An algorithm to efficiently generate an approximation of a theory set - Malinao, Jasmine A.; Dadios, Elmer P.; Ang, Marcelo Jr., H.
A theory set essentially consists of patterns that summarizes the observed inherent behavior of each cluster of observation in a data set. Furthermore, it is used in evaluating the cluster membership of new sets of data. Due to the large amount of computational resources needed to generate a theory set of a given data set, we propose an algorithm to approximate this set efficiently. The Approximate Crisp Theory Set Formation (ACTSF) algorithm is proposed to efficiently generate an approximation of theory set of a given k-tagged linearly inseparable data set. It is based on the methodologies developed in the Logical Analysis of Data (LAD) introduced by Peter Hammer. Since ACTSF is an approximation algorithm, it is inevitable to have an increased number of unclassified observations. To compensate for this, we extend ACTSF to include a discriminant function. This paper shows the improvement in the classification power of the theory sets as this discriminant function is injected in the proposed methodology. We show the effectiveness of this algorithm by testing it on a data set from the UCI Repository of Machine Learning Databases, University of California. In particular, we use the famous multivariate Iris data set created by Fisher in the 1988. Then, we compare the average performance of our algorithm against other known algorithms in the literature to measure its competency. ACTSF performed better than almost all of them.
Keywords: Approximate crisp theory set formation (ACTSF).; Logical Analysis of Data (LAD).; Neural Networks; Support Vector Machines; Data binarization