import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

import os

path='data'+os.sep+'Logireg_data.txt'

pdData=pd.read_csv(path,header=None,names=['Exam1','Exam2','Admitted'])

pdData.head()

print(pdData.head())

print(pdData.shape)

positive=pdData[pdData['Admitted']==1]#定义正

nagative=pdData[pdData['Admitted']==0]#定义负

fig,ax=plt.subplots(figsize=(10,5))

ax.scatter(positive['Exam1'],positive['Exam2'],s=30,c='b',marker='o',label='Admitted')

ax.scatter(nagative['Exam1'],nagative['Exam2'],s=30,c='r',marker='x',label='not Admitted')

ax.legend()

ax.set_xlabel('Exam 1 score')

ax.set_ylabel('Exam 2 score')

plt.show()#画图

##实现算法 the logistics regression 目标建立一个分类器 设置阈值来判断录取结果

##sigmoid 函数

def sigmoid(z):

    return 1/(1+np.exp(-z))

#画图

nums=np.arange(-10,10,step=1)

fig,ax=plt.subplots(figsize=(12,4))

ax.plot(nums,sigmoid(nums),'r')#画图定义

plt.show()

#按照理论实现预测函数

def model(X,theta):

    return sigmoid(np.dot(X,theta.T))

pdData.insert(0,'ones',1)#插入一列

orig_data=pdData.as_matrix()

cols=orig_data.shape[1]

X=orig_data[:,0:cols-1]

y=orig_data[:,cols-1:cols]

theta=np.zeros([1,3])

print(X[:5])

print(X.shape,y.shape,theta.shape)

##损失函数

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))

print(cost(X,y,theta))

#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())):  # for each parmeter

        term = np.multiply(error, X[:, j])

        grad[0, j] = np.sum(term) / len(X)

    return grad

##比较3种不同梯度下降方法

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

import numpy.random

#打乱数据洗牌

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):

    # 梯度下降求解

    init_time = time.time()

    i = 0  # 迭代次数

    k = 0  # batch

    X, y = shuffledata(data)

    grad = np.zeros(theta.shape)  # 计算的梯度

    costs = [cost(X, y, theta)]  # 损失值

    while True:

        grad = gradient(X[k:k + batchSize], y[k:k + batchSize], theta)

        k += batchSize  # 取batch数量个数据

        if k >= n:

            k = 0

            X, y = shuffledata(data)  # 重新洗牌

        theta = theta - alpha * grad  # 参数更新

        costs.append(cost(X, y, theta))  # 计算新的损失

        i += 1

        if stopType == STOP_ITER:

            value = i

        elif stopType == STOP_COST:

            value = costs

        elif stopType == STOP_GRAD:

            value = grad

        if stopCriterion(stopType, value, thresh): break

    return theta, i - 1, costs, grad, time.time() - init_time

#选择梯度下降

def runExpe(data, theta, batchSize, stopType, thresh, alpha):

    #import pdb; pdb.set_trace();

    theta, iter, costs, grad, dur = descent(data, theta, batchSize, stopType, thresh, alpha)

    name = "Original" if (data[:,1]>2).sum() > 1 else "Scaled"

    name += " data - learning rate: {} - ".format(alpha)

    if batchSize==n: strDescType = "Gradient"

    elif batchSize==1:  strDescType = "Stochastic"

    else: strDescType = "Mini-batch ({})".format(batchSize)

    name += strDescType + " descent - Stop: "

    if stopType == STOP_ITER: strStop = "{} iterations".format(thresh)

    elif stopType == STOP_COST: strStop = "costs change < {}".format(thresh)

    else: strStop = "gradient norm < {}".format(thresh)

    name += strStop

    print ("***{}\nTheta: {} - Iter: {} - Last cost: {:03.2f} - Duration: {:03.2f}s".format(

        name, theta, iter, costs[-1], dur))

    fig, ax = plt.subplots(figsize=(12,4))

    ax.plot(np.arange(len(costs)), costs, 'r')

    ax.set_xlabel('Iterations')

    ax.set_ylabel('Cost')

    ax.set_title(name.upper() + ' - Error vs. Iteration')

    return theta

n= 100

runExpe(orig_data,theta,n,STOP_ITER,thresh=5000,alpha=0.000001)

plt.show()

runExpe(orig_data,theta,n,STOP_GRAD,thresh=0.05,alpha=0.001)

plt.show()

runExpe(orig_data,theta,n,STOP_COST,thresh=0.000001,alpha=0.001)

plt.show()

