写一个线性判别分析(Linear Discriminant Analysis的图像python代码

好的，下面是一个简单的线性判别分析的 Python 代码，用于对二维数据进行分类并绘制决策边界的图像：

import numpy as np
import matplotlib.pyplot as plt

class LinearDiscriminantAnalysis():
    def __init__(self):
        self.w = None
        
    def fit(self, X, y):
        n_features = X.shape[1]
        class_labels = np.unique(y)
        
        mean_overall = np.mean(X, axis=0)
        Sw = np.zeros((n_features, n_features))
        Sb = np.zeros((n_features, n_features))
        
        for c in class_labels:
            X_c = X[y == c]
            mean_c = np.mean(X_c, axis=0)
            Sw += (X_c - mean_c).T.dot(X_c - mean_c)
            
            n_c = X_c.shape[0]
            mean_diff = (mean_c - mean_overall).reshape(n_features, 1)
            Sb += n_c * (mean_diff).dot(mean_diff.T)
            
        self.w = np.linalg.inv(Sw).dot(Sb).dot(mean_diff)
        
    def predict(self, X):
        projection = X.dot(self.w)
        return projection
    
    def plot_decision_boundary(self, X, y):
        x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1
        x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1
        xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, 0.1),
                               np.arange(x2_min, x2_max, 0.1))
        Z = self.predict(np.c_[xx1.ravel(), xx2.ravel()])
        Z = Z.reshape(xx1.shape)
        plt.contourf(xx1, xx2, Z, alpha=0.4)
        plt.scatter(X[:, 0], X[:, 1], c=y, alpha=0.8)
        plt.xlabel('Feature 1')
        plt.ylabel('Feature 2')
        plt.show()

其中，plot_decision_boundary 函数用于绘制决策边界，传入的参数 X 是一个二维的 numpy 数组，表示特征矩阵；y 是一个一维的 numpy 数组，表示每个样本对应的标签。该函数会将决策边界绘制在特征平面上，同时将样本点按照类别用不同的颜色进行标记。