  This work proposes a hierarchical clustering algorithm for high-dimensional
datasets using the cyclic space of reversible finite cellular automata. In
cellular automaton (CA) based clustering, if two objects belong to the same
cycle, they are closely related and considered as part of the same cluster.
However, if a high-dimensional dataset is clustered using the cycles of one CA,
closely related objects may belong to different cycles. This paper identifies
the relationship between objects in two different cycles based on the median of
all elements in each cycle so that they can be grouped in the next stage.
Further, to minimize the number of intermediate clusters which in turn reduces
the computational cost, a rule selection strategy is taken to find the best
rules based on information propagation and cycle structure. After encoding the
dataset using frequency-based encoding such that the consecutive data elements
maintain a minimum hamming distance in encoded form, our proposed clustering
algorithm iterates over three stages to finally cluster the data elements into
the desired number of clusters given by user. This algorithm can be applied to
various fields, including healthcare, sports, chemical research, agriculture,
etc. When verified over standard benchmark datasets with various performance
metrics, our algorithm is at par with the existing algorithms with quadratic
time complexity.
