K-Means Extensions for Clustering Categorical Data on Concept Lattice

Abstract

Formal Concept Analysis (FCA) is a key tool in knowledge discovery, representing data relationships through concept lattices. However, the complexity of these lattices often hinders interpretation, prompting the need for innovative solutions. In this context, the study proposes clustering formal concepts within a concept lattice, ultimately aiming to minimize lattice size. To address this, The study introduces introduce two novel extensions of the k-means algorithm to handle categorical data efficiently, a crucial aspect of the FCA framework. These extensions, namely K-means Dijkstra on Lattice (KDL) and Kmeans Vector on Lattice (KVL), are designed to minimize the concept lattice size. However, the current study focuses on introducing and refining these new methods, laying the groundwork for our future goal of lattice size reduction. The KDL utilizes FCA to build a graph of formal concepts and their relationships, applying a modified Dijkstra algorithm for distance measurement, thus replacing the Euclidean distance in traditional k-means. The defined centroids are formal concepts with minimal intra-cluster distances, enabling effective categorical data clustering. In contrast, the KVL extension transforms formal concepts into numerical vectors to leverage the scalability offered by traditional k-means, potentially at the cost of clustering quality due to oversight of the data's inherent hierarchy. After rigorous testing, KDL and KVL proved robust in managing categorical data. The introduction and demonstration of these novel techniques lay the groundwork for future research, marking a significant stride toward addressing current challenges in categorical data clustering within the FCA framework.