G\"odel Number based Clustering Algorithm with Decimal First Degree Cellular Automata

TL;DR

This paper introduces a novel clustering algorithm using decimal first degree cellular automata and G"odel number encoding, which improves clustering performance by reducing data representation size and leveraging CA dynamics.

Contribution

It proposes a new clustering method based on FDCA and G"odel encoding, with an iterative algorithm and theoretical rule selection, outperforming existing algorithms.

Findings

Higher clustering accuracy as per benchmark metrics

Reduced data encoding length while preserving features

Superior performance compared to state-of-the-art algorithms

Abstract

In this paper, a decimal first degree cellular automata (FDCA) based clustering algorithm is proposed where clusters are created based on reachability. Cyclic spaces are created and configurations which are in the same cycle are treated as the same cluster. Here, real-life data objects are encoded into decimal strings using G\"odel number based encoding. The benefits of the scheme is, it reduces the encoded string length while maintaining the features properties. Candidate CA rules are identified based on some theoretical criteria such as self-replication and information flow. An iterative algorithm is developed to generate the desired number of clusters over three stages. The results of the clustering are evaluated based on benchmark clustering metrics such as Silhouette score, Davis Bouldin, Calinski Harabasz and Dunn Index. In comparison with the existing state-of-the-art clustering algorithms, our proposed algorithm gives better performance.