Parameter-free discrete clustering via adaptive hypergraph fusion

Graph-based clustering has garnered significant attention due to its outstanding performance in uncovering sample structures. However, existing graph-based methods face two major challenges: 1) In graph construction, they typically focus only on direct connections between samples or an exact high-order relationship, neglecting the impact of hidden complex relationships on clustering performance; 2) The separation of spectral analysis and category acquisition into two distinct stages often results in a loss of effectiveness. To handle these problems, we propose a parameter-free discrete clustering method, called parameter-free discrete clustering via adaptive hypergraph fusion (DCAHF). Specifically, DCAHF first produces multiple different hypergraphs, each serving as a biased approximation of the data's intrinsic manifold. These complementary approximations capture distinct local-to-global geometric patterns. Then, it introduces an adaptive fusion strategy that learns optimal weights to combine them into a single consensus hypergraph on manifold space, effectively reconstructing the real manifold structure with reduced bias and improved integrity. Finally, discrete spectral analysis is performed directly on the consensus hypergraph to generate discrete sample categories, thereby avoiding the performance loss associated with two-stage approaches. Thus, DCAHF is a high-performance, parameter-free clustering model that can flexibly adapt to various clustering tasks. Since the DCAHF model cannot be solved using gradient descent methods, we develop a coordinate descent-based optimization algorithm to efficiently solve the model. Extensive experimental results demonstrate that DCAHF significantly enhances clustering effectiveness while maintaining comparable efficiency to state-of-the-art methods.