Date of Award
Doctor of Philosophy (PhD)
J. Bush Jones
K-systems analysis is a factor analysis technique created through the generalization of key reconstructability analysis definitions and algorithms. The method is applied to functions on systems of discrete variables to discover a set of factors which can explain the bulk of the function's variation from the mean. K-systems analysis uses principles of information theory to reveal interactions which are often masked by the assumptions implicit in traditional methods. The method has been used successfully to analyze systems in several disciplines. Despite the success of k-systems analysis, obstacles to the creation of a mature methodology still exist. Some issues and open questions are examined, and a requirement for creating disjoint subsets of equations for calculating the unbiased reconstruction is confirmed, at least in the context of the greedy reconstructability algorithm. There is also a need for a framework to compare reconstructions. One approach for deriving comparison measures is suggested, based on the similarity between k-systems and the concept of a fitness landscape. One of the most serious obstacles to the generalized use of k-systems analysis is the exponential growth of system size as the number of variables and the values they assume increases. Searching the entire substate set for candidate factors limits the size of systems which can be effectively reconstructed. Methods exist which limit the search to a fraction of the substate space, but often lead to less compact reconstructions. An algorithm is presented which performs a search of the smaller state space to choose factors to use as starting points for a directed search of the substate space. Complexity analysis and experimental evidence indicate that the directed search technique provides a notable reduction in computation for the search process, while still providing a compact reconstruction. Combining directed search with state sampling techniques should further extend this capability. In addition to the directed search algorithm, a technique is proposed which can significantly reduce the computation required to update substate function values. This technique is based on a substate labeling scheme which imposes a total ordering on the substate set.
Branton, Christopher W., "Directed Search in K-System Reconstruction." (1998). LSU Historical Dissertations and Theses. 6806.