ML之LoR：LoR之二分類之線性決策算法實現(xiàn)根據(jù)兩課成績分?jǐn)?shù)~預(yù)測期末通過率(合格還是不合格)

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目錄

輸出結(jié)果

代碼設(shè)計

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輸出結(jié)果

LoR之二分類算法實現(xiàn)預(yù)測期末考試成績合格還是不合格

LoR回歸函數(shù)

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代碼設(shè)計

import pandas as pd import numpy as np import matplotlib as mpl import matplotlib.pyplot as pltfrom scipy.optimize import minimizefrom sklearn.preprocessing import PolynomialFeaturespd.set_option('display.notebook_repr_html', False) pd.set_option('display.max_columns', None) pd.set_option('display.max_rows', 150) pd.set_option('display.max_seq_items', None)import seaborn as sns sns.set_context('notebook') sns.set_style('white')def loaddata(file, delimeter):data = np.loadtxt(file, delimiter=delimeter)print('Dimensions: ',data.shape)print(data[1:6,:])return(data)def plotData(data, label_x, label_y, label_pos, label_neg, axes=None):# 獲得正負(fù)樣本的下標(biāo)(即哪些是正樣本，哪些是負(fù)樣本)neg = data[:,2] == 0pos = data[:,2] == 1if axes == None:axes = plt.gca()axes.scatter(data[pos][:,0], data[pos][:,1], marker='^', c='b', s=60, linewidth=2, label=label_pos)axes.scatter(data[neg][:,0], data[neg][:,1], c='y', s=60, label=label_neg)axes.set_xlabel(label_x)axes.set_ylabel(label_y)axes.legend(frameon= True, fancybox = True);data = loaddata('data1.txt', ',') X = np.c_[np.ones((data.shape[0],1)), data[:,0:2]] y = np.c_[data[:,2]] plotData(data, 'Exam 1 score', 'Exam 2 score', 'Pass', 'Fail') #繪圖#定義sigmoid函數(shù) def sigmoid(z):return(1 / (1 + np.exp(-z)))#定義損失函數(shù) def costFunction(theta, X, y):m = y.sizeh = sigmoid(X.dot(theta))J = -1*(1/m)*(np.log(h).T.dot(y)+np.log(1-h).T.dot(1-y))if np.isnan(J[0]):return(np.inf)return(J[0])#求解梯度 def gradient(theta, X, y):m = y.sizeh = sigmoid(X.dot(theta.reshape(-1,1)))grad =(1/m)*X.T.dot(h-y)return(grad.flatten())initial_theta = np.zeros(X.shape[1]) cost = costFunction(initial_theta, X, y) grad = gradient(initial_theta, X, y) print('Cost: \n', cost) print('Grad: \n', grad)#最小化損失函數(shù)(梯度下降)，直接調(diào)用scipy里面的最小化損失函數(shù)的minimize函數(shù) res = minimize(costFunction, initial_theta, args=(X,y), method=None, jac=gradient, options={'maxiter':400})#進(jìn)行預(yù)測 def predict(theta, X, threshold=0.5):p = sigmoid(X.dot(theta.T)) >= thresholdreturn(p.astype('int'))# 第一門課45分，第二門課85分的同學(xué)，拿到通過考試的概率 sigmoid(np.array([1, 45, 85]).dot(res.x.T)) p = predict(res.x, X) print('Train accuracy {}%'.format(100*sum(p == y.ravel())/p.size))#繪制二分類決策邊界 plt.scatter(45, 85, s=60, c='r', marker='v', label='(45, 85)') plotData(data, 'Exam 1 score', 'Exam 2 score', 'Pass', 'Failed') x1_min, x1_max = X[:,1].min(), X[:,1].max(), x2_min, x2_max = X[:,2].min(), X[:,2].max(), xx1, xx2 = np.meshgrid(np.linspace(x1_min, x1_max), np.linspace(x2_min, x2_max)) h = sigmoid(np.c_[np.ones((xx1.ravel().shape[0],1)), xx1.ravel(), xx2.ravel()].dot(res.x)) h = h.reshape(xx1.shape) plt.contour(xx1, xx2, h, [0.5], linewidths=1, colors='b');

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