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.

Clustering is widely used to organize large-scale multimedia collections, but standard clustering methods can inherit and amplify demographic imbalance in the underlying data. Existing fair clustering methods still face two practical limitations: many scale poorly to high-dimensional visual datasets, and many rely on a fairness-weight coefficient that must be tuned for each dataset. We propose FairFBC, a scalable fair fuzzy clustering framework for large-scale data. FairFBC first constructs a group-balanced anchor graph to obtain a sparse and scalable representation. It then learns a shared fuzzy partition by maximizing the sum of group-specific trace-sqrt quality terms, which encourages balanced structure across sensitive groups without introducing an explicit fairness-accuracy trade-off coefficient. Finally, a confidence-aware quota-constrained assignment step converts fuzzy memberships into a discrete partition while preserving consistency with the learned structure. Experiments on ten datasets from vision, vision-language, and tabular domains, including FairFace, CelebA, and ChestX-ray, show that FairFBC achieves a strong accuracy-fairness trade-off while remaining stable on large datasets where several competitive baselines fail to run. The code for our method is publicly available at https://github.com/Whale-Waves/FairFBC.

Fuzzy clustering ensemble techniques have been proven to yield more accurate and robust clustering results, with the mainstream methods relying on the fuzzy co-association (FCA) matrix. However, the inherent issues of low-value density and uniform dispersion in the FCA matrix significantly affect the performance of fuzzy clustering ensembles, an aspect that has been overlooked. To address this issue, we propose a novel framework for fuzzy clustering ensemble based on fuzzy matrix self-enhancement (FMSE). Specifically, we initially employ singular value decomposition to extract the principal components of the FCA matrix, thereby alleviating its low-value density. Second, on the basis of the criterion of fuzzy entropy, we measure the fuzziness of samples, design a metric for the fuzzy representativeness of samples, and incorporate it into a fusion-weighted structure for the reconstruction of the FCA matrix, mitigating uniform dispersion. Subsequently, on the basis of the self-enhanced fuzzy matrix model, we utilize a prototype diffusion approach to identify core samples and gradually allocate remaining samples to obtain a consensus clustering solution. Extensive comparative experiments on benchmark datasets against state-of-the-art clustering ensemble methods demonstrate the effectiveness and superiority of the proposed approach.

Causal feature selection has recently received increasing attention in machine learning and data mining, especially in the era of Big Data. Existing causal feature selection algorithms select unique causal features of the single class label as the optimal feature subset. However, a single class label usually has multiple classes, and it is unreasonable to select the same causal features for different classes of a single class label. To address this problem, we employ the class-specific mutual information to evaluate the causal information carried by each class of the single class label, and theoretically analyze the unique relationship between each class and the causal features. Based on this, aLabel-awareCausalFeatureSelection algorithm (LaCFS) is proposed to identifies the causal features for each class of the class label. Specifically, LaCFS uses the pairwise comparisons of class-specific mutual information and the size of class-specific mutual information values from the perspective of each class, and follows a divide-and-conquer framework to find causal features. The correctness and application condition of LaCFS are theoretically proved, and extensive experiments are conducted to demonstrate the efficiency and superiority of LaCFS compared to the state-of-the-art approaches.

Fair feature selection for classification decision tasks has recently garnered significant attention from researchers. However, existing fair feature selection algorithms fall short of providing a full explanation of the causal relationship between features and sensitive attributes, potentially impacting the accuracy of fair feature identification. To address this issue, we propose a fair causal feature selection algorithm, called FairCFS . Specifically, FairCFS constructs a localized causal graph that identifies the Markov blankets of class and sensitive variables, to block the transmission of sensitive information for selecting fair causal features. Extensive experiments on seven public real-world datasets validate that FairCFS has accuracy comparable to eight state-of-the-art feature selection algorithms while presenting more superior fairness.

Clustering ensemble often provides robust and stable results without accessing original features of data, and thus has been widely studied. The conventional clustering ensemble methods often take the full multiple base partitions as inputs and provide a consensus clustering result. However, in many real-world applications, full base partitions are hard to obtain because some data may be missing in some base partitions. To tackle this problem, in this paper, we propose a novel partial clustering ensemble method, which takes the partial multiple base partitions as inputs. In this method, we simultaneously fill the missing values in the base partitions and ensemble them by fully considering the consensus and diversity. Moreover, to address the unreliability issue in the partial data scenario, we seamlessly plug it into a self-paced learning framework. The extensive experiments on benchmark data sets demonstrate the effectiveness and efficiency of the proposed method when handling incomplete data.

