基于三支决策的高斯混合聚类研究

Gaussian mixture clustering based on three-way decision

针对隶属关系不明确的情况,即样本点属于多个类别的概率接近,高斯混合模型聚类存在较大的误判风险的问题,将三支决策思想融入高斯混合模型中,提出一种基于三支决策的高斯混合聚类算法。新算法计算出数据对象属于各个类簇的后验概率作为决策评价函数,用于确定聚类结果的正域和边界域。由于新算法对边界对象采取了比一般高斯混合聚类算法更加谨慎的操作,避免了直接做出对象属于某一类或不属于某一类的决策所需承担的风险,从而有效减小了误判代价。实验进一步表明,所提出的算法不仅继承了高斯混合聚算法的特点,具有良好的聚类性能,而且还对于非球形数据簇表现出优良的聚类效果。

When the membership relationship is not clear,i.e.,the data object belongs to multiple clusters with similar probabilities,the clustering of Gaussian mixture model(GMM)has a large risk of misjudgment.In this paper,the idea of three-way decision is integrated into GMM,and a Gaussian mixture clustering algorithm based on three-way decision is proposed.In the new algorithm,the posterior probability of the data object belonging to each cluster is calculated and then used as the decision evaluation function to determine the positive and boundary regions of the clustering result.A prudent operation strategy is also adopted to deal with boundary objects to avoid the risk of directly making the decision of assigning the data object to a certain cluster or not.The proposed algorithm can effectively reduce the cost of misjudgment.The experimental results show that the proposed algorithm not only inherits the characteristics of GMM,but also has good clustering performance for non-spherical data clusters.