使用Python和Numpy进行波士顿房价预测任务（一）【深度学习入门_学习笔记】

柔情只为你懂 2023-02-13 11:41 8阅读 0赞

波士顿房价预测是一个经典的机器学习任务，类似于程序员世界的“Hello World”。和大家对房价的普遍认知相同，波士顿地区的房价是由诸多因素影响的。  
下载数据集：[https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data][https_archive.ics.uci.edu_ml_machine-learning-databases_housing_housing.data]  
该数据集统计了13种可能影响房价的因素和该类型房屋的均价，期望构建一个基于13个因素进行房价预测的模型，如图所示。  
![在这里插入图片描述][20200528235939566.png]

import numpy as np
    import matplotlib.pyplot as plt
    
    def load_data():
        # 1.从文件导入数据
        datafile = './housing.data'
        data = np.fromfile(datafile, sep=' ')
    
        # 每条数据包括14项，其中前面13项是影响因素，第14项是相应的房屋价格中位数
        feature_names = [ 'CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', \
                          'DIS', 'RAD', 'TAX', 'PTRATIO', 'B', 'LSTAT', 'MEDV' ]
        feature_num = len(feature_names)
    
        # 2.将原始数据进行Reshape，变成[N, 14]这样的形状
        data = data.reshape([data.shape[0] // feature_num, feature_num])
    
        # 3.将原数据集拆分成训练集和测试集
        # 这里使用80%的数据做训练，20%的数据做测试
        # 测试集和训练集必须是没有交集的
        ratio = 0.8
        offset = int(data.shape[0] * ratio)
        training_data = data[:offset]
    
        # 计算train数据集的最大值，最小值，平均值
        maximums, minimums, avgs = training_data.max(axis=0), training_data.min(axis=0), \
                                     training_data.sum(axis=0) / training_data.shape[0]
    
        # 4.对数据进行归一化处理
        for i in range(feature_num):
            #print(maximums[i], minimums[i], avgs[i])
            data[:, i] = (data[:, i] - avgs[i]) / (maximums[i] - minimums[i])
    
        # 训练集和测试集的划分比例
        training_data = data[:offset]
        test_data = data[offset:]
        return training_data, test_data
    
    class Network(object):
        def __init__(self, num_of_weights):
            # 随机产生w的初始值
            # 为了保持程序每次运行结果的一致性，此处设置固定的随机数种子
            #np.random.seed(0)
            self.w = np.random.randn(num_of_weights, 1)
            self.b = 0.
            
        def forward(self, x):
            z = np.dot(x, self.w) + self.b
            return z
        
        def loss(self, z, y):
            error = z - y
            num_samples = error.shape[0]
            cost = error * error
            cost = np.sum(cost) / num_samples
            return cost
        
        def gradient(self, x, y):
            z = self.forward(x)
            N = x.shape[0]
            gradient_w = 1. / N * np.sum((z-y) * x, axis=0)
            gradient_w = gradient_w[:, np.newaxis]
            gradient_b = 1. / N * np.sum(z-y)
            return gradient_w, gradient_b
        
        def update(self, gradient_w, gradient_b, eta = 0.01):
            self.w = self.w - eta * gradient_w
            self.b = self.b - eta * gradient_b
                
                    
        def train(self, training_data, num_epoches, batch_size=10, eta=0.01):
            n = len(training_data)
            losses = []
            for epoch_id in range(num_epoches):
                # 在每轮迭代开始之前，将训练数据的顺序随机的打乱，
                # 然后再按每次取batch_size条数据的方式取出
                np.random.shuffle(training_data)
                # 将训练数据进行拆分，每个mini_batch包含batch_size条的数据
                mini_batches = [training_data[k:k+batch_size] for k in range(0, n, batch_size)]
                for iter_id, mini_batch in enumerate(mini_batches):
                    #print(self.w.shape)
                    #print(self.b)
                    x = mini_batch[:, :-1]
                    y = mini_batch[:, -1:]
                    a = self.forward(x)
                    loss = self.loss(a, y)
                    gradient_w, gradient_b = self.gradient(x, y)
                    self.update(gradient_w, gradient_b, eta)
                    losses.append(loss)
                    print('Epoch {:3d} / iter {:3d}, loss = {:.4f}'.
                                     format(epoch_id, iter_id, loss))
            
            return losses
    
    # 获取数据
    train_data, test_data = load_data()
    
    # 创建网络
    net = Network(13)
    # 启动训练
    losses = net.train(train_data, num_epoches=50, batch_size=100, eta=0.1)
    
    # 画出损失函数的变化趋势
    plot_x = np.arange(len(losses))
    plot_y = np.array(losses)
    plt.plot(plot_x, plot_y)
    plt.show()

![在这里插入图片描述][20200529000739957.png]

[https_archive.ics.uci.edu_ml_machine-learning-databases_housing_housing.data]: https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data
[20200528235939566.png]: https://img-blog.csdnimg.cn/20200528235939566.png
[20200529000739957.png]: https://img-blog.csdnimg.cn/20200529000739957.png