Date of Award
Doctor of Philosophy (PhD)
J. Bush Jones
K-systems analysis is a generalization of reconstructability analysis (RA), where any general, complete multivariate system (g-system) can be transformed into an isomorphic, dimensionless system (a K-system) that has sufficient properties to be analyzed using probabilistic RA algorithms. In particular, a g-system consists of a set of states formed from a complete combination of the variables assigned specific values from a finite set of possible values and an associated system function value. The g-system must be complete in that all possible states must have an associated system function value. K-systems analysis has been applied to a variety of systems, but many real-world systems consist of data that is incomplete. Impediments in real-world systems have been previously identified as state contradictions, data scattering and missing data [JONE 85d]. The problem of state contradictions has been adequately addressed, but while techniques for the resolution of data scattering and missing data have been proposed, additional issues remain. The author has condensed the understanding of data scattering and missing data into the single problem of an incomplete system. Within this context, techniques for resolving incomplete systems and, thereby, inducing a complete system have been developed. If a g-system is incomplete, it may be viewed solely from the perspective of missing data. A new algorithm has been developed based on the state distance and uses this distance to determine unbiased estimates of the values for the system function. The state distance is a generalized Hamming distance and is shown to satisfy the properties of a metric on the state space and to be superior to current methods for imputing system function values. An incomplete system may be viewed from the perspective of data scattering. In general, scattered data may be resolved through clustering and, previously, this clustering has been done in one dimension. A method is developed that allows the meaningful use of two dimensions in the clustering. Further, a new pairwise similarity measure is developed based on the maximum entropy principle and mathematics that form the foundation of K-systems analysis. Use of this similarity measure is demonstrated within the context of an existing clustering algorithm.
Asmus, Gary J., "Techniques for Resolving Incomplete Systems in K-Systems Analysis." (1998). LSU Historical Dissertations and Theses. 6800.