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。
