Multiscale major factor selections for complex system data with structural dependency and heterogeneity

The unknown multiscale structure hidden in large complex systems is explored bottom-up through discovered heterogeneity under structural dependency embedded within structured data sets. Via two real complex systems, we demonstrate computed hierarchical structures with broken symmetry constituting data’s information content. Through graphic displays, such information content indirectly, but efficiently resolves system-related scientific issues that are difficult to resolve directly. All bottom-up explorations and computations are based on conditional entropy and mutual information evaluated upon contingency table platforms after categorizing all quantitative features. Categorical Exploratory Data Analysis (CEDA) first extracts global major factors that share significant mutual information with the targeted response (Re) variable against many covariate (Co) features under the presence of structural dependency. Then each global major factor is taken as one perspective of heterogeneity to subdivide the entire data set according to its categories into sub-collections. This simple “de-associating” protocol significantly reduces structural dependency among the rest of the features such that another run of major factor selection performed on the sub-collection scale can precisely identify which feature sets could provide extra information beyond the global major factor. Finally, informative patterns collected from multiple perspectives of heterogeneity are displayed to explicitly resolve issues of prediction, classification, and detecting minute dynamic changes.