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.

Multi-label classification represented by hierarchical classification (HC) plays an important role in current large-scale problems, which can acquire a more accurate expression of data that conforms to the human multi-granularity cognitive process. To compress the original dataset and simultaneously enhance the expressive force of models, selecting an appropriate granularity for approximately describing the classification is the main task in the rough set theory. Nevertheless, the current rough set theory merely concerns flat classification and encounters new problems when approximately describing HC. 1) There lacks a measure to correctly reflect misclassification in accordance with the hierarchical accuracy of HC on the training set. 2) There lacks a measure relying on the distribution of the dataset to reflect the difference between two distinct feature sets describing HC in generalization ability. To address the mentioned issues, this paper utilizes the knowledge distance to characterize HC and proposes a cost-sensitive granularity selection for HC. First, HC and features are respectively granulated according to hierarchical quotient space and neighborhood granular structures. Then, knowledge distance and its extended form are employed to formulate misclassification and test costs. On this basis, a cost-sensitive neighborhood granularity selection is presented for HC. Finally, we experimentally demonstrate the excellent performance of the proposed method in terms of efficiency and HC accuracy both in synthetic and real datasets.

To effectively improve the convergence and diversity of the multiobjective particle swarm optimization (MOPSO), we proposed a novel MOPSO based on ranking and cyclic distance (RCDMOPSO) that comprehensively considers the spatial target and congestion information of particles. RCDMOPSO introduced a method namely global proportional ranking (GPR) which differs from nondominated ranking under the Pareto framework, and designed a novel external archive maintenance and the global selection strategies of learning sample by combining GPR with cyclic distance. In this paper, RCDMOPSO together with eight classic and state-of-the-art algorithms were examined on ZDT, UF, and DTLZ series to test functions. The results show that RCDMOPSO is highly competitive in achieving the objectives of both convergence and diversity. RCDMOPSO outperformed other popular algorithms such as MOPSOs and multiobjective genetic algorithms based on comprehensive performance evaluation indicators inverted generational distance and hypervolume, thus supporting that RCDMOPSO is an effective approach to tackle multiobjective optimization problems.