Benefit from avoiding the utilization of labeled samples, which are usually insufficient in the real world, unsupervised learning has been regarded as a speedy and powerful strategy on clustering tasks. However, clustering directly from primal data sets leads to high computational cost, which limits its application on large-scale and high-dimensional problems. Recently, anchor-based theories are proposed to partly mitigate this problem and field naturally sparse affinity matrix, while it is still a challenge to get excellent performance along with high efficiency. To dispose of this issue, we first presented a fast semisupervised framework (FSSF) combined with a balanced $K$ -means-based hierarchical $K$ -means (BKHK) method and the bipartite graph theory. Thereafter, we proposed a fast self-supervised clustering method involved in this crucial semisupervised framework, in which all labels are inferred from a constructed bipartite graph with exactly $k$ connected components. The proposed method remarkably accelerates the general semisupervised learning through the anchor and consists of four significant parts: 1) obtaining the anchor set as interim through BKHK algorithm; 2) constructing the bipartite graph; 3) solving the self-supervised problem to construct a typical probability model with FSSF; and 4) selecting the most representative points regarding anchors from BKHK as an interim and conducting label propagation. The experimental results on toy examples and benchmark data sets have demonstrated that the proposed method outperforms other approaches.

Embedded feature selection approach guides subsequent projection matrix (selection matrix) learning through the acquisition of pseudolabel matrix to conduct feature selection tasks. Yet the continuous pseudolabel matrix learned from relaxed problem based on spectral analysis deviates from reality to some extent. To cope with this issue, we design an efficient feature selection framework inspired by classical least-squares regression (LSR) and discriminative K-means (DisK-means), which is called the fast sparse discriminative K-means (FSDK) for the feature selection method. First, the weighted pseudolabel matrix with discrete trait is introduced to avoid trivial solution from unsupervised LSR. On this condition, any constraint imposed into pseudolabel matrix and selection matrix is dispensable, which is significantly beneficial to simplify the combinational optimization problem. Second, the $\ell_{2,p}$ -norm regularizer is introduced to satisfy the row sparsity of selection matrix with flexible $p$ . Consequently, the proposed FSDK model can be treated as a novel feature selection framework integrated from the DisK-means algorithm and $\ell_{2,p}$ -norm regularizer to optimize the sparse regression problem. Moreover, our model is linearly correlated with the number of samples, which is speedy to handle the large-scale data. Comprehensive tests on various data terminally illuminate the effectiveness and efficiency of FSDK.

Spectral clustering (SC) has been applied to analyze varieties of data structures over the past few decades owing to its outstanding breakthrough in graph learning. However, the time-consuming eigenvalue decomposition (EVD) and information loss during relaxation and discretization impact the efficiency and accuracy especially for large-scale data. To address above issues, this brief proposes a simple and fast method named efficient discrete clustering with anchor graph (EDCAG) to circumvent postprocessing by binary label optimization. First of all, sparse anchors are adopted to accelerate graph construction and obtain a parameter-free anchor similarity matrix. Subsequently, inspired by intraclass similarity maximization in SC, we design an intraclass similarity maximization model between anchor–sample layer to cope with anchor graph cut problem and exploit more explicit data structures. Meanwhile, a fast coordinate rising (CR) algorithm is employed to alternatively optimize discrete labels of samples and anchors in designed model. Experimental results show excellent rapidity and competitive clustering effect of EDCAG.

These days, clustering is one of the most classical themes to analyze data structures in machine learning and pattern recognition. Recently, the anchor-based graph has been widely adopted to promote the clustering accuracy of plentiful graph-based clustering techniques. In order to achieve more satisfying clustering performance, we propose a novel clustering approach referred to as the progressive self-supervised clustering method with novel category discovery (PSSCNCD), which consists of three separate procedures specifically. First, we propose a new semisupervised framework with novel category discovery to guide label propagation processing, which is reinforced by the parameter-insensitive anchor-based graph obtained from balanced $K$ -means and hierarchical $K$ -means (BKHK). Second, we design a novel representative point selected strategy based on our semisupervised framework to discover each representative point and endow pseudolabel progressively, where every pseudolabel hypothetically corresponds to a real category in each self-supervised label propagation. Third, when sufficient representative points have been found, the labels of all samples will be finally predicted to obtain terminal clustering results. In addition, the experimental results on several toy examples and benchmark data sets comprehensively demonstrate that our method outperforms other clustering approaches.

Hyperspectral images can provide spectral characteristics related to the physical properties of different materials, which arouses great interest in many fields. Band selection (BS) could effectively solve the problem of high dimensions and redundant information of HSI data. However, most BS methods utilize a single measurement criterion to evaluate band importance so that the assessment of bands is not comprehensive. To dispose of these issues, we propose the hypergraph spectral clustering band selection (HSCBS) method in this letter. First, a novel hypergraph construction method is proposed to combine bands selected by different priority criteria. Second, based on the hypergraph Laplacian matrix, an unsupervised band selection model named HSCBS is presented to cluster the bands into compact clusters with high within-class similarity and low between-class similarity. The results of comprehensive experimental on two public real datasets demonstrate the effectiveness of HSCBS.

Graph-based clustering technique has garnered significant attention due to precise information characterization by pairwise graph similarity. Nevertheless, the post-processing step in traditional methods often limits clustering effects because of crucial information loss. Therefore, the Constrained Laplacian Rank (CLR) theory emerges to directly obtain discrete labels from optimally structural graph, achieving desirable outcomes. However, CLR suffers from substantial time overhead, making it infeasible for large-scale data analysis. To overcome this issue, we propose Anchor-based CLR (ACLR), a simple yet effective method for efficient large-scale clustering. The ACLR method comprises four stages: (1) anchors that roughly cover original data are opted to prepare bipartite graph construction; (2) a novel two-step probability transition (TSPT) strategy initializes a small-scale graph with random walk probability among anchors; (3) the main ACLR model alternately optimizes the graph connected structure and directly produces discrete anchor labels, achieving a time complexity independent of the number of samples due to dramatically reduced graph scale; and (4) labels are propagated from anchors to samples using $K$-NN algorithm. Extensive experiments demonstrate that ACLR yields superior accuracy and efficiency, particularly when applied to large-scale data. The codes are available at https://github.com/MarathonZhenyuMa/2025-TKDE-ACLR.