Modeling repetitive patterns: A bridge between pattern theory and data mining

Traditional learning algorithms generate a predictive model by effectively partitioning the input or feature space in search for regions having a dominant single class. In this paper we point to the existence of problems where the relation among these regions corresponds to repetitive patterns that can be mapped to high-level models. We show how a formalism for the representation of patterns, also known as pattern theory, is instrumental to capture such relations. The idea is to verify patterns using mathematical constructs by combining primitive structures. We illustrate our ideas using parity problems, and show how bridging the gap between traditional supervised learning and pattern theory is a challenge that can bring large benefits to the data mining community.