lda线性判别分析代码

LDA（Linear Discriminant Analysis）是一种常用的分类算法，它通过将数据投影到一个低维空间中，以便更好地区分不同类别的样本。下面是一个简单的LDA代码示例：

import numpy as np

class LDA:
    def fit(self, X, y):
        # 分别计算每个类别的样本均值
        class_means = []
        for c in np.unique(y):
            class_means.append(np.mean(X[y == c], axis=0))
        
        # 计算类内散布矩阵Sw
        n_features = X.shape[1]
        S_w = np.zeros((n_features, n_features))
        for c, mean in zip(np.unique(y), class_means):
            class_scatter = np.zeros((n_features, n_features))
            for row in X[y == c]:
                row, mean = row.reshape(n_features, 1), mean.reshape(n_features, 1)
                class_scatter += (row - mean).dot((row - mean).T)
            S_w += class_scatter
        
        # 计算类间散布矩阵Sb
        overall_mean = np.mean(X, axis=0)
        S_b = np.zeros((n_features, n_features))
        for c in range(len(class_means)):
            n = X[y == c].shape[0]
            class_means[c] = class_means[c].reshape(n_features, 1)
            overall_mean = overall_mean.reshape(n_features, 1)
            S_b += n * (class_means[c] - overall_mean).dot((class_means[c] - overall_mean).T)
        
        # 计算投影矩阵W
        eigen_values, eigen_vectors = np.linalg.eig(np.linalg.inv(S_w).dot(S_b))
        sorted_indexes = np.argsort(eigen_values)[::-1]
        self.projection_matrix = eigen_vectors[:, sorted_indexes[:1]]
    
    def transform(self, X):
        return np.dot(X, self.projection_matrix)

# 使用样例
X = np.array([[1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7]])
y = np.array([0, 0, 0, 1, 1, 1])
lda = LDA()
lda.fit(X, y)
X_lda = lda.transform(X)
print(X_lda)

这是一个简单的LDA实现代码，主要包括了计算类内散布矩阵Sw、类间散布矩阵Sb以及投影矩阵W，最后可以通过fit方法获取投影后的数据。