线性回归算法实现-Toy模板网

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回归算法是一种有监督算法。
回归算法是一种比较常用的机器学习算法，用来建立“解释”变量(自变量X)和观测值(因变量Y)之间的关系；从机器学习的角度来讲，用于构建一个算法模型(函数)来做属性(X)与标签(Y)之间的映射关系，在算法的学习过程中，试图寻找一个函数使得参数之间的关系拟合性最好。回归算法中算法(函数)的最终结果是一个连续的数据值，输入值(属性值)是一个d 维度的属性/数值向量。

本文主要用于线性回归代码的实现，相关理论知识请参考博主的另一篇文章：机器学习（三）线性回归原理

一、目录结构

线性回归算法实现

二、数据预处理

import numpy as np

from utils.features.generate_sinusoids import generate_sinusoids


def prepare(data, polynomial_degree=0, sinusoid_degree=0, normalize_data=True):
    num_examples = data.shape[0]
    data_processed = np.copy(data)    
    features_mean = 0    
    features_deviation = 0    
    data_normalized = data_processed
    if normalize_data:
        (            
            data_normalized,
            features_mean,           
            features_deviation
        ) = normalize(data_processed)
      
    data_processed = data_normalized
    # 特征变换
    if sinusoid_degree > 0:
        sinusoids = generate_sinusoids(data_normalized, sinusoid_degree)        
        data_processed = np.concatenate((data_processed, sinusoids), axis=1)    
    # # 特征变换    
    # if polynomial_degree > 0:    
    #     polynomials = generate_polynomials(data_normalized, polynomial_degree, normalize_data)    
    #     data_processed = np.concatenate((data_processed, polynomials), axis=1)    
    data_processed = np.hstack((np.ones((num_examples, 1)), data_processed))    
    return data_processed, features_mean, features_deviation


def normalize(features):
    features_normalized = np.copy(features).astype(float)    
    # 计算均值    
    features_mean = np.mean(features, 0)    
    # 计算标准差    
    features_deviation = np.std(features, 0)    
    # 标准化操作    
    if features.shape[0] > 1:
        features_normalized -= features_mean

    # 防止除0    
    features_deviation[features_deviation == 0] = 1    
    features_normalized /= features_deviation

    return features_normalized, features_mean, features_deviation

三、generate_sinusoids函数的定义

import numpy as np


def generate_sinusoids(dataset, sinusoid_degree):
    num_examples = dataset.shape[0]    
    sinusoids = np.empty((num_examples, 0))    
    for degree in range(1, sinusoid_degree + 1):
        sinusoid_features = np.sin(degree * dataset)        
        sinusoids = np.concatenate((sinusoids, sinusoid_features), axis=1)    
    return sinusoids

四、线性回归

import numpy as np
from utils.features import pre_for_training


class LinearRegression:
    def __init__(self,
                     data,                 
                     labels,                 
                     polynomial_degree=0,                 
                     sinusoid_degree=0,                
                      normalize_data=True):
        """        
        对数据预处理，获取所有特征个数，初始化参数矩阵        
        :param data: 训练特征集        
        :param labels: 训练目标值        
        :param polynomial_degree: 特征变换        
        :param sinusoid_degree: 特征变换        
        :param normalize_data: 标准化数据处理        
        """        
        (data_processed, features_mean, features_deviation) = \
            pre_for_training.prepare(data=data, polynomial_degree=polynomial_degree, 
                                      sinusoid_degree=sinusoid_degree, normalize_data=normalize_data)
        self.data = data_processed                              
        self.labels = labels
        self.features_mean = features_mean
        self.features_deviation = features_deviation
        self.polynomial_degree = polynomial_degree
        self.sinusoid_degree = sinusoid_degree
        self.normalize_data = normalize_data
        num_features = self.data.shape[1]        
        self.theta = np.zeros((num_features, 1))    
        
