中文摘要：

类属型数据广泛分布于生物信息学等许多应用领域，其离散取值的特点使得类属数据聚类成为统计机器学习领域一项困难的任务．当前的主流方法依赖于类属属性的模进行聚类优化和相关属性的权重计算．提出一种非模的类属型数据统计聚类方法．首先，基于新定义的相异度度量，推导了属性加权的类属数据聚类目标函数．该函数以对象与簇之间的平均距离为基础，从而避免了现有方法以模为中心导致的问题．其次，定义了一种类属型数据的软子空间聚类算法．该算法在聚类过程中根据属性取值的总体分布，而不仅限于属性的模，赋予每个属性衡量其与簇类相关程度的权重，实现自动的特征选择．在合成数据和实际应用数据集上的实验结果表明，与现有的基于模的聚类算法和基于蒙特卡罗优化的其他非模算法相比，该算法有效地提高了聚类结果的质量．

英文摘要：

While categorical data are widely used in many applications such as Bioinformatics, clustering categorical data is a difficult task in the filed of statistical machine learning due to the characteristic of the data which can only take discrete values. Typically, the mainstream methods are dependent on the mode of the categorical attributes in order to optimize the clusters and weight the relevant attributes. A non-mode approach is proposed for statistically clustering of categorical data in this paper. First, based on a newly defined dissimilarity measure, an objective function with attributes weighting is derived for categorical data clustering. The objective function is defined based on the average distance between the objects and the clusters, therefore overcomes the problems in the existing methods based on the mode category. Then, a soft-subspace clustering algorithm is proposed for clustering categorical data. In this algorithm, each attribute is assigned with weights measuring its degree of relevance to the clusters in terms of the overall distribution of categories instead of the mode category, enabling automatic feature selection during the clustering process. Experimental results carried out on some synthetic datasets and real-world datasets demonstrate that the proposed method significantly improves clustering quality.