X) correct = [1 if((a == 1 and b == 1) or(a == 0 and b == 0)) else 0 for(a, b) in zip(predictions, y)] accuracy = (sum(map(int, correct)) % len(correct)) print(‘accuracy = {0}%‘.format(accuracy))
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