A Knowledge-Based Approach To Pattern Clustering
The primary objective of this thesis is to develop a methodology for clustering of objects based on their functionality typified by the notion of concept. We begin by giving a formal definition of concept. By assigning a functional interpretation to the underlying concept, we demonstrate the applicability of the functionally interpreted concept for clustering objects. This functional interpretation leads us to identifying two classes of concepts, namely, the Necessary class and the Quality-Improvement class. Next, we categorize the functional cohesiveness among objects into three different classes. Further, we axiomatize the restrictions imposed, on the execution of functions of objects, by the non-availability of sufficient resources. To facilitate describing functional clusters in a succinct manner, we define connectives that capture the imposed restrictions. Also we justify the adequacy of these connectives for describing functional clusters. We then propose a suitable data structure to represent the functionally interpreted concept, and develop an algorithm to perform this axiomatic functional partitioning of objects. We illustrate the functional partitioning of objects through a real-world example. We formally establish the invariance of the resulting cluster descriptions, with respect to the order in which the given set of objects is examined. This invariance would facilitate parallel implementations of the proposed methodology. We then analyze different functional cluster configurations from a structural viewpoint. In doing so, we identify the presence of a specific property among certain cluster configurations. We also state a sufficient condition for the presence of this property in any cluster. A separate class of concepts, namely the Concept Transformer class, displaying certain properties, is identified and studied in detail. We also demonstrate its applicability to functional clustering. Finally, we examine a knowledge-based pattern synthesis problem from a functional angle as a significant application of the functional interpretation of concept and associated data structures. Here, we show that a concept, from the functional view-point, can be viewed as the synthesis of various other concepts; the synthesis is an outcome of a knowledge-based goal-directed pattern-matching activity. The proposed methodology has the potential to cluster objects that imply functions by virtue of their physical properties.