基于多目标优化方法的一类k-Means自适应算法

A Class of k-Means Adaptive Algorithms Based on Multi-Objective Optimization Method

【目的】针对k-Means聚类算法及MinMax k-Means聚类算法需要人为提前给定聚类数量而导致数据划分准确率偏低以及MinMax k-Means算法聚类效果受类簇边缘点影响较大等不足提出解决方案。【方法】将k-Means和MinMax k-Means算法的目标函数相结合,建立多目标优化模型,提出基于多目标优化方法的k-Means算法。分析簇数异常情况下最小中心方差与最大簇内方差之间的关系。【结果】发现当分类簇数大于最优簇数时,最小中心方差小于最大簇内方差,据此提出了基于多目标优化方法的k-Means自适应算法。【结论】数值实验表明:提出的自适应算法在人工数据集和UCI标准数据集均具有较好的自适应性且聚类效果较优。

[Purposes]In view of the shortcomings of k-Means clustering algorithm and MinMax k-Means clustering algorithm,which need to be artificially given the number of clusters in advance,the accuracy of data division is low,and the clustering effect of MinMax k-Means algorithm is greatly affected by the edge points of clusters.[Methods]The multi-objective optimization model is established by combining the objective function of k-Means and MinMax k-Means algorithm,and the k-Means algorithm based on multi-objective optimization method is proposed.Analyze the relationship between the minimum central variance and the maximum intra-cluster variance in the case of abnormal cluster number.[Findings]It is found that when the number of classified clusters is greater than the optimal number of clusters,the minimum central variance is less than the maximum intra-cluster variance.Based on this,a k-Means adaptive algorithm based on multi-objective optimization method is proposed.[Conclusions]Numerical experiments show that the adaptive algorithm proposed here has good adaptability and clustering effect in both artificial dataset and UCI standard dataset.