输出结果

LoR之二分类算法实现预测期末考试成绩合格还是不合格

LoR回归函数

代码设计

import pandas as pd

import numpy as np

import matplotlib as mpl

import matplotlib.pyplot as plt

from scipy.optimize import minimize

from sklearn.preprocessing import PolynomialFeatures

pd.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):

   # 获得正负样本的下标(即哪些是正样本，哪些是负样本)

   neg = data[:,2] == 0

   pos = data[:,2] == 1

   

   if 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')  #绘图

#定义sigmoid函数

def sigmoid(z):

   return(1 / (1 + np.exp(-z)))

#定义损失函数

def costFunction(theta, X, y):

   m = y.size

   h = 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.size

   h = 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)

#最小化损失函数(梯度下降)，直接调用scipy里面的最小化损失函数的minimize函数

res = minimize(costFunction, initial_theta, args=(X,y), method=None, jac=gradient, options={'maxiter':400})

#进行预测

def predict(theta, X, threshold=0.5):

   p = sigmoid(X.dot(theta.T)) >= threshold

   return(p.astype('int'))

# 第一门课45分，第二门课85分的同学，拿到通过考试的概率

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))

#绘制二分类决策边界

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');