        def train(self, alpha, num_iterations=500):
            """        
            执行梯度下降        
            :param alpha: 学习绿        
            :param num_iterations: 学习次数        
            :return: 特征参数，历史损失值        
            """        
            loss_history = self.gradient_descent(alpha=alpha, num_iterations=num_iterations)        
        return self.theta, loss_history

    def gradient_descent(self, alpha, num_iterations):
        """        
        迭代下降参数        
        :param alpha: 学习率        
        :param num_iterations: 训练次数        
        :return: 历史损失列表        
        """        
        loss_history = list()        
        for _ in range(num_iterations):
            self.gradient_step(alpha)            
            loss_history.append(self.loss_function(self.data, self.labels))        
        return loss_history

    def gradient_step(self, alpha):
        """        
        梯度下降，参数更新        
        :param alpha: 学习率        
        :return: 拟合参数       
         """        
        num_examples = self.data.shape[0]        
        predictions = LinearRegression.hypothesis(self.data, self.theta)        
        delta = predictions - self.labels
        theta = self.theta
        theta = theta - alpha * (1 / num_examples) * (np.dot(delta.T, self.data)).T
        self.theta = theta

    def loss_function(self, data, labels):
        """        
        计算损失        
        :param data: 特征参数        
        :param labels: 特目标值        
        :return:  损失结果        
        """        
        num_examples = data.shape[0]        
        delta = LinearRegression.hypothesis(data=self.data, theta=self.theta) - labels
        loss = (1 / 2) * np.dot(delta.T, delta)/num_examples
        # print(loss, loss.shape)        
        return loss[0][0]    
        
    @staticmethod    
    def hypothesis(data, theta):
            predictions = np.dot(data, theta)        
            return predictions


    def get_loss(self, data, labels):
        data_processed = pre_for_training.prepare(data=data, 
                                                  polynomial_degree=self.polynomial_degree, 
                                                  sinusoid_degree=self.sinusoid_degree,  
                                                  normalize_data=self.normalize_data)[0] 
                                                  
        return self.loss_function(data=data_processed, labels=labels)
        
        
    def predict(self, data):
        """        
        预测        
        :param data: 参数        
        :return: 预测结果        
        """        
        data_processed = pre_for_training.prepare(data=data, polynomial_degree=self.polynomial_degree, 
                                                 sinusoid_degree=self.sinusoid_degree,  
                                                 normalize_data=self.normalize_data)[0] 
        predictions = LinearRegression.hypothesis(data=data_processed, theta=self.theta)      
        return predictions

五、单参数预测

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

from linearRegression import linear_regression
from utils.features import pre_for_training

data = pd.read_csv("../data/wind_dataset.csv")

for i in data.columns:
    if not np.all(pd.notnull(data[i])):
        data[i].fillna(data[i].mean())
train_data = data.sample(frac=0.8)
test_data = data.drop(train_data.index)

input_param_name = "RAIN"
output_param_name = "WIND"

x_train = train_data[[input_param_name]].values
y_train = train_data[[output_param_name]].values

x_test = test_data[[input_param_name]].values
y_test = test_data[[output_param_name]].values

num_iterations = 500
learning_rate = 0.01

linearRegression = linear_regression.LinearRegression(x_train, y_train)
(theta, loss_history) = linearRegression.train(alpha=learning_rate, num_iterations=num_iterations)

print("开始时损失值：", loss_history[0])
print("结束时损失值：", loss_history[-1])

plt.plot(range(num_iterations), loss_history)
plt.xlabel("Iter")
plt.ylabel("Loss")
plt.title("Gradient")
plt.show()

predictions_num = 100
x_predictions = np.linspace(x_train.min(), x_train.max(), predictions_num).reshape((predictions_num, 1))
y_predictions = linearRegression.predict(x_predictions)


plt.scatter(x_train, y_train, label="Train data")
plt.scatter(x_test, y_test, label="Test data")
plt.plot(x_predictions, y_predictions, "r", label="Prediction")
plt.xlabel(input_param_name)
plt.ylabel(output_param_name)
plt.title("Wind Prediction")
plt.legend()
plt.show()