Softmax回归Python实现

落日映苍穹つ 2022-05-29 00:22 271阅读 0赞

# 1. 前言 #

前面讲解了Softmax回归和Logistic回归的理解（[博客链接][Link 1]），在本文中将着重对其使用Python脚本实现，并且比较实现几种梯度优化算子，常用的梯度优化算子的讲解请参考我的[这篇博客][Link 2]。

# 2. 编码实现 #

## 2.1 数据生成 ##

# 产生数据
    def get_data(num_data=100):
        x = np.reshape(np.random.normal(1, 1, num_data), (num_data, 1))
        y = np.reshape(np.random.normal(0, 1, num_data), (num_data, 1))
        bias = np.ones((num_data, 1))
        class1 = np.concatenate((x, y, bias), axis=1)
        x = np.reshape(np.random.normal(5, 1, num_data), (num_data, 1))
        y = np.reshape(np.random.normal(6, 1, num_data), (num_data, 1))
        class2 = np.concatenate((x, y, bias), axis=1)
    
        plt.plot(class1[:, 0], class1[:, 1], 'rs', class2[:, 0], class2[:, 1], 'go')
        plt.grid(True)
        plt.title('Distribution')
        plt.xlabel('X1')
        plt.ylabel('X2')
        plt.show()
    
        label_data = np.zeros((2*num_data, 1))
        label_data[num_data:2*num_data] = 1.0
    
        return np.concatenate((class1[:, :], class2[:, :]), axis=0), label_data

![这里写图片描述][Image 1]

## 2.2 梯度下降求解 ##

# 梯度下降法
    def grad_ascent(train_data, label_data, num_iter, alpha=0.001):
        weights = np.ones((train_data.shape[1], 1))
        train_data = np.mat(train_data)
        label_data = np.mat(label_data)
        weights_x1 = []
        weights_x2 = []
        weights_bias = []
        for i in np.arange(num_iter):
            temp = sigmoid(train_data*weights)
            error = label_data - temp
            weights = weights + alpha * train_data.T * error
            weights_x1.append(weights[0])
            weights_x2.append(weights[1])
            weights_bias.append(weights[2])
    
        weights = np.array(weights)
        weights = weights[:, 0]
    
        # 显示参数变化曲线
        x = np.arange(num_iter)
        weights_x1 = np.array(weights_x1)[:, 0, 0]
        weights_x2 = np.array(weights_x2)[:, 0, 0]
        weights_bias = np.array(weights_bias)[:, 0, 0]
        plt.subplot(311)
        plt.plot(x, weights_x1, 'b-')
        plt.title('weight_x1')
        plt.grid(True)
        plt.subplot(312)
        plt.plot(x, weights_x2, 'b-')
        plt.title('weight_x2')
        plt.grid(True)
        plt.subplot(313)
        plt.plot(x, weights_bias, 'b-')
        plt.title('weight_bias')
        plt.grid(True)
        plt.show()
    
        return weights

## 2.3 其它组件 ##

# 画出决策直线
    def plot_decision(train_data, data_num, weights):
        x = np.linspace(-2, 9, train_data.shape[0])
        y = np.array((-weights[2]-weights[0]*x)/weights[1])
    
        plt.plot(train_data[0:data_num, 0], train_data[0:data_num, 1], 'bs',
                 train_data[data_num:2*data_num, 0], train_data[data_num:2*data_num, 1], 'go',
                 x, y, 'r-')
        plt.grid(True)
        plt.title('line')
        plt.xlabel('X1')
        plt.ylabel('X2')
        plt.show()
    
    if __name__ == '__main__':
        data_num = 100
        train_data, train_label = get_data(data_num)
        # 梯度下降法
        weights = grad_ascent(train_data, train_label, 1000)
    
        # 随机梯度下降法
        # weights = stoc_grad_ascent(train_data, train_label, 400)
    
        # 改进的随机梯度下降法
        #weights = stoc_grad_ascent1(train_data, train_label, 800)
        # 画出决策直线
        plot_decision(train_data, data_num, weights)

其它完整代码请访问我的[Git地址][Git]

# 3. 结果 #

![这里写图片描述][Image 1]

[Link 1]: http://blog.csdn.net/m_buddy/article/details/79536824
[Link 2]: http://blog.csdn.net/m_buddy/article/details/79543476
[Image 1]: 
[Git]: https://github.com/uestc-buddy/Machine_learning/tree/master/softmax