import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import os
path = 'LogiReg_data.txt'
pdData = pd.read_csv(path, header=None, names=['Exam 1', 'Exam 2', 'Admitted'])
#n = 100
#theta = 5000
#alpha=0.000001
def sigmoid(z):
return 1 / (1 + np.exp(-z))#1/(1+e的-z次幂)
# 上述画出函数图
# nums = np.arange(-10, 10, step=1)
# fig, ax = plt.subplots(figsize=(12, 4))
# ax.plot(nums, sigmoid(nums), 'r')
# plt.show()
#(θ0 θ1 θ2)*（1 x1 x2）的转置
#np.dot表示矩阵的乘法
def model(X, theta):
return sigmoid(np.dot(X, theta.T))
#插入一列名为Ones的全为1的列
pdData.insert(0, 'Ones', 1)
#X，y表示0到cols-1和cols-1到cols
orig_data = pdData.as_matrix()
cols = orig_data.shape[1]
X = orig_data[:,0: cols-1]
y = orig_data[:,cols-1: cols]
#填充0组成的一行三列的矩阵
theta = np.zeros([1, 3])
#损失函数如图
def cost(X, y, theta):
left = np.multiply(-y, np.log(model(X, theta)))
right = np.multiply(1 - y, np.log(1 - model(X, theta)))
return np.sum(left - right) / (len(X))
#计算梯度
def gradient(X, y, theta):
grad = np.zeros(theta.shape)
error = (model(X, theta)-y).ravel()
for j in range(len(theta.ravel())):
term = np.multiply(error, X[ :,j])
grad[0, j] = np.sum(term) / len(X)
return grad
STOP_ITER = 0
STOP_COST = 1
STOP_GRAD = 2
def stopCriterion(type, value, threshold):
if type == STOP_ITER:
return value > threshold
elif type == STOP_COST:
return abs(value[-1]-value[-2]) < threshold
elif type == STOP_GRAD:
return np.linalg.norm(value) < threshold
#洗牌
import numpy.random
def shuffleData(data):
np.random.shuffle(data)
cols = data.shape[1]
X = data[:, 0:cols-1]
y = data[:, cols-1:]
return X, y
import time
def descent(data, theta, batchSize, stopType, thresh, alpha):
init_time = time.time()
i = 0#迭代次数
k = 0#batch
X, y = shuffleData(data)
grad = np.zeros(theta, )#计算梯度
costs = [cost(X, y, theta)]#损失值
while(True):
grad = gradient(X[k:k+batchSize], theta)
k += batchSize
if k >= n:
k = 0
X, y = shuffleData(data)#洗牌
theta = theta - alpha*grad#参数更新
costs.append(costs(X, y, theta))
i += 1
if stopType == STOP_ITER: value = i
elif stopType == STOP_COST: value = costs
elif stopType == STOP_GRAD: value = grad
if stopCriterion(stopType, value, theta): break
return theta, i-1, costs, grad, time.time() - init_time
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