逻辑回归和梯度下降简单应用案例

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import time
import numpy as np
import numpy.random
import pandas as pd
import matplotlib.pyplot as plt
import os

# 读取本地e盘一个记录成绩的文本(随机生成的一堆数字)
path = ‘e:\data.txt‘
# 两次考试成绩和是否被录取
pdData = pd.read_csv(path, header=None, names=[‘Exam1‘, ‘Exam2‘, ‘Admitted‘])

‘‘‘
print(pdData.shape)
(100, 3)
获得数据的维度（100行3列）
说明现在一共有100条数据
‘‘‘

‘‘‘
# 这里画一张图，大概观察下数据(见图1)
positive = pdData[pdData[‘Admitted‘] == 1]
negative = pdData[pdData[‘Admitted‘] == 0]
fig, ax = plt.subplots(figsize=(10, 5))
ax.scatter(positive[‘Exam1‘], positive[‘Exam2‘], s=30, c=‘b‘, marker=‘o‘, label=‘Admitted‘)
ax.scatter(negative[‘Exam1‘], negative[‘Exam2‘], s=30, c=‘r‘, marker=‘x‘, label=‘Not Admitted‘)
ax.legend()
ax.set_xlabel(‘Exam1 Score‘)
ax.set_ylabel(‘Exam2 Score‘)
#plt.show()
‘‘‘


# 定义sigmoid函数
def sigmoid(z):
    return 1 / (1 + np.exp(-z))


‘‘‘
# 可以画sigmoid函数图形观察(图2):
nums = np.arange(-10, 10, step=1)
fig, ax = plt.subplots(figsize=(12, 4))
ax.plot(nums, sigmoid(nums), ‘b‘)
plt.show()
‘‘‘


# 预测函数
def model(X, theta):
    return sigmoid(np.dot(X, theta.T))


# 添加一列：全为1
pdData.insert(0, ‘Ones‘, 1)

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])


# 定义损失函数
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))


# 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


STOP_ITER = 0
STOP_COST = 1
STOP_GRAD = 2


def stopCriterion(type, value, threshold):
    # 设定三种不同的停止策略
    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
def shuffleData(data):
    np.random.shuffle(data)
    cols = data.shape[1]
    X = data[:, 0:cols - 1]
    y = data[:, cols - 1:]
    return X, y


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


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


# 选择的梯度下降方法是基于所有样本的

n = 100

# 设定迭代次数(图3)
runExpe(orig_data, theta, n, STOP_ITER, thresh=5000, alpha=0.000001)

# 根据损失值停止(图4)
runExpe(orig_data, theta, n, STOP_COST, thresh=0.000001, alpha=0.001)

# 根据梯度变化停止(图5)
runExpe(orig_data, theta, n, STOP_GRAD, thresh=0.05, alpha=0.001)
# plt.show()

from sklearn import preprocessing as pp

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

theta = runExpe(scaled_data, theta, 1, STOP_GRAD, thresh=0.002/5, alpha=0.001)

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


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))

#最后结论：accuracy = 89%