A clustering ensemble provides an elegant framework to learn a consensus result from multiple prespecified clustering partitions. Though conventional clustering ensemble methods achieve promising performance in various applications, we observe that they may usually be misled by some unreliable instances due to the absence of labels. To tackle this issue, we propose a novel active clustering ensemble method, which selects the uncertain or unreliable data for querying the annotations in the process of the ensemble. To fulfill this idea, we seamlessly integrate the active clustering ensemble method into a self-paced learning framework, leading to a novel self-paced active clustering ensemble (SPACE) method. The proposed SPACE can jointly select unreliable data to label via automatically evaluating their difficulty and applying easy data to ensemble the clusterings. In this way, these two tasks can be boosted by each other, with the aim to achieve better clustering performance. The experimental results on benchmark datasets demonstrate the significant effectiveness of our method. The codes of this article are released in http://Doctor-Nobody.github.io/codes/space.zip.

Consensus clustering, which learns a consensus clustering result from multiple weak base results, has been widely studied. However, conventional consensus clustering methods only focus on the ensemble process while ignoring the quality improvement of the base results, and thus they just use the fixed base results for consensus learning. In this paper, we provide an alternative idea to improve the final consensus clustering performance by considering the base results refining. In our framework, we adaptively refine the base results in the process of the ensemble. In more detail, on one hand, we ensemble multiple K-means results to learn the consensus one by considering the consensus and diversity; on the other hand, we apply the consensus result to design a graph filter to learn a more cluster-friendly embedding for refining the base K-means results. In our framework, the consensus learning and base results refining are integrated into one unified objective function so that these two tasks can be boosted by each other. Then we design an effective iterative algorithm to optimize the carefully designed objective function. The extensive experiments on benchmark data sets demonstrate that the proposed method can outperform both the single clustering and the state-of-the-art consensus clustering methods. The codes of this paper are released in http://Doctor-Nobody.github.io/codes/ACMK.zip .

To partition samples into distinct clusters, Fuzzy C-Means (FCM) calculates the membership degrees of samples to cluster centers and provides soft labels, gaining significant attention in recent years. However, existing FCM methods encounter the following challenges. First, traditional FCM focuses on learning membership degrees, neglecting the data similarity structures. Second, graph-based FCM typically separates graph construction from clustering, overlooking the knowledge interaction between graphs and clustering, obtaining suboptimal performance. Third, exploring the similarity structures among all samples is computationally expensive for large-scale tasks. To solve these dilemmas, we propose a scalable fuzzy clustering with collaborative structure learning and preservation (CSLP), which simultaneously leverages both cluster information and similarity structures to learn an optimal membership degree representation. Specifically, a self-weighted manner is devised to measure the sample importance, thereby reducing the adverse impacts of outliers. Moreover, the graph is updated according to the data similarities in the membership degree representation, such that CSLP collaboratively learns the graph and membership degrees in a mutually reinforcing manner. Thus, the similarity structures are fully explored during clustering processes and preserved in the learned membership degrees, enhancing the discrimination of clustering labels. To further improve efficiency, an acceleration solution is developed to reduce the computational cost of CSLP by propagating membership degrees from potential centers to samples, making CSLP scalable for large-scale tasks. An iterative strategy is designed to solve the formulated objective function. Extensive experiments demonstrate that CSLP outperforms other fuzzy clustering methods in terms of both effectiveness and scalability.

In many real-world unsupervised learning applications, given data with balanced distribution, that is, there are an approximately equal number of instances in each class, we often need to construct a model to reveal such balance. However, in many data, especially the high-dimensional ones, the data in the original feature space often do not present such balance due to the redundant and noisy features. To tackle this problem, we apply an unsupervised spectral feature selection method to select some informative features, which can better reveal the balanced structure of data. Although spectral feature selection is one of the most popular unsupervised feature selection methods and has been widely studied, none of the existing spectral feature selection methods consider the balance property of data. To address this issue, in this article, we propose a novel balanced spectral feature selection (BSFS) method, which not only selects the discriminative features but also picks those to reveal the balanced structure of data. To the best of our knowledge, this is the first spectral feature selection method considering balance structure of data. By introducing a balanced regularization term, we integrate the balanced spectral clustering and feature selection into a unified framework seamlessly. At last, the experiments on benchmark datasets show that the proposed one outperforms the conventional feature selection methods in both clustering performance and balance, which demonstrates the effectiveness and efficiency of the proposed method.

Consensus clustering provides an elegant framework to aggregate multiple weak clustering results to learn a consensus one that is more robust and stable than a single result. However, most of the existing methods usually use all data for consensus learning, whereas ignoring the side effects caused by some unreliable or difficult data. To address this issue, in this article, we propose a novel self-paced consensus clustering method with adaptive bipartite graph learning to gradually involve data from more reliable to less reliable ones in consensus learning. At first, we construct an initial bipartite graph from the base results, where the nodes represent the clusters and instances, and the edges indicate that an instance belongs to a cluster. Then, we adaptively learn a structured bipartite graph from this initial one by self-paced learning, i.e., we automatically determine the reliability of each edge with adaptive cluster similarity measuring and involve the edges in bipartite graph learning in order of their reliability. At last, we obtain the final consensus result from the learned structured bipartite graph. We conduct extensive experiments on both toy and benchmark datasets, and the results show the effectiveness and superiority of our method. The codes of this article are released in http://Doctor-Nobody.github.io/codes/code_SCCABG.zip.