Design of Experiment in Complex Systems based on Computational Taxonomy

Via Computational Taxonomy (CT), we develop Design of Experiment(DoE) based on rigorously redefined constituting ingredients of complex system dynamics: randomness, nonlinearity and even class, through a data-driven constructed Taxonomic Hierarchy. As an opposite quest of Classification without man-made assumptions and structures, we illustrate this new perspective of DoE through a civil engineering complex system: Concrete Compressive Strength (CCS). CT begins by building a Taxonomic Hierarchy as a heterogeneity-vs-homogeneity map framed with a tree geometry to represent CCS-system dynamics. At each internal node of this hierarchy, a heatmap is computed via Scientific Data Analysis (SDA) to reveal locality-embraced heterogeneity through block structured covariate homogeneity annotated with response's locality-split. Only arriving at each ending-node of this hierarchy, coherence of homogeneity is achieved on both response and covariate sides. As such a class of finite sample nature is computationally recognized and confirmed. In contrast, nonlinearity is evidently observed as incoherence of response-vs-covariate homogeneity when comparing two classes located on two distinct branches. This hierarchy explicitly maps out system's randomness and nonlinearity to serve as a scientific basis for any DoE quest. Design of Experiment (DoE) for any designated class is redefined as a search for a covariate subspace that embraces the class-representative randomness and at the same time avoids potential nonlinearities with respect to the rest of classes. This is a brand-new theme of DoE.