【機器學習】線性迴歸預測

airl發表於2022-06-23
機器學習

前言

迴歸分析就是用於預測輸入變數（自變數）和輸出變數（因變數）之間的關係，特別當輸入的值發生變化時，輸出變數值也發生改變！迴歸簡單來說就是對資料進行擬合。線性迴歸就是通過線性的函式對資料進行擬合。機器學習並不能實現預言，只能實現簡單的預測。我們這次對房價關於其他因素的關係。

波士頓房價預測

下載相關資料集

  • 資料集是506行14列的波士頓房價資料集，資料集是開源的。
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')

對資料集進行處理


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 變為506*14
housing_data = housing_data.reshape(housing_data.shape[0]//feature_num,feature_num)
print(housing_data.shape[0])
# 列印第一行資料
print(housing_data[:1])


## 歸一化

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]

模型定義

## 例項化模型
def Model():
    model = linear_model.LinearRegression()
    return model

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

視覺化模型效果

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()

整體程式碼

## 基於線性迴歸實現房價預測
## 擬合函式模型
## 梯度下降方法

## 開源房價策略資料集

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

import pandas as pd

from sklearn import  linear_model


## 下載之後註釋掉
'''
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
'''
## 資料載入

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 變為506*14
housing_data = housing_data.reshape(housing_data.shape[0]//feature_num,feature_num)
print(housing_data.shape[0])
# 列印第一行資料
print(housing_data[:1])


## 歸一化

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)


## 劃分資料集  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
## 線性迴歸

## 例項化模型
def Model():
    model = linear_model.LinearRegression()
    return model

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


## 模型訓練

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)

## 模型評估

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

image

總結

線性迴歸預測還是比較簡單的，可以簡單理解為函式擬合，資料集是使用的開源的波士頓房價的資料集，演算法也是打包好的包，方便我們引用。

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