从全局合理性的角度对SMOTE算法进行改进，给出详细的python代码

为了从全局合理性的角度对SMOTE算法进行改进，我们可以考虑以下两个方面：

1. 保留原始数据分布的特征，避免过度合成数据导致的模型过拟合问题

2. 在合成新样本时，考虑样本之间的相对重要性，避免重要样本被过度合成

基于以上两点，我们可以进行如下改进：

1. 在进行SMOTE合成时，引入随机采样的机制，确保合成数据的分布与原始数据相似。

2. 在选择合成目标样本时，引入重要性权重机制，确保合成数据对于模型的影响不会过于突出。

下面是一个简单的python实现，其中包含了以上两点改进的内容：

from collections import Counter
from sklearn.neighbors import NearestNeighbors
import numpy as np

def SMOTE(X, y, k=5, ratio=1.0):
    # k: number of nearest neighbors to consider
    # ratio: target ratio of synthetic samples to real samples
    
    # Determine the minority class samples
    minority_class = Counter(y).most_common()[-1][0]
    X_minority = X[y==minority_class]
    
    # Determine the number of synthetic samples to generate
    n_synthetic = int(ratio * len(X_minority) - len(X_minority))
    
    # Create synthetic samples
    if n_synthetic > 0:
        # Determine the k nearest neighbors for each minority class sample
        knn = NearestNeighbors(n_neighbors=k).fit(X_minority)
        neighbors = knn.kneighbors(X_minority, return_distance=False)
        
        # Generate synthetic samples
        synthetic_samples = []
        for i in range(n_synthetic):
            # Select a random minority class sample
            idx = np.random.randint(len(X_minority))
            sample = X_minority[idx]
            
            # Compute the importance weights for the k nearest neighbors
            weights = []
            for neighbor in neighbors[idx]:
                if y[neighbor] == minority_class:
                    weights.append(1.0)
                else:
                    # Compute the distance between the sample and the neighbor
                    distance = np.linalg.norm(sample - X[neighbor])
                    # Compute the inverse distance as the weight
                    weights.append(1.0 / distance)
            weights = np.array(weights)
            
            # Normalize the weights so they sum to 1
            weights /= weights.sum()
            
            # Generate a synthetic sample as a weighted sum of the k nearest neighbors
            synthetic_sample = np.zeros_like(sample)
            for j in range(k):
                neighbor = neighbors[idx][j]
                weight = weights[j]
                synthetic_sample += weight * (X[neighbor] - sample)
            synthetic_samples.append(sample + synthetic_sample)
            
        # Combine the original and synthetic samples
        X_resampled = np.vstack((X, np.array(synthetic_samples)))
        y_resampled = np.hstack((y, np.array([minority_class] * n_synthetic)))
    else:
        X_resampled = X
        y_resampled = y
    
    return X_resampled, y_resampled

注意，这只是一个简单的实现，可能需要根据具体问题进行调整。此外，还需要注意，在合成数据时，需要避免合成的数据过于贴近边界，这可能导致模型过度拟合边界而忽略了真正的数据分布。