用Python写一个线性判别分析

Linear Discriminant Analysis (LDA) 是一种常见的分类算法，它可以用于降维和特征提取。下面是用 Python 实现 LDA 的代码：

import numpy as np

class LDA:
    def __init__(self, n_components=None):
        self.n_components = n_components

    def fit(self, X, y):
        n_samples, n_features = X.shape
        class_labels = np.unique(y)

        # 计算每个类别的均值向量
        mean_overall = np.mean(X, axis=0)
        S_W = np.zeros((n_features, n_features))
        S_B = np.zeros((n_features, n_features))

        for c in class_labels:
            X_c = X[y == c]
            mean_c = np.mean(X_c, axis=0)
            S_W += (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)
            S_B += n_c * mean_diff.dot(mean_diff.T)

        # 计算特征值和特征向量
        eigenvalues, eigenvectors = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))
        eigenvectors = eigenvectors.T
        # 排序特征向量
        idxs = np.argsort(abs(eigenvalues))[::-1]
        eigenvalues = eigenvalues[idxs]
        eigenvectors = eigenvectors[idxs]
        # 选择前 n_components 个特征向量
        if self.n_components is not None:
            eigenvectors = eigenvectors[:self.n_components]

        self.eigenvalues = eigenvalues
        self.eigenvectors = eigenvectors

    def transform(self, X):
        return np.dot(X, self.eigenvectors.T)

这个实现假设每个类别的协方差矩阵相等，这在实际应用中可能不成立。如果你需要更复杂的 LDA 实现，可以参考 scikit-learn 中的实现。