Pattern Theoretic Knowledge Discovery

y Abstract Future research directions in Knowledge Discovery in Databases (KDD) include the ability to extract an overlying concept relating useful data. Current limitations involve the search complexity to nd that concept and what it means to be \useful." The Pattern Theory research crosses over in a natural way to the aforementioned domain. The goal of this paper is threefold. First, we present a new approach to the problem of learning by Discovery and robust pattern nding. Second, we explore the current limitations of a Pattern Theoretic approach as applied to the general KDD problem. Third, we exhibit its performance with experimental results on binary functions, and we compare those results with C4.5. This new approach to learning demonstrates a powerful method for nd-ing patterns in a robust manner. 1 The Pattern Theory Approach Pattern Theory is a discipline that arose out of machine learning 3] 7] and switching theory 6]. The original goal was to develop formal methods of algorithm design from speciications. The approach is based on a technique called function decomposition and a measure called decomposed function cardinality (DFC). Since Pattern Theory is able to extrapolate on available information based on the inherent structure in the data, it is directly related to KDD. Decomposing a function involves breaking it up into smaller subfunctions. These smaller functions are further broken down until all subfunctions will no longer decompose. For a given function, the number of ways to choose two sets of variables (the partition space) is exponential. The decomposition space is even larger, since there are several ways the subfunctions can be Figure 1: Lookup Table Figure 2: Decomposition combined and there are several levels of subfunctions possible. The complexity measure that we use to determine the relative predictive power of diierent function decompositions is called DFC. DFC is calculated by adding the cardinalities of each of the subfunctions in the decomposition. The cardinality of an n-variable binary function is 2 n : We illustrate the measure in the above gures. In Figure 1, we have a function on four variables with cardinality 2 4 = 16: In Figure 2, we show the same function after it has been decomposed. The DFC of this representation for the original function is 2 2 + 2 2 + 2 2 = 12: The DFC measures the relative complexity of a function. When we search through the possible decompositions for a …