kFuse: A novel density based agglomerative clustering

TL;DR

kFuse tackles the parameter sensitivity and unstable distance issues inherent in traditional agglomerative clustering by introducing a two-stage, density-based approach. It employs parameter-free natural neighbors to partition the data into sub-clusters around local density peaks, then merges these sub-clusters using a fusion index built from boundary connectivity and density similarity, requiring only the final cluster count. The method yields $O(n^2)$ complexity and demonstrates superior performance across synthetic and real-world datasets, including MNIST and Olivetti Faces, as measured by FMI, ARI, and NMI with statistical significance. Overall, kFuse provides a robust, non-iterative clustering framework capable of identifying arbitrary-shaped clusters with strong empirical validation and practical applicability.

Abstract

Agglomerative clustering has emerged as a vital tool in data analysis due to its intuitive and flexible characteristics. However, existing agglomerative clustering methods often involve additional parameters for sub-cluster partitioning and inter-cluster similarity assessment. This necessitates different parameter settings across various datasets, which is undoubtedly challenging in the absence of prior knowledge. Moreover, existing agglomerative clustering techniques are constrained by the calculation method of connection distance, leading to unstable clustering results. To address these issues, this paper introduces a novel density-based agglomerative clustering method, termed kFuse. kFuse comprises four key components: (1) sub-cluster partitioning based on natural neighbors; (2) determination of boundary connectivity between sub-clusters through the computation of adjacent samples and shortest distances; (3) assessment of density similarity between sub-clusters via the calculation of mean density and variance; and (4) establishment of merging rules between sub-clusters based on boundary connectivity and density similarity. kFuse requires the specification of the number of clusters only at the final merging stage. Additionally, by comprehensively considering adjacent samples, distances, and densities among different sub-clusters, kFuse significantly enhances accuracy during the merging phase, thereby greatly improving its identification capability. Experimental results on both synthetic and real-world datasets validate the effectiveness of kFuse.

Figures (14)

• Figure 1: The clustering process of kFuse on the AwayCustomDatasets dataset.
• Figure 2: Representative points on AwayCustomDatasets, FlameClusteringDatasets, Zelnik1ZelnikDatasets, Path-basedClusteringDatasets datasets.
• Figure 3: Adjacent samples between two clusters. (a) Groudh truth of $S_1$ and $S_2$. (b) Augmented sub-cluster of $S_1$. (c) Augmented sub-cluster of $S_2$. (d) Adjacent samples of $S_1$ and $S_2$.
• Figure 4: The contribution of inter cluster distance to boundary connectivity. (a) The ground truth of dataset. (b) Adjacent samples between $S_1$ and $S_2$. (c) Adjacent samples between $S_2$ and $S_3$. (d) Initial partitioning of kFuse on the dataset. (e) minimum distance between $S_1$ and $S_2$. (f) minimum distance between $S_2$ and $S_3$.
• Figure 5: The limitation of using only boundary connectivity for evaluating sub-cluster cohesion. (a) The ground truth of PoleCustomDatasets dataset. (b) Initial partitioning of kFuse on the Pole. (c) Distance and adjacent samples between sparse cluster $S_4$ and dense cluster $S_6$.