机器学习作业1

import pandas as pd
import numpy as np
from matplotlib import pyplot as plt

# 1
#所给数据绘制散点图
data = pd.read_csv('ex1data1.txt', header=None, names=['Population', 'Profit'])
data.head()

data.describe()
data.plot(kind='scatter', x='Population', y='Profit', figsize=(12,8))
plt.show()

#处理数据
# 新增一列，x0
data.insert(0, 'Ones', 1)
data.head()
""" Ones Population Profit 0 1 6.1101 17.5920 1 1 5.5277 9.1302 2 1 8.5186 13.6620 3 1 7.0032 11.8540 4 1 5.8598 6.8233"""
cols = data.shape[1]
X = data.iloc[:, 0:cols-1]
Y = data.iloc[:, cols-1:cols]

X = np.matrix(X.values)
Y = np.matrix(Y.values)
theta = np.matrix(np.array([0, 0]))

# 代价函数
def computeCost(X, Y, theta):
    inner = np.power((X * theta.T) - Y, 2)
    return np.sum(inner) / (2 * len(X))

#通过求解正规方程来计算最佳直线拟合
def normalEqn(X, Y):
    theta = np.linalg.inv(X.[email protected])@X.[email protected]
    return theta

theta = normalEqn(X, Y)
# 梯度下降的theta为 matrix([[-3.24140214, 1.1272942 ]])
theta

computeCost(X, Y, theta.reshape(1, -1))

# 画出拟合图像
x = np.linspace(data.Population.min(), data.Population.max(), 100)
f = theta[0,0] + theta[1,0] * x

plt.figure(figsize=(12, 8))
plt.xlabel('Population')
plt.ylabel('Profit')
l1 = plt.plot(x, f, label='Prediction', color='red')
#上画直线
l2 = plt.scatter(data.Population, data.Profit, label='Traing Data', )
#上画散点
plt.legend(loc='best')
plt.title('Predicted Profit vs Population Size')
plt.show()