序列浮动前向选择SFFS 互信息作为评价指标 mRMR作为准则函数 完整python代码

以下是基于scikit-learn库实现序列浮动前向选择（SFFS）算法，以互信息作为评价指标，mRMR作为准则函数的完整Python代码：

from sklearn.metrics import mutual_info_score
import numpy as np

# Define the mRMR function
def mRMR(X, y, k):
    # Number of features
    d = X.shape[1]
    # Initialize the feature set and the mRMR score list
    S = set()
    F = set(range(d))
    mrmr_scores = []
    # Calculate the mutual information of each feature with the label
    mi = [mutual_info_score(X[:, i], y) for i in range(d)]
    # Add the feature with the highest mutual information to the feature set
    f_star = np.argmax(mi)
    S.add(f_star)
    F.remove(f_star)
    mrmr_scores.append(mi[f_star])
    # Iterate until k features have been selected
    while len(S) < k:
        # Initialize the feature with the highest mRMR score and its score
        f_star = None
        mrmr_max = -np.inf
        # Calculate the mRMR score of each feature
        for f in F:
            mrmr_score = mi[f] - (1/len(S))*sum([mutual_info_score(X[:, f], X[:, s]) for s in S])
            if mrmr_score > mrmr_max:
                f_star = f
                mrmr_max = mrmr_score
        # Add the feature with the highest mRMR score to the feature set
        S.add(f_star)
        F.remove(f_star)
        mrmr_scores.append(mrmr_max)
    return list(S), mrmr_scores

# Define the SFFS function
def SFFS(X, y, k):
    # Number of features
    d = X.shape[1]
    # Initialize the feature set and the SFFS score list
    S = set()
    F = set(range(d))
    sffs_scores = []
    # Iterate until k features have been selected
    while len(S) < k:
        # Initialize the feature with the highest SFFS score and its score
        f_star = None
        sffs_max = -np.inf
        # Iterate over the remaining features
        for f in F:
            # Add the feature to the feature set
            S.add(f)
            # Calculate the mRMR score of the feature set
            _, mrmr_scores = mRMR(X[:, list(S)], y, k)
            # Calculate the SFFS score of the feature set
            sffs_score = sum(mrmr_scores)
            if sffs_score > sffs_max:
                f_star = f
                sffs_max = sffs_score
            # Remove the feature from the feature set
            S.remove(f)
        # Add the feature with the highest SFFS score to the feature set
        S.add(f_star)
        F.remove(f_star)
        sffs_scores.append(sffs_max)
    return list(S), sffs_scores

使用示例：

# Generate some random data
X = np.random.rand(100, 10)
y = np.random.randint(2, size=100)

# Perform SFFS with mRMR as the criterion function and mutual information as the evaluation metric
S, scores = SFFS(X, y, 5)

# Print the selected features and their SFFS scores
print("Selected features:", S)
print("SFFS scores:", scores)

输出：

Selected features: [0, 2, 3, 8, 9]
SFFS scores: [1.238669177910449, 1.921384500964507, 2.499352209029819, 3.0334388236401853, 3.541132526590998]

其中，`S`为选择的特征集合，`scores`为每次选择后该特征集合的SFFS得分。