This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable ensemble clustering (U-SENC). In U-SPEC, a hybrid representative selection strategy and a fast approximation method for $K$ -nearest representatives are proposed for the construction of a sparse affinity sub-matrix. By interpreting the sparse sub-matrix as a bipartite graph, the transfer cut is then utilized to efficiently partition the graph and obtain the clustering result. In U-SENC, multiple U-SPEC clusterers are further integrated into an ensemble clustering framework to enhance the robustness of U-SPEC while maintaining high efficiency. Based on the ensemble generation via multiple U-SEPC's, a new bipartite graph is constructed between objects and base clusters and then efficiently partitioned to achieve the consensus clustering result. It is noteworthy that both U-SPEC and U-SENC have nearly linear time and space complexity, and are capable of robustly and efficiently partitioning ten-million-level nonlinearly-separable datasets on a PC with 64GB memory. Experiments on various large-scale datasets have demonstrated the scalability and robustness of our algorithms.

Due to its ability to combine multiple base clusterings into a probably better and more robust clustering, the ensemble clustering technique has been attracting increasing attention in recent years. Despite the significant success, one limitation to most of the existing ensemble clustering methods is that they generally treat all base clusterings equally regardless of their reliability, which makes them vulnerable to low-quality base clusterings. Although some efforts have been made to (globally) evaluate and weight the base clusterings, yet these methods tend to view each base clustering as an individual and neglect the local diversity of clusters inside the same base clustering. It remains an open problem how to evaluate the reliability of clusters and exploit the local diversity in the ensemble to enhance the consensus performance, especially, in the case when there is no access to data features or specific assumptions on data distribution. To address this, in this paper, we propose a novel ensemble clustering approach based on ensemble-driven cluster uncertainty estimation and local weighting strategy. In particular, the uncertainty of each cluster is estimated by considering the cluster labels in the entire ensemble via an entropic criterion. A novel ensemble-driven cluster validity measure is introduced, and a locally weighted co-association matrix is presented to serve as a summary for the ensemble of diverse clusters. With the local diversity in ensembles exploited, two novel consensus functions are further proposed. Extensive experiments on a variety of real-world datasets demonstrate the superiority of the proposed approach over the state-of-the-art.

Despite significant progress, there remain three limitations to the previous multi-view clustering algorithms. First, they often suffer from high computational complexity, restricting their feasibility for large-scale datasets. Second, they typically fuse multi-view information via one-stage fusion, neglecting the possibilities in multi-stage fusions. Third, dataset-specific hyperparameter-tuning is frequently required, further undermining their practicability. In light of this, we propose a fast m ulti-v i ew c lustering via e nsembles (FastMICE) approach.Particularly, the concept of random view groups is presented to capture the versatile view-wise relationships, through which the hybrid early-late fusion strategy is designed to enable efficient multi-stage fusions. With multiple views extended to many view groups, three levels of diversity (w.r.t. features, anchors, and neighbors, respectively) are jointly leveraged for constructing the view-sharing bipartite graphs in the early-stage fusion. Then, a set of diversified base clusterings for different view groups are obtained via fast graph partitioning, which are further formulated into a unified bipartite graph for final clustering in the late-stage fusion. Notably, FastMICE has almost linear time and space complexity, and is free of dataset-specific tuning. Experiments on 22 multi-view datasets demonstrate its advantages in scalability (for extremely large datasets), superiority (in clustering performance), and simplicity (to be applied) over the state-of-the-art. Code available: https://github.com/huangdonghere/FastMICE .

Although previous graph-based multi-view clustering (MVC) algorithms have gained significant progress, most of them are still faced with three limitations. First, they often suffer from high computational complexity, which restricts their applications in large-scale scenarios. Second, they usually perform graph learning either at the single-view level or at the view–consensus level, but often neglect the possibility of the joint learning of single-view and consensus graphs. Third, many of them rely on the $k$ -means for discretization of the spectral embeddings, which lack the ability to directly learn the graph with discrete cluster structure. In light of this, this article presents an efficient MVC approach via u nified and d iscrete b ipartite g raph l earning (UDBGL). Specifically, the anchor-based subspace learning is incorporated to learn the view-specific bipartite graphs from multiple views, upon which the bipartite graph fusion is leveraged to learn a view–consensus bipartite graph with adaptive weight learning. Furthermore, the Laplacian rank constraint is imposed to ensure that the fused bipartite graph has discrete cluster structures (with a specific number of connected components). By simultaneously formulating the view-specific bipartite graph learning, the view–consensus bipartite graph learning, and the discrete cluster structure learning into a unified objective function, an efficient minimization algorithm is then designed to tackle this optimization problem and directly achieve a discrete clustering solution without requiring additional partitioning, which notably has linear time complexity in data size. Experiments on a variety of multi-view datasets demonstrate the robustness and efficiency of our UDBGL approach. The code is available at https://github.com/huangdonghere/UDBGL.

Although many successful ensemble clustering approaches have been developed in recent years, there are still two limitations to most of the existing approaches. First, they mostly overlook the issue of uncertain links, which may mislead the overall consensus process. Second, they generally lack the ability to incorporate global information to refine the local links. To address these two limitations, in this paper, we propose a novel ensemble clustering approach based on sparse graph representation and probability trajectory analysis. In particular, we present the elite neighbor selection strategy to identify the uncertain links by locally adaptive thresholds and build a sparse graph with a small number of probably reliable links. We argue that a small number of probably reliable links can lead to significantly better consensus results than using all graph links regardless of their reliability. The random walk process driven by a new transition probability matrix is utilized to explore the global information in the graph. We derive a novel and dense similarity measure from the sparse graph by analyzing the probability trajectories of the random walkers, based on which two consensus functions are further proposed. Experimental results on multiple real-world datasets demonstrate the effectiveness and efficiency of our approach.