DL之GD：利用LogisticGD算法(梯度下降)依次基于一次函数和二次函数分布的数据集实现二分类预测(超平面可视化)

一时失言乱红尘 2022-12-26 08:26 61阅读 0赞

**目录**

利用LogisticGD算法(梯度下降)依次基于一次函数和二次函数分布的数据集实现二分类预测(超平面可视化)

设计思路

输出结果

核心代码

--------------------

**相关文章**  
[DL之GD：利用LogisticGD算法(梯度下降)依次基于一次函数和二次函数分布的数据集实现二分类预测(超平面可视化)][DL_GD_LogisticGD]  
[DL之GD：利用LogisticGD算法(梯度下降)依次基于一次函数和二次函数分布的数据集实现二分类预测(超平面可视化)实现][DL_GD_LogisticGD 1]

# 利用LogisticGD算法(梯度下降)依次基于一次函数和二次函数分布的数据集实现二分类预测(超平面可视化) #

## 设计思路 ##

后期更新……

## 输出结果 ##

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70][]![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 1][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 2][]![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 3][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 4][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 5][]![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 6][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 7][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 8][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 9][]

![watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 10][]

[ 1.          0.06747879 -0.97085008]
    data_x 
     (300, 3) [[ 1.          0.83749402  0.80142971]
     [ 1.         -0.93315714  0.91389867]
     [ 1.         -0.72558136 -0.43234329]
     [ 1.          0.21216637  0.88845027]
     [ 1.          0.70547108 -0.99548153]]
    因为Linear_function函数无意义，经过Linear_function函数处理后，data_x等价于data_z
    data_y 
     (300,) [-1. -1. -1. -1.  1.]
    data_x: (300, 3)
    data_z: (300, 3)
    data_y: (300,)
    [228 106 146 250  91 214  47  49 178  90]
    Number of iterations: 26
    
    Plot took 0.10 seconds.
    Plot took 0.04 seconds.
    Target weights: [ -0.49786797   5.28778784 -11.997255  ]
    Target in-sample error: 3.33%
    Target out-of-sample error: 6.21%
    Hypothesis (N=300) weights: [-0.45931854  3.20434478 -7.70825364]
    Hypothesis (N=300) in-sample error: 4.33%
    Hypothesis (N=300) out-of-sample error: 6.08%
    Hypothesis (N=10) weights: [-1.35583449  3.90067866 -5.99553537]
    Hypothesis (N=10) in-sample error: 10.00%
    Hypothesis (N=10) out-of-sample error: 12.87%
    Error history took 88.89 seconds.
    Plot took 17.72 seconds.
    Plot took 35.88 seconds.
    GD_w_hs[-1] [-1.35583449  3.90067866 -5.99553537]
    dimension_z 5
    data_x 
     (30, 3) [[ 1.         -0.0609991  -0.15447425]
     [ 1.         -0.13429796 -0.89691689]
     [ 1.          0.12475253  0.36980185]
     [ 1.         -0.0182513   0.74771272]
     [ 1.          0.50585605 -0.04961719]]
    因为Linear_function函数无意义，经过Linear_function函数处理后，data_x等价于data_z
    data_y 
     (30,) [-1.  1.  1.  1. -1.]
    
    Plot took 1.02 seconds.
    Number of iterations: 105
    
    Plot took 1.03 seconds.
    Target weights: [-3  2  3  6  9 10]
    Hypothesis weights: [-1.23615696 -0.9469097   1.76449666  2.09453304  5.62678124  5.06054409]
    Hypothesis in-sample error: 10.00%
    Hypothesis out-of-sample error: 15.47%
    Plot took 16.58 seconds.
    GD_w_hs[-1] [-1.23615696 -0.9469097   1.76449666  2.09453304  5.62678124  5.06054409]

## 核心代码 ##

def in_sample_error(z, y, logisticGD_function):
        y_h = (logisticGD_function(z) >= 0.5)*2-1
        return np.sum(y != y_h) / float(len(y))
    
    
    def estimate_out_of_sample_error(Product_x_function, NOrderPoly_Function,Pre_Logistic_function, logisticGD_function, N=10000, Linear_function_h=None):
        x = np.array([Product_x_function() for i in range(N)])
        z = np.apply_along_axis(NOrderPoly_Function, 1, x)
        if not Linear_function_h is None:
            z_h = np.apply_along_axis(Linear_function_h, 1, x)
        else:
            z_h = z
        y = Pre_Logistic_function(z)
        y_h = (logisticGD_function(z_h) >= 0.5)*2-1
        return np.sum(y != y_h) / float(N)
    
    
    def ErrorCurve_Plot(N,GD_w_hs, cross_entropy_error):
        start_time = time.time()
        fig = plt.figure()   #  figsize=(8, 6)
        ax = fig.add_subplot(1, 1, 1)
        ax.set_xlabel(r'Iteration', fontsize=12)
        ax.set_ylabel(r'In-Sample Error ($E_{in}$)', fontsize=12)
        ax.set_title(r'Gradient Descent Evolution, N={}'.format(N), fontsize=12)
        ax.set_xlim(0, GD_w_hs.shape[0]-1)
        ax.set_ylim(0, 1)
        ax.xaxis.grid(color='gray', linestyle='dashed')
        ax.yaxis.grid(color='gray', linestyle='dashed')
        ax.set_axisbelow(True)
        ax.plot(range(GD_w_hs.shape[0]), np.apply_along_axis(cross_entropy_error, 1, GD_w_hs), 'r-')
        plt.show()
        print('Plot took {:.2f} seconds.'.format(time.time()-start_time))

[DL_GD_LogisticGD]: https://yunyaniu.blog.csdn.net/article/details/110594141
[DL_GD_LogisticGD 1]: https://yunyaniu.blog.csdn.net/article/details/111348052
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70]: https://img-blog.csdnimg.cn/20201203232320801.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 1]: /images/20221120/e3cf829fc45042fa9194aaeeeccc84fb.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 2]: https://img-blog.csdnimg.cn/20201203232529298.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 3]: /images/20221120/ca1f003d674e400cbb059a718a5e5af7.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 4]: /images/20221120/f7a936f3d5ee4bf1a4e14d4cdacdab4c.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 5]: https://img-blog.csdnimg.cn/20201203232712934.png?x-oss-process=image/watermark,type_ZmFuZ3poZW5naGVpdGk,shadow_10,text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4,size_16,color_FFFFFF,t_70
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 6]: /images/20221120/199fa64acd7e4101b0e2a722198e1336.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 7]: /images/20221120/136b71d99dc142ceb22501a614e812ec.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 8]: /images/20221120/41f47d3307e14bcbbc220b6f8ef20ca7.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 9]: /images/20221120/1c7c3c4d86d94bb98ba46a2f6e1c1366.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3FxXzQxMTg1ODY4_size_16_color_FFFFFF_t_70 10]: /images/20221120/e946ac538968400589e7ecaf4635f93a.png