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                                             Ordinal Data Analysis

                                                           Gerd Stumme

                       Knowledge & Data Engineering Group, Dept. of Electrical Engineering and
                      Computer Science & Research Center for Information System Design (ITeG),
                                          University of Kassel, Germany
                                                    stumme@cs.uni-kassel.de

                      Orders are ruling our live: social hierarchies, rankings in online shops, clas-
                 sification systems, waiting queues and many more. However, the majority of
                 data analysis approaches has been developed for numerical features. There are
                 – at least – two reasons for this: i) These features exist in many datasets, be-
                 cause many of the properties can be measured by real numbers, and ii), they
                 allow to make use of a rich set of mathematical tools, such as computing differ-
                 ences/distances, means, deviations, weighted averages, etc.
                      In 1946, S. S. Stevens aimed at providing a solid mathematical foundation to
                 the question whether and how it is possible to measure human sensation. To this
                 end, he introduced four different levels of measurement - nominal, ordinal, inter-
                 val, and ratio. This triggered a discussion about the meaning of ‘measurement’
                 in the various cases and the statistical manipulations that can legitimately be
                 applied. This discussion has been very productive, even though vicious at times,
                 and is still going on today.
                      In the meanwhile, many analysis methods have been developed for data on
                 the nominal, interval and ratio levels. However, there exists up to now no compre-
                 hensive theory for analysing ordinal data. There are only few data science/data
                 analysis/machine learning techniques that are particularly suited for ordinal data
                 (e. g., decision trees work well for ordinal data). Because of the appeal of analysis
                 and machine learning techniques for numerical data, many scientists also apply
                 these techniques to ordinal data. In clustering, for instance, ranks are frequently
                 treated as being interval-scaled, so that distances one is used to (e. g., Euclidean
                 distance) can be applied. However, this may lead to significant misinterpretations
                 of the data.
                      The aim of this talk is to inspire the audience to venture into the development
                 of tools for ordinal data analysis. To this end, we will illustrate various roles of
                 orders in human live by real-world examples and summarize the main issues of
                 the discussion about the various levels of measurement before discussing different
                 types of ordinal data analysis tasks. We conclude the talk by presenting ongoing
                 work of our group on ordinal data analysis.




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