Modern multi-view clustering (MVC) is dominated by two paradigms: multi-view fusion and pseudo-label-guided learning. Pseudo-labeling methods can suffer from confirmation bias; their reliance on a fixed-granularity supervision from an initial clustering can cause learned embeddings to drift from the data's true structure and lose discriminative power. Conversely, fusion methods excel at integrating information but often struggle to robustly differentiate between high-quality and noisy views, which can obscure final cluster boundaries and degrade performance. To address these complementary challenges, we propose GAPS (Granularity-Aware Pseudo Supervision), a novel MVC framework. GAPS introduces a granularity-aware supervision mechanism that generates a full hierarchy of pseudo-labels, enabling the selection of a supervision level that best aligns with the data's intrinsic multi-scale structure. Furthermore, to ensure a high-quality supervisory signal, it incorporates a reliability-aware view selection strategy using a novel Separation-Compactness Index (SCI) to identify and leverage the most informative view for pseudo-label generation. This dual approach ensures the supervisory signal is both structurally adaptive and derived from the most reliable source, leading to highly effective final representations. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness and superiority of GAPS over other competitors.

Clustering on high-dimensional and low sample size (HDLSS) data remains a critical, persistent challenge where extreme sparsity and noise confound cluster analysis. This creates a dilemma: spectral methods fail as distance metrics degrade, while deep clustering tends to over-fit scarce data. To break this dilemma, a Self-Enhanced Density Clustering (SEDC) framework that integrates the cluster structure discovery and embedding representation learning into an iterative enhancement process is proposed in this paper. Specifically, SEDC uses adaptive density-derived centroids to parameterize probabilistic soft labels, which in turn supervise a lightweight multilayer perceptron (MLP) to learn the low-dimensional embedding from data. The resulting embedding provides a refined metric space for further generating superior labels in the subsequent interaction process. This feedback forms a mutual reinforcement that progressively enhances the discrimination of embedding while rigorously mitigating over-fitting. Extensive experiments on 43 challenging HDLSS datasets demonstrate state-of-the-art performance, substantially outperforming popular clustering methods. This work delivers a principled and promising solution for robust data clustering in HDLSS situations.

As a foundational clustering paradigm, Density Peak Clustering (DPC) partitions samples into clusters based on their density peaks, garnering widespread attention. However, traditional DPC methods usually focus on high-density regions, neglecting representative peaks in relatively low-density areas, particularly in datasets with varying densities and multiple peaks. Moreover, existing DPC variants struggle to identify clusters correctly in high-dimensional spaces due to the indistinct distance differences among samples and sparse data distributions. Additionally, existing methods typically adopt a one-step label assignment strategy, making them prone to cascading errors when initial misassignments occur. To address these challenges, we propose an Enhanced Density Peak Clustering (EDPC) method, which creatively incorporates multilayer perceptron (MLP)-based dimensionality reduction and a hierarchical label assignment strategy to significantly improve clustering performance in high-dimensional scenarios. Specifically, we introduce an effective selection condition that combines average densities and density-related distances to generate potential cluster centers, ensuring that peaks across different density regions are considered simultaneously. Furthermore, an MLP, guided by pseudo-labels from sub-clusters, is designed to learn low-dimensional embeddings for high-dimensional data, preserving data locality while enhancing clusterability. Extensive experiments demonstrate the effectiveness and superiority of EDPC against state-of-the-art DPC methods.

Multi-view clustering aims to integrate complementary information from multiple views to improve clustering performance. However, existing ensemble-based methods suffer from information loss due to their reliance on single-granularity labels, limiting the discriminative capability of learned representations. Meanwhile, representation and graph fusion-based approaches face challenges such as explicit view alignment and manual weight tuning, making them less effective for heterogeneous views with varying data distributions. To address these limitations, we propose a novel multi-view clustering framework via Multi-granularity Ensemble (MGE), fully using the multi-granularity information across diverse views for accurate and consistent clustering. Specifically, MGE first modifies the hierarchical clustering and then leverages it on each view (including the fused view) to achieve multi-granularity labels. Moreover, the cross-view and cross-granularity fusion strategy is designed to learn a robust co-association similarity matrix, which effectively preserves the fine-grained and coarse-grained structures of multi-view data and facilitates subsequent clustering. Therefore, MGE can provide a comprehensive representation of local and global patterns within data, eliminating the requirement for view alignment and weight tuning. Experiments demonstrate that MGE consistently outperforms state-of-the-art methods across multiple datasets, validating its effectiveness and superiority in handling heterogeneous views.

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.