Combinatorial Data Analysis

Combinatorial data analysis (CDA) as a generic term can be discussed within the framework of two distinct tasks of data analysis: exploratory and confirmatory. A confirmatory CDA approach compares some given data set to a specific structure that is conjectured for it a priori; the empirically observed degree of correspondence is evaluated by reference to what could be observed using all possible structures of the same form that could have been conjectured (for example, one-way analysis-of-variance can be viewed as comparing a given structure defined by a partitioning of subjects into groups, to all possible partitions that could have been formed). Alternatively, an exploratory strategy would seek one possible structure from some given class that best fits the given data set. In both cases, the data and the various structures considered are typically coded as matrices; thus, a confirmatory task usually involves an assessment of similar patterning across matrices; an exploratory task seeks to optimize such a pattern of correspondence by locating the most appropriate matrix reorganization.