An approach to symbolic data analysis based on the quantile method

符号数据分析旨在分析由直方图、区间、有限集等混合描述的复杂数据表。我们通常通过对大量数据集的聚合和汇总过程来获得符号数据表。我们假设直方图、区间、有限集等的特征值具有适当的累积分布函数。然后。我们可以得到相应的(m+1)个分位数的向量。本研究的主要贡献是实现了符号数据表的主成分分析的分位数方法。分位数方法将给定的(N个对象)×(d个特征)符号数据表转换为对于预先选择的整数m的大小为(N×(m+1)个子对象)×(d个特征)的标准数值数据表，其控制每个符号对象的表示质量。我们将标准主成分分析应用于转换后的数据表。在所获得的因子平面中，每个符号对象被再现为组合(m+1)个子对象的一系列m个相连的箭头线。我们向《统计分析和数据挖掘杂志》报告了所提出的方法的有效性。

Symbolic data analysis aims to analyze complex data table described by the mixture of histograms, intervals, finite sets, and others. We usually obtain symbolic data tables by the process of aggregation and summarization of vastly many data sets. We assume proper cumulative distribution functions for feature values of histograms, intervals, finite sets, and others. Then. We can obtain the respective (m+1) vectors of quantile values. A main contribution to this study is the realization of the quantile method of principal component analysis for symbolic data tables. The quantile method transforms the given (N objects) ×(d features) symbolic data table to a standard numerical data table of the size (N×(m+1) sub-objects)×(d features) for a preselected integer number m which controls the representation quality for each symbolic object. We apply the standard principal component analysis to the transformed data table. In the obtained factor planes, each symbolic object is reproduced as a series of m connected arrow lines that combine (m+1) sub-objects. We reported the usefulness of the proposed method to the Journal of Statistical Analysis and Data Mining.