Chameleon2++: An Efficient Chameleon2 Clustering with Approximate Nearest Neighbors

Clustering algorithms are fundamental tools in data analysis, with hierarchical methods being particularly valuable for their flexibility. Chameleon is a widely used hierarchical clustering algorithm that excels at identifying high-quality clusters of arbitrary shapes, sizes, and densities. Chameleon2 is the most recent variant that has demonstrated significant improvements, but suffers from critical failings and there are certain improvements that can be made. The first failure we address is that the complexity of Chameleon2 is claimed to be $O(n^2)$, while we demonstrate that it is actually $O(n^2\log{n})$, with $n$ being the number of data points. Furthermore, we suggest improvements to Chameleon2 that ensure that the complexity remains $O(n^2)$ with minimal to no loss of performance. The second failing of Chameleon2 is that it lacks transparency and it does not provide the fine-tuned algorithm parameters used to obtain the claimed results. We meticulously provide all such parameter values to enhance replicability. The improvement which we make in Chameleon2 is that we replace the exact $k$-NN search with an approximate $k$-NN search. This further reduces the algorithmic complexity down to $O(n\log{n})$ without any performance loss. Here, we primarily configure three approximate nearest neighbor search algorithms (Annoy, FLANN and NMSLIB) to align with the overarching Chameleon2 clustering framework. Experimental evaluations on standard benchmark datasets demonstrate that the proposed Chameleon2++ algorithm is more efficient, robust, and computationally optimal.