对于FIM和FIM’，分别输入PCA+SVM的人脸识别程序中进行人脸识别分类预测。python实现

首先，需要明确一下 FIM 和 FIM' 的含义。FIM 是 Fisher Information Matrix 的缩写，FIM' 则是 FIM 的逆矩阵。

PCA 和 SVM 都是常用的人脸识别算法。PCA 用于降维，SVM 用于分类。

以下是使用 PCA+SVM 进行人脸识别的 Python 实现：

1. 导入必要的库和数据集

import numpy as np
from sklearn.decomposition import PCA
from sklearn.svm import SVC
from sklearn.datasets import fetch_lfw_people
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

# 获取人脸数据集
lfw_people = fetch_lfw_people(min_faces_per_person=70, resize=0.4)

X = lfw_people.data
y = lfw_people.target

2. 使用 PCA 进行降维处理

# 进行 PCA 降维处理
n_components = 150
pca = PCA(n_components=n_components, whiten=True)
pca.fit(X)

X_pca = pca.transform(X)

3. 将 PCA 处理后的数据集分为训练集和测试集

# 将数据集分为训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(X_pca, y, test_size=0.25, random_state=42)

4. 使用 SVM 进行分类预测

# 使用 SVM 进行分类预测
clf = SVC(kernel='rbf', C=10, gamma=0.001, probability=True)
clf.fit(X_train, y_train)

y_pred = clf.predict(X_test)

5. 计算分类预测的准确率

# 计算准确率
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)

接下来，我们来使用 FIM 和 FIM' 来对 PCA+SVM 进行优化。

6. 计算 FIM

# 计算 FIM
cov = np.cov(X_train.T)
FIM = np.linalg.inv(cov)

7. 计算 FIM'，并进行分类预测

# 计算 FIM'
FIM_inv = np.linalg.inv(FIM)

X_train_fim = X_train.dot(FIM_inv)
X_test_fim = X_test.dot(FIM_inv)

clf_fim = SVC(kernel='rbf', C=10, gamma=0.001, probability=True)
clf_fim.fit(X_train_fim, y_train)

y_pred_fim = clf_fim.predict(X_test_fim)

8. 计算 FIM' 优化后的准确率

# 计算 FIM' 优化后的准确率
accuracy_fim = accuracy_score(y_test, y_pred_fim)
print("Accuracy with FIM':", accuracy_fim)

完整代码如下：

import numpy as np
from sklearn.decomposition import PCA
from sklearn.svm import SVC
from sklearn.datasets import fetch_lfw_people
from sklearn.model_selection import train_test_split
from sklearn.metrics import accuracy_score

# 获取人脸数据集
lfw_people = fetch_lfw_people(min_faces_per_person=70, resize=0.4)

X = lfw_people.data
y = lfw_people.target

# 进行 PCA 降维处理
n_components = 150
pca = PCA(n_components=n_components, whiten=True)
pca.fit(X)

X_pca = pca.transform(X)

# 将数据集分为训练集和测试集
X_train, X_test, y_train, y_test = train_test_split(X_pca, y, test_size=0.25, random_state=42)

# 使用 SVM 进行分类预测
clf = SVC(kernel='rbf', C=10, gamma=0.001, probability=True)
clf.fit(X_train, y_train)

y_pred = clf.predict(X_test)

# 计算准确率
accuracy = accuracy_score(y_test, y_pred)
print("Accuracy:", accuracy)

# 计算 FIM
cov = np.cov(X_train.T)
FIM = np.linalg.inv(cov)

# 计算 FIM'
FIM_inv = np.linalg.inv(FIM)

X_train_fim = X_train.dot(FIM_inv)
X_test_fim = X_test.dot(FIM_inv)

clf_fim = SVC(kernel='rbf', C=10, gamma=0.001, probability=True)
clf_fim.fit(X_train_fim, y_train)

y_pred_fim = clf_fim.predict(X_test_fim)

# 计算 FIM' 优化后的准确率
accuracy_fim = accuracy_score(y_test, y_pred_fim)
print("Accuracy with FIM':", accuracy_fim)