Existing clustering ensemble methods often directly integrate multiple weak base results to obtain a consensus one which can improve the clustering performance. However, since the base results are weak and the clustering ensemble can improve the performance, why not refine the weak base results via the clustering ensemble, and then boost the clustering ensemble with the refined base results? To fulfill this idea, in this article, we propose a novel clustering ensemble method with an adaptive multiplex. We first use the multiplex to represent the multiple weak base results. Then, we learn an updated representation by diffusing the representation on the multiplex with a manifold ranking model. Since the multiplex characterizes the structure information of all base results, the learned representation can ensemble such structure information during diffusion. Next, the multiplex is refined by such representation, which is a process of refining base results via ensemble. We iteratively learn the representation (i.e., do ensemble) and update the multiplex (i.e., do refinement), which can make the ensemble and refinement be boosted by each other. At last, the final consensus result is obtained from the refined multiplex. The extensive experiments demonstrate the effectiveness and superiority of the proposed framework.

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.

Causal feature selection has received increasing attention in recent years. However, the state-of-the-art causal feature selection algorithms use the conditional independence tests, which require enumerating conditioning sets, leading to an exponential increase in computational complexity along with an increase in feature space. To address this problem, in this paper, we theoretically analyze the unique performance of causal features in mutual information, and propose a novelCausalFeatureSelection algorithm usingMutualInformation, called CFS-MI. Specifically, CFS-MI separately instantiates the pairwise comparison of mutual information in two stages to reduce computational complexity, and thus improves the efficiency on high-dimensional data. Extensive experiments on 5 benchmark Bayesian networks and 16 real-world datasets validate that CFS-MI has comparable accuracy compared to 7 state-of-the-art causal feature selection algorithms, while presenting more superior computational efficiency.

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 inhttp://Doctor-Nobody.github.io/codes/ACMK.zip.

Multi-view classification has received considerable attention in recent years. We observed that the existing multi-view classification methods learn a consensus result by collecting all views and thus have two critical limitations. First, it is not scalable. Second, in many applications views of data are available over time; it is in-feasible to apply the existing multi-view learning methods to such streaming views. To address the two limitations, in this paper we propose a novel incremental multi-view SVM method, i.e., instead of processing all views simultaneously, we integrate them one by one in an incremental way. We first learn an initial model from the first view; next when a new view is available, we update the model and then apply it to learn a new consensus result. This incremental method is scalable and applicable to streaming views. We present a block coordinate descent algorithm whose convergence is theoretically guaranteed to optimize the induced objective function. Experimental results on several benchmark data sets further demonstrate the effectiveness of our method.

In classification tasks, labeled data is a necessity but sometimes difficult or expensive to obtain. On the contrary, unlabeled data is usually abundant. Recently, different active learning algorithms are proposed to alleviate this issue by selecting the most informative data points to label. One family of active learning methods comes from Optimum Experimental Design (OED) in statistics. Instead of selecting data points one by one iteratively, OED-based approaches select data in a one-shot manner, that is, a fixed-sized subset is selected from the unlabeled dataset for manually labeling. These methods usually use kernels to represent pair-wise similarities between different data points. It is well known that choosing optimal kernel types (e.g. Gaussian kernel) and kernel parameters (e.g. kernel width) is tricky, and a common way to resolve it is by Multiple Kernel Learning (MKL), i.e., to construct a few candidate kernels and merge them to form a consensus kernel. There would be different ways to combine multiple kernels, one of which, called the the globalised approach is to assign a weight to each candidate kernel. In practice different data points in the same candidate kernel may not have the same contribution in the consensus kernel, this requires assigning different weights to different data points in the same candidate kernel, leading to the localized approach. In this paper, we introduce MKL to OED-based active learning, specifically we propose globalised and localized multiple kernel active learning methods, respectively. Our experiments on six benchmark datasets demonstrate that the proposed methods have better performance than existing OED-based active learning methods.

With unstructured heterogeneous multimedia data such as texts, images being more and more widely used on the web, cross-media retrieval has become an increasingly important task. One of the key techniques in cross-media retrieval is how to compute distances or similarities among different types of media data. In this paper, we propose a novel heterogeneous metric learning method to compute distances between images and texts. We extend Locally Linear Embedding (LLE) to deal with heterogeneous data, so that we can not only preserve homogeneous local information but also capture heterogeneous constraints. In order to handle the out-of-sample problem, we learn two map functions from the embedding, and use them to transform heterogeneous data into a homogeneous space and do the retrieval in the new space. The experimental results on two real-world datasets show the effectiveness of our approach.

In this paper, we consider the problem of feature selection in unsupervised learning scenario. Recently, spectral feature selection methods, which leverage both the graph Laplacian and the learning mechanism, have received considerable attention. However, when there are lots of irrelevant or noisy features, such graphs may not be reliable and then mislead the selection of features. In this paper, we propose the Local and Global Discriminative learning for unsupervised Feature Selection (LGDFS), which integrates a global and a set of locally linear regression model with weighted l2-norm regularization into a unified learning framework. By exploring the discriminative and geometrical information in the weighted feature space, which alleviates the effects of the irrelevant features, our approach can find the most representative features to well respect the cluster structure of the data. Experimental results on several benchmark data sets are provided to validate the effectiveness of the proposed approach.