In a method and apparatus for analyzing multivariable data sets, a general computerized platform is provided for evaluating the relationship between large number of measurements of sets of variables characterizing components of complex states of a system under induced stimulation or controlled conditions. The linked responses of variables and their temporal relations tell about the network of interactions and their hierarchy. Processing of data sets by a simple neural network gives a matrix of weight parameters, that allow to identify fingerprints of complex states characterized by patterns of measured variable and estimate the interactions between the components characterized by the measured variables. The results are provided numerically and by color-coded presentation indicating dominating relations between variables and strongly responding variables. When applied to dynamic responses of a system, the analysis can construct a schematic hierarchical architecture of the network of interaction between the components of the studied system. Applications in biology include analysis of measurements characterizing responses of molecular components in cells under changes induced by stimuli (e.g. drugs, growth factors, hormones, mutations or forced expression of a proteins), and identification of complex cellular states (e.g. proliferation, differentiation, transformation, starvation, necrosis, apoptosis, and the time dependencies of the above effects).