An approach to symbolic data analysis based on the quantile method

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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.