fisher线性判别分析python

Fisher线性判别分析是一种经典的模式识别算法，用于将数据分成两个或多个类别。它的目标是找到一个线性投影，使得不同类别之间的距离最大化，同一类别内部的距离最小化。在Python中，可以使用scikit-learn库中的LinearDiscriminantAnalysis类来实现Fisher线性判别分析。

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fisher线性判别分析python头歌

Fisher线性判别分析是一种监督学习算法，用于将多维数据投影到低维空间中，以便于分类。下面是使用Python实现Fisher线性判别分析的代码示例：

首先，需要导入必要的库：

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

接下来，定义Fisher线性判别分析的函数：

def fisher_lda(X, y):
    '''
    X: array-like, shape (n_samples, n_features)
    y: array-like, shape (n_samples,)
    '''
    n_features = X.shape[1]
    classes = np.unique(y)
    n_classes = len(classes)
    
    # 计算每个类别的均值向量和总的均值向量
    mean_vectors = []
    overall_mean = np.mean(X, axis=0)
    for c in classes:
        mean_vectors.append(np.mean(X[y==c], axis=0))
    
    # 计算类间散度矩阵和类内散度矩阵
    S_B = np.zeros((n_features, n_features))
    S_W = np.zeros((n_features, n_features))
    for i, mean_vec in enumerate(mean_vectors):
        n = X[y==classes[i]].shape[0]
        mean_vec = mean_vec.reshape(n_features, 1)
        overall_mean = overall_mean.reshape(n_features, 1)
        S_B += n * (mean_vec - overall_mean).dot((mean_vec - overall_mean).T)
        S_W += np.cov(X[y==classes[i]].T)
    
    # 计算Fisher线性判别分析的投影矩阵
    eigenvalues, eigenvectors = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))
    eig_pairs = [(np.abs(eigenvalues[i]), eigenvectors[:,i]) for i in range(n_features)]
    eig_pairs = sorted(eig_pairs, key=lambda k: k[0], reverse=True)
    projection_matrix = np.hstack((eig_pairs[0][1].reshape(n_features, 1), eig_pairs[1][1].reshape(n_features, 1)))
    
    # 返回投影后的数据
    X_lda = X.dot(projection_matrix)
    return X_lda

最后，读取数据并调用函数进行Fisher线性判别分析：

# 读取数据
data = pd.read_csv('data.csv')
X = data.drop('target', axis=1).values
y = data['target'].values

# 进行Fisher线性判别分析
X_lda = fisher_lda(X, y)

# 绘制投影后的数据
plt.scatter(X_lda[:, 0], X_lda[:, 1], c=y)
plt.xlabel('LD1')
plt.ylabel('LD2')
plt.show()

上述代码中，`data.csv`是包含多维数据和目标变量的CSV文件。`X`是多维数据，`y`是目标变量。`fisher_lda`函数将多维数据投影到低维空间并返回投影后的数据。最后，使用`matplotlib`库将投影后的数据绘制出来。

Fisher 线性判别分析 python模板

以下是 Fisher 线性判别分析的 Python 模板：

import numpy as np

class FisherLDA:
    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)

        # Calculate the mean of each class
        mean_vectors = []
        for label in class_labels:
            mean_vectors.append(np.mean(X[y==label], axis=0))

        # Calculate the within-class scatter matrix
        S_W = np.zeros((n_features, n_features))
        for i, label in enumerate(class_labels):
            Xi = X[y==label]
            mean_vec = mean_vectors[i]
            for x in Xi:
                x = x.reshape(n_features, 1)
                mean_vec = mean_vec.reshape(n_features, 1)
                S_W += (x - mean_vec).dot((x - mean_vec).T)

        # Calculate the between-class scatter matrix
        overall_mean = np.mean(X, axis=0)
        S_B = np.zeros((n_features, n_features))
        for i, mean_vec in enumerate(mean_vectors):
            n = X[y==class_labels[i]].shape[0]
            mean_vec = mean_vec.reshape(n_features, 1)
            overall_mean = overall_mean.reshape(n_features, 1)
            S_B += n * (mean_vec - overall_mean).dot((mean_vec - overall_mean).T)

        # Calculate the eigenvalues and eigenvectors of S_W^-1 * S_B
        eigenvalues, eigenvectors = np.linalg.eig(np.linalg.inv(S_W).dot(S_B))

        # Sort the eigenvalues in descending order
        eigenvectors = eigenvectors.T
        idxs = np.argsort(eigenvalues)[::-1]
        eigenvalues = eigenvalues[idxs]
        eigenvectors = eigenvectors[idxs]

        # Select the first n_components eigenvectors
        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)

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