Visual comparison of orderings and rankings

In many data analysis problems, sequentially ordered (or ranked) data occurs that needs to be understood and compared. Ranking information is essential in applications such as multimedia search where retrieval rankings need to be inspected; alignments of gene sequences in bio-molecular applications; or for a more abstract example, considering the permutations of rows and columns for purpose of matrix visualization. In each of these examples, often many different orderings of a given data set are possible. E.g., a search engine may produce, based on different user parameterizations, different rankings. A relevant problem then is to understand the commonalities and differences of a potentially large set of rankings. E.g., finding global or partial orderings in which different ranking or sorting algorithms agree can support the certainty in the respective ranking by the user. We consider the problem of comparing sets of rankings with these questions in mind. We present an approach for a visual comparison of sets of rankings that effectively allows to spot commonalities and differences among rankings. The approach relies on a small-multiple view of glyphs each of which visually contrasts a pair of rankings. The glyph in turn is defined on a radial node-link representation which allows effective perception of agreements and differences in pairs of rankings. We apply our approach on different use cases and demonstrate its effectiveness in spotting patterns of similarity and differences in sets of rankings.