#对比

runExpe(orig_data, theta, 1, STOP_ITER, thresh=5000, alpha=0.001)

plt.show()

runExpe(orig_data, theta, 1, STOP_ITER, thresh=15000, alpha=0.000002)

plt.show()

runExpe(orig_data, theta, 16, STOP_ITER, thresh=15000, alpha=0.001)

plt.show()

##对数据进行标准化 将数据按其属性(按列进行)减去其均值，然后除以其方差。

#最后得到的结果是，对每个属性/每列来说所有数据都聚集在0附近，方差值为1

from sklearn import preprocessing as pp

scaled_data = orig_data.copy()

scaled_data[:, 1:3] = pp.scale(orig_data[:, 1:3])

runExpe(scaled_data, theta, n, STOP_ITER, thresh=5000, alpha=0.001)

#设定阈值

def predict(X, theta):

    return [1 if x >= 0.5 else 0 for x in model(X, theta)]

# if __name__=='__main__':

scaled_X = scaled_data[:, :3]

y = scaled_data[:, 3]

predictions = predict(scaled_X, theta)

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))

    Exam1      Exam2  Admitted

0  34.623660  78.024693         0

1  30.286711  43.894998         0

2  35.847409  72.902198         0

3  60.182599  86.308552         1

4  79.032736  75.344376         1

(100, 3)

[[ 1.         34.62365962 78.02469282]

 [ 1.         30.28671077 43.89499752]

 [ 1.         35.84740877 72.90219803]

 [ 1.         60.18259939 86.3085521 ]

 [ 1.         79.03273605 75.34437644]]

(100, 3) (100, 1) (1, 3)

0.6931471805599453

***Original data - learning rate: 1e-06 - Gradient descent - Stop: 5000 iterations

Theta: [[-0.00027127  0.00705232  0.00376711]] - Iter: 5000 - Last cost: 0.63 - Duration: 1.42s

***Original data - learning rate: 0.001 - Gradient descent - Stop: gradient norm < 0.05

Theta: [[-2.37033409  0.02721692  0.01899456]] - Iter: 40045 - Last cost: 0.49 - Duration: 11.63s

***Original data - learning rate: 0.001 - Gradient descent - Stop: costs change < 1e-06

Theta: [[-5.13364014  0.04771429  0.04072397]] - Iter: 109901 - Last cost: 0.38 - Duration: 32.27s

***Original data - learning rate: 0.001 - Stochastic descent - Stop: 5000 iterations

Theta: [[-0.36946801  0.0618896   0.05188799]] - Iter: 5000 - Last cost: 2.28 - Duration: 0.60s

***Original data - learning rate: 2e-06 - Stochastic descent - Stop: 15000 iterations

Theta: [[-0.00201976  0.01010609  0.00105193]] - Iter: 15000 - Last cost: 0.63 - Duration: 1.67s

***Original data - learning rate: 0.001 - Mini-batch (16) descent - Stop: 15000 iterations

Theta: [[-1.03184406  0.02958433  0.02230517]] - Iter: 15000 - Last cost: 0.80 - Duration: 2.10s

***Scaled data - learning rate: 0.001 - Gradient descent - Stop: 5000 iterations

Theta: [[0.3080807  0.86494967 0.77367651]] - Iter: 5000 - Last cost: 0.38 - Duration: 1.51s

accuracy = 60%