线性回归预测 – hjk

前言

回归分析就是用于预测输入变量（自变量）和输出变量（因变量）之间的关系，特别当输入的值发生变化时，输出变量值也发生改变！回归简单来说就是对数据进行拟合。线性回归就是通过线性的函数对数据进行拟合。机器学习并不能实现预言，只能实现简单的预测。我们这次对房价关于其他因素的关系。

波士顿房价预测

下载相关数据集

• 数据集是506行14列的波士顿房价数据集，数据集是开源的。

wget.download(url="https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data",out= "housing.data")
wget.download(url="https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.names",out="housing.names")
wget.download(url="https://archive.ics.uci.edu/ml/machine-learning-databases/housing/Index",out="Index")

对数据集进行处理

feature_names = ["CRIM","ZN","INDUS","CHAS","NOX","RM","AGE","DIS","RAD","TAX","PTRATIO","B","LSTAT","MEDV"]
feature_num = len(feature_names)
print(feature_num)

# 把7084 变为506*14
housing_data = housing_data.reshape(housing_data.shape[0]//feature_num,feature_num)
print(housing_data.shape[0])
# 打印第一行数据
print(housing_data[:1])


## 归一化

feature_max = housing_data.max(axis=0)
feature_min = housing_data.min(axis=0)
feature_avg = housing_data.sum(axis=0)/housing_data.shape[0]

模型定义

## 实例化模型
def Model():
    model = linear_model.LinearRegression()
    return model

# 拟合模型
def train(model,x,y):
    model.fit(x,y)

可视化模型效果

def draw_infer_result(groud_truths,infer_results):
    title = "Boston"
    plt.title(title,fontsize=24)
    x = np.arange(1,40)
    y = x
    plt.plot(x,y)
    plt.xlabel("groud_truth")
    plt.ylabel("infer_results")
    plt.scatter(groud_truths,infer_results,edgecolors="green",label="training cost")
    plt.grid()
    plt.show()

整体代码

## 基于线性回归实现房价预测
## 拟合函数模型
## 梯度下降方法

## 开源房价策略数据集

import wget
import numpy as np
import os
import matplotlib
import matplotlib.pyplot as plt

import pandas as pd

from sklearn import  linear_model


## 下载之后注释掉
"""
wget.download(url="https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data",out= "housing.data")
wget.download(url="https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.names",out="housing.names")
wget.download(url="https://archive.ics.uci.edu/ml/machine-learning-databases/housing/Index",out="Index")
"""
"""
    1. CRIM      per capita crime rate by town
    2. ZN        proportion of residential land zoned for lots over 
                 25,000 sq.ft.
    3. INDUS     proportion of non-retail business acres per town
    4. CHAS      Charles River dummy variable (= 1 if tract bounds 
                 river; 0 otherwise)
    5. NOX       nitric oxides concentration (parts per 10 million)
    6. RM        average number of rooms per dwelling
    7. AGE       proportion of owner-occupied units built prior to 1940
    8. DIS       weighted distances to five Boston employment centres
    9. RAD       index of accessibility to radial highways
    10. TAX      full-value property-tax rate per $10,000
    11. PTRATIO  pupil-teacher ratio by town
    12. B        1000(Bk - 0.63)^2 where Bk is the proportion of blacks 
                 by town
    13. LSTAT    % lower status of the population
    14. MEDV     Median value of owner-occupied homes in $1000"s
"""
## 数据加载

datafile = "./housing.data"

housing_data = np.fromfile(datafile,sep=" ")

print(housing_data.shape)


feature_names = ["CRIM","ZN","INDUS","CHAS","NOX","RM","AGE","DIS","RAD","TAX","PTRATIO","B","LSTAT","MEDV"]
feature_num = len(feature_names)
print(feature_num)

# 把7084 变为506*14
housing_data = housing_data.reshape(housing_data.shape[0]//feature_num,feature_num)
print(housing_data.shape[0])
# 打印第一行数据
print(housing_data[:1])


## 归一化

feature_max = housing_data.max(axis=0)
feature_min = housing_data.min(axis=0)
feature_avg = housing_data.sum(axis=0)/housing_data.shape[0]

def feature_norm(input):
    f_size = input.shape
    output_features = np.zeros(f_size,np.float32)
    for batch_id in range(f_size[0]):
        for index in range(13):
            output_features[batch_id][index] = (input[batch_id][index]-feature_avg[index])/(feature_max[index]-feature_min[index])

    return output_features


housing_features = feature_norm(housing_data[:,:13])

housing_data = np.c_[housing_features,housing_data[:,-1]].astype(np.float32)


## 划分数据集  8：2
ratio =0.8

offset = int(housing_data.shape[0]*ratio)

train_data = housing_data[:offset]
test_data = housing_data[offset:]

print(train_data[:2])


## 模型配置
## 线性回归

## 实例化模型
def Model():
    model = linear_model.LinearRegression()
    return model

# 拟合模型
def train(model,x,y):
    model.fit(x,y)


## 模型训练

X, y = train_data[:,:13], train_data[:,-1:]

model = Model()
train(model,X,y)

x_test, y_test = test_data[:,:13], test_data[:,-1:]
prefict = model.predict(x_test)

## 模型评估

infer_results = []
groud_truths = []

def draw_infer_result(groud_truths,infer_results):
    title = "Boston"
    plt.title(title,fontsize=24)
    x = np.arange(1,40)
    y = x
    plt.plot(x,y)
    plt.xlabel("groud_truth")
    plt.ylabel("infer_results")
    plt.scatter(groud_truths,infer_results,edgecolors="green",label="training cost")
    plt.grid()
    plt.show()


draw_infer_result(y_test,prefict)

效果展示

总结

线性回归预测还是比较简单的，可以简单理解为函数拟合，数据集是使用的开源的波士顿房价的数据集，算法也是打包好的包，方便我们引用。