In order to cope with system complexity and dynamic environments, modern industries are investing in a variety of sensor networks and data acquisition systems to increase information visibility. Multi-sensor systems bring the proliferation of high-dimensional functional Big Data that capture rich information on the evolving dynamics of natural and engineered processes. With spatially and temporally dense data readily available, there is an urgent need to develop advanced methodologies and associated tools that will enable and assist (i) the handling of the big data communicated by the contemporary complex systems, (ii) the extraction and identification of pertinent knowledge about the environmental and operational dynamics driving these systems, and (iii) the exploitation of the acquired knowledge for more enhanced design, analysis, monitoring, diagnostics and control. My methodological and theoretical research as well as a considerable portion of my applied and collaborative work in this dissertation aims at addressing high-dimensional functional big data communicated by the systems. An innovative contribution of my work is the establishment of a series of systematic methodologies to investigate the complex system informatics including multi-dimensional modeling, feature extraction and selection, model-based monitoring and root cause diagnostics. This study presents systematic methodologies to investigate spatiotemporal informatics of complex systems from multi-dimensional modeling and feature extraction to model-driven monitoring, fault identification and root cause diagnostics. In particular, we developed a multiscale adaptive basis function model to represent and characterize the high-dimensional nonlinear functional profiles, thereby reducing the large amount of data to a parsimonious set of variables (i.e., model parameters) while preserving the information. Furthermore, the complex interdependence structure among variables is identified by a novel self-organizing network algorithm, in which the homogeneous variables are clustered into sub-network communities. Then we minimize the redundancy of variables in each cluster and integrate the new set of clustered variables with predictive models to identify a sparse set of sensitive variables for process monitoring and fault diagnostics. We evaluated and validated our methodologies using real-world case studies that extract parameters from representation models of vectorcardiogram (VCG) signals for the diagnosis of myocardial infarctions. The proposed systematic methodologies are generally applicable for modeling, monitoring and diagnosis in many disciplines that involve a large number of highly-redundant variables extracted from the big data. The self-organizing approach was also innovatively developed to derive the steady geometric structure of a network from the recurrence-based adjacency matrix. As such, novel network-theoretic measures can be achieved based on actual node-to-node distances in the self-organized network topology.

Despite recent advances in statistics, artificial neural network theory, and machine learning, nonlinear function estimation in high-dimensional space remains a nontrivial problem. As the response surface becomes more complicated and the dimensions of the input data increase, the dreaded "curse of dimensionality" takes hold, rendering the best of function approximation methods ineffective. This thesis takes a novel approach to solving the high-dimensional function estimation problem. In this work, we propose and develop two distinct parametric projection pursuit learning networks with wide-ranging applicability. Included in this work is a discussion of the choice of basis functions used as well as a description of the optimization schemes utilized to find the parameters that enable each network to best approximate a response surface. The essence of these new modeling methodologies is to approximate functions via the superposition of a series of piecewise one-dimensional models that are fit to specific directions, called projection directions. The key to the effectiveness of each model lies in its ability to find efficient projections for reducing the dimensionality of the input space to best fit an underlying response surface. Moreover, each method is capable of effectively selecting appropriate projections from the input data in the presence of relatively high levels of noise. This is accomplished by rigorously examining the theoretical conditions for approximating each solution space and taking full advantage of the principles of optimization to construct a pair of algorithms, each capable of effectively modeling high-dimensional nonlinear response surfaces to a higher degree of accuracy than previously possible.