A study of symbolic data analysis based on neighborhood graphs.

本研究的目的是开发新的符号数据分析方法。SDA是广义数据表的一个新的研究领域，其中每个对象不仅描述了定量的特征值，而且还描述了定性的特征值。以下是我们的研究结果的总结。1）分类问题的特征选择当我们只有有限数量的训练样本时，通过添加新的特征来描述给定的训练样本可能不会提高分类性能。这意味着我们必须在类间可扩展性和类描述的通用性之间取得平衡。我们介绍了笛卡尔系统模型（CSM）作为一个数学模型来处理符号数据。然后，我们定义了基于邻域关系的内视图和外视图的概念。对于一个特征子集，外视图的大小和内视图的大小反映了类间的区别和类的通用性 ...更多信息 分别描述。我们的类间分析是通过结合一个简单的局部特征选择方法与内部和外部视图的大小。我们使用UCI数据库的数据集显示我们的方法的有用性。由于我们的类间分析方法是独立于分类器的，因此我们可以将其用作许多模式分类器设计中的预处理过程。2）广义相关系数Pearson相关系数对于检测线性因果关系是有用的。我们需要更通用的工具来处理非线性因果关系和更广泛的协变关系。如果两个特征变量跟随一个函数结构，则数据样本的散点图指示几何上薄的结构。从这个角度出发，我们提出了两个数量特征变量的卡尔霍恩相关系数和一种基于样本相对邻域关系的方法。在这项研究中，我们发现了另一种方法的基础上链连接覆盖（CCC）。CCC能够处理一般的符号对象，并检测嵌入在符号数据表中的单调结构。这种方法可能有助于推广PCA和聚类方法。少

The purpose of this research is to develop new methods for Symbolic Data Analysis (SDA). The SDA is a new research field for generalized data table in which each object is described not only quantitative feature values but also qualitative feature values. The following is a summary of our research results.1) Feature selection for classification problemsWhen we have only finite number of training samples, the classification performance may not be improved by the addition of new features to describe the given training samples. This means that we have to strike the balance between the interclass distinguish-ability and the generality of class descriptions. We introduce the Cartesian System Model (CSM) as a mathematical model to treat symbolic data. Then, we define the notions of the inside view and the outside view based on the neighborhood relations. For a feature subset, the size of outside view and the size of inside view indicate the interclass distinction and the generality of class … More descriptions, respectively. Our interclass analysis is realized by combining a simple local feature selection method with the sizes of inside and outside views. We showed the usefulness of our approach by using data sets of UCI database. Since our method of interclass analysis is classifier independent, we can use it as a preprocessing process in the design of many pattern classifiers.2) Generalized correlation coefficientPearson's correlation coefficient is useful to detect linear causal relations. We need more general tools to treat nonlinear causal relations and wider covariant relations. If two feature variables follow to a functional structure, the scatter diagram of data samples indicates a geometrically thin structure. From this viewpoint, we developed the Calhoun correlation coefficient for two quantitative feature variables and a method based on the relative neighborhood relations of samples. In this study we found another method based on the chain connected covering (CCC). The CCC is able to treat general symbolic objects, and to detect monotonic structures embedded in symbolic data tables. This approach may be useful to generalize the PCA and clustering methods. Less