Outlier detection is a significant problem in data mining and machine learning which aims to discover objects in a data set that do not conform to well-defined notions of expected behavior. Generally, the input of the existing outlier detection algorithms is a collection of $n$ objects and each object is described by a feature vector. However, in many real world applications, an object is not only described by one feature vector, but a number of feature vectors. In this paper, we define an object described by more than one feature vector as a matrix-object. Inspired by the concepts of cohesion and coupling in software engineering, we define the coupling of a matrix-object based on the average distance between it and other matrix-objects, and define its cohesion based on information entropy and mutual information. On this basis, the outlier factor of a matrix-object is given, and an outlier detection algorithm for categorical matrix-object data is proposed. The experimental results on real and synthetic data sets have shown that the proposed outlier detection algorithm can effectively detect outliers for the matrix-object data set compared with other algorithms.

离群检测是数据挖掘和机器学习中的一个重要问题，旨在发现数据集中不符合预期行为的明确定义的对象。通常，现有离群值检测算法的输入是$ñ$对象，每个对象由特征向量描述。但是，在许多实际应用中，对象不仅由一个特征向量描述，而且由多个特征向量描述。在本文中，我们将由多个特征向量描述的对象定义为矩阵对象。受到软件工程中内聚和耦合概念的启发，我们基于矩阵对象与其他矩阵对象之间的平均距离来定义其耦合，并基于信息熵和互信息来定义其内聚。在此基础上，给出了矩阵对象的离群因子，提出了一种分类矩阵对象数据的离群值检测算法。