ML：基于自定义数据集利用Logistic、梯度下降算法GD、LoR逻辑回归、Perceptron感知器、SVM支持向量机、LDA线性判别分析算法进行二分类预测(决策边界可视化)

ML：基于自定义数据集利用Logistic、梯度下降算法GD、LoR逻辑回归、Perceptron感知器、支持向量机(SVM_Linear、SVM_Rbf)、LDA线性判别分析算法进行二分类预测(决策边界可视化)

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ML：基于自定义数据集利用Logistic、梯度下降算法GD、LoR逻辑回归、Perceptron感知器、SVM支持向量机、LDA线性判别分析算法进行二分类预测(决策边界可视化)
ML：基于自定义数据集利用Logistic、梯度下降算法GD、LoR逻辑回归、Perceptron感知器、SVM支持向量机、LDA线性判别分析算法进行二分类预测(决策边界可视化)实现

基于自定义数据集利用Logistic、梯度下降算法GD、LoR逻辑回归、Perceptron感知器、支持向量机(SVM_Linear、SVM_Rbf)、LDA线性判别分析算法进行二分类预测(决策边界可视化)

设计思路

输出结果

w_target.shape:  (3,) [ 1.17881511 -5.13265596 -6.55556511]
Pre_Logistic_function
 <class 'function'>
Product_x_function
 [1.         0.10262954 0.43893794]
data_x
 (300, 3) [[ 1.         -0.15378708  0.9615284 ]
 [ 1.          0.36965948 -0.0381362 ]
 [ 1.         -0.21576496 -0.31364397]
 [ 1.          0.45809941 -0.12285551]
 [ 1.         -0.88064421 -0.20391149]]

核心代码

def gradient_descent(data_x, data_y, w_h=None, eta=1.0, max_iterations=10000, epsilon=0.001):
    if w_h == None:
        w_h = np.array([0.0 for i in range(data_x.shape[1])])
    w_h_i = [np.copy(w_h)]  

    for i in range(max_iterations):
        subset_indices = range(data_x.shape[0])
        grad_E_in = np.mean(np.tile(- data_y[subset_indices] /
                                        ( 1.0 + np.exp(data_y[subset_indices] * w_h.dot(data_x[subset_indices].T)) ),
                                    (data_x.shape[1], 1)).T *   data_x[subset_indices], axis=0)
        w_h -= eta * grad_E_in
        w_h_i.append(np.copy(w_h))
        if np.linalg.norm(grad_E_in) <= np.linalg.norm(w_h) * epsilon:
            break
    return np.array(w_h_i)

LoR = linear_model.LogisticRegression()
LoR.fit(data_x,data_y)
y_train=LoR.predict(data_x)

LoRpp_function = lambda z: LoR.predict_proba(z)[:,0]
BG_Grid_BaseLoR = apply_to_fill(z_grid, LoRpp_function)

full_N_fig = plot_dataset_and_hypothesis(3,data_x, data_y, xy_1, xy_2, BG_Grid_BaseLoR,title=r'LoR: Hypothesis, $N={:}$'.format(N))

SVM_Linear = svm.SVC(kernel='linear')
SVM_Linear.fit(data_x,data_y)

SVM_LinearPre_function = lambda z: SVM_Linear.predict(z)
BG_Grid_BaseSVM_Linear = apply_to_fill(z_grid, SVM_LinearPre_function)

full_N_fig = plot_dataset_and_hypothesis(5,data_x, data_y, xy_1, xy_2, BG_Grid_BaseSVM_Linear, title=r'SVM_Linear: Hypothesis, $N={:}$'.format(N))
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