Hierarchical Topology-Based Cluster Representation for Scalable Evolutionary Multiobjective Clustering

Evolutionary multiobjective clustering (MOC) algorithms have shown promising potential to outperform conventional single-objective clustering algorithms, especially when the number of clusters
$k$
is not set before clustering. However, the computational burden becomes a tricky problem due to the extensive search space and fitness computational time of the evolving population, especially when the data size is large. This article proposes a new, hierarchical, topology-based cluster representation for scalable MOC, which can simplify the search procedure and decrease computational overhead. A coarse-to-fine-trained topological structure that fits the spatial distribution of the data is utilized to identify a set of seed points/nodes, then a tree-based graph is built to represent clusters. During optimization, a bipartite graph partitioning strategy incorporated with the graph nodes helps in performing a cluster ensemble operation to generate offspring solutions more effectively. For the determination of the final result, which is underexplored in the existing methods, the usage of a cluster ensemble strategy is also presented, whether
$k$
is provided or not. Comparison experiments are conducted on a series of different data distributions, revealing the superiority of the proposed algorithm in terms of both clustering performance and computing efficiency.