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)
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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
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
[ 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))
