logistic 迴歸（線性和非線性）

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一：線性logistic 迴歸

代碼如下：

import numpy as npimport pandas as pdimport matplotlib.pyplot as pltimport scipy.optimize as optimport seaborn as sns#讀取資料集path = ‘ex2data1.txt‘data = pd.read_csv(path, header=None, names=[‘Exam 1‘, ‘Exam 2‘, ‘Admitted‘])#將正負資料集分開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函數實現def sigmoid(h):    return 1 / (1 + np.exp(-h))‘‘‘#測試sigmoid函數nums = np.arange(-10, 11, step=1)fig, ax = plt.subplots(figsize=(12, 8))ax.plot(nums, sigmoid(nums), ‘k‘)plt.show()‘‘‘#計算損失函數值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)#在原矩陣第1列前加一列全1data.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) #這裡是一個行向量#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#通過進階演算法計算出最好的theta值result = opt.fmin_tnc(func=cost, x0=theta, fprime=gradient, args=(X, y))#print(cost(result[0], X, y))#測試所得theta的效能#計算原資料集的預測情況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))#訓練集測試準確度89%# 作圖theta_temp = theta_mintheta_temp = theta_temp / theta_temp[2]x = np.arange(130, step=0.1)y = -(theta_temp[0] + theta_temp[1] * x)#畫出原點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}           )#畫出分界線plt.plot(x, y, ‘grey‘)plt.xlim(0, 130)plt.ylim(0, 130)plt.title(‘Decision Boundary‘)plt.show()

二：非線性logistic 迴歸（正則化）

代碼如下：

import pandas as pdimport numpy as npimport scipy.optimize as optimport matplotlib.pyplot as pltpath = ‘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])]‘‘‘#顯示未經處理資料的分布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() #顯示右上方的Accepted 和 Unaccepted標籤ax.set_xlabel(‘Test 1 Score‘)ax.set_ylabel(‘Test 2 Score‘)plt.show()‘‘‘degree = 5x1 = data[‘Test 1‘]x2 = data[‘Test 2‘]#在data的第三列插入一列全1data.insert(3, ‘Ones‘, 1)#建立多項式特徵值，最高階為4for 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)#刪除原資料中的test 1和test 2兩列data.drop(‘Test 1‘, axis=1, inplace=True)data.drop(‘Test 2‘, axis=1, inplace=True)#sigmoid函數實現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) + reglearnRate = 1cols = 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])#計算原資料集的預測情況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 gradresult = 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))

 

logistic 迴歸（線性和非線性）