Multi-view data is widely present in the real world. Multi-view clustering is an unsupervised method for capturing the grouping structure of such data. However, multi-view clustering struggles to meet the requirements of real-world scenarios, such as distributed storage of different views and data protection needs. These requirements align with the setting of vertical federated clustering. However, vertical federated clustering still faces two challenges: (1) Under the constraints of privacy protection mechanisms, how to theoretically analyze the clustering consistency between the data uploaded by clients to the server and the original client data is challenging. (2) The feature space differences among different clients make cross-view information sharing and fusion difficult. To address the first challenge, we provide a theoretical analysis of the upper bound of the loss of k-means for transformation matrix mapping, revealing the relationship between the k-means loss of the transformed data and the original data. We then propose a vertical federated clustering method (V-HDKM). In this method, clients handle the second challenge by transposing the feature matrix. Guided by the projected k-means loss bound, we expand the feature space and perform k-means clustering to obtain feature cluster centers, which are then uploaded to the server. The server aggregates the global centers and feeds back the optimized results, achieving cross-view knowledge fusion through iterative interactions. Experimental results show that V-HDKM significantly improves local clustering performance and performances better than other seven vertical federated mthods on 20 multi-view datasets. Furthermore, sensitivity analysis on 8 UCI datasets with respect to the number of clients demonstrates the stability of the method. The code is available at https://github.com/jiangjh/V-HDKM.

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.

Ensemble clustering has emerged as a powerful paradigm to improve clustering robustness by aggregating multiple base results. However, traditional methods treat ensemble features statically, failing to account for the inconsistencies and variations that arise from differing base clustering outputs. To tackle this, we propose a novel iterative ensemble clustering framework that adaptively refines consensus representations via high-order graph diffusion and feedback-driven refinement. Unlike static consensus methods, our approach uniquely embeds evolving cluster structures within the feature space, enabling progressive self-correction through global inconsistency suppression and reliability-aware weighting. Our approach uniquely integrates: (1) Adaptive affinity weighting to prioritize reliable base clusterings, (2) Higher-order graph diffusion to capture topological dependencies and suppress high-frequency noise, and (3) Feedback-driven consensus evolution that iteratively replaces unreliable base clusterings with improved consensus outputs. Our method consistently outperforms 9 state-of-the-art ensemble techniques across 10 multimedia datasets, achieving \(\mathbf {+2.2-17.8\%}\) accuracy and \(\mathbf {+3-11.6\%}\) consensus quality, alongside cluster balance improvement up to \(\mathbf {+10.5\%}\). The proposed framework is scalable, model-agnostic, and ideal for real-world multimedia tasks with heterogeneous data sources.

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.

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.

The problem of feature selection has raised considerable interests in the past decade. Traditional unsupervised methods select the features which can faithfully preserve the intrinsic structures of data, where the intrinsic structures are estimated using all the input features of data. However, the estimated intrinsic structures are unreliable/inaccurate when the redundant and noisy features are not removed. Therefore, we face a dilemma here: one need the true structures of data to identify the informative features, and one need the informative features to accurately estimate the true structures of data. To address this, we propose a unified learning framework which performs structure learning and feature selection simultaneously. The structures are adaptively learned from the results of feature selection, and the informative features are reselected to preserve the refined structures of data. By leveraging the interactions between these two essential tasks, we are able to capture accurate structures and select more informative features. Experimental results on many benchmark data sets demonstrate that the proposed method outperforms many state of the art unsupervised feature selection 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 unsupervised feature selection. Recently, spectral feature selection algorithms, which leverage both graph Laplacian and spectral regression, have received increasing attention. However, existing spectral feature selection algorithms suffer from two major problems: 1) since the graph Laplacian is constructed from the original feature space, noisy and irrelevant features may have adverse effect on the estimated graph Laplacian and hence degenerate the quality of the induced graph embedding, 2) since the cluster labels are discrete in natural, relaxing and approximating these labels into a continuous embedding can inevitably introduce noise into the estimated cluster labels. Without considering the noise in the cluster labels, the feature selection process may be misguided. In this paper, we propose a Robust Spectral learning framework for unsupervised Feature Selection (RSFS), which jointly improves the robustness of graph embedding and sparse spectral regression. Compared with existing methods which are sensitive to noisy features, our proposed method utilizes a robust local learning method to construct the graph Laplacian and a robust spectral regression method to handle the noise on the learned cluster labels. In order to solve the proposed optimization problem, an efficient iterative algorithm is proposed. We also show the close connection between the proposed robust spectral regression and robust Huber M-estimator. Experimental results on different datasets show the superiority of RSFS.

The problem of software artifact retrieval has the goal to effectively locate software artifacts, such as a piece of source code, in a large code repository. This problem has been traditionally addressed through the textual query. In other words, information retrieval techniques will be exploited based on the textual similarity between queries and textual representation of software artifacts, which is generated by collecting words from comments, identifiers, and descriptions of programs. However, in addition to these semantic information, there are rich information embedded in source codes themselves. These source codes, if analyzed properly, can be a rich source for enhancing the efforts of software artifact retrieval. To this end, in this paper, we develop a feature extraction method on source codes. Specifically, this method can capture both the inherent information in the source codes and the semantic information hidden in the comments, descriptions, and identifiers of the source codes. Moreover, we design a heterogeneous metric learning approach, which allows to integrate code features and text features into the same latent semantic space. This, in turn, can help to measure the artifact similarity by exploiting the joint power of both code and text features. Finally, extensive experiments on real-world data show that the proposed method can help to improve the performances of software artifact retrieval with a significant margin.

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.

Due to the fast evolution of the information on the Internet, update summarization has received much attention in recent years. It is to summarize an evolutionary document collection at current time supposing the users have read some related previous documents. In this paper, we propose a graph-ranking-based method. It performs constrained reinforcements on a sentence graph, which unifies previous and current documents, to determine the salience of the sentences. The constraints ensure that the most salient sentences in current documents are updates to previous documents. Since this method is NP-hard, we then propose its approximate method, which is polynomial time solvable. Experiments on the TAC 2008 and 2009 benchmark data sets show the effectiveness and efficiency of our method.

Nonnegative matrix factorization (NMF) is a popular technique for learning parts-based representation and data clustering. It usually uses the squared residuals to quantify the quality of factorization, which is optimal specifically to zero-mean, Gaussian noise and sensitive to outliers in general cases. In this paper, we propose a robust NMF method based on the correntropy induced metric, which is much more insensitive to outliers. A half-quadratic optimization algorithm is developed to solve the proposed problem efficiently. The proposed method is further extended to handle outlier rows by incorporating structural knowledge about the outliers. Experimental results on data sets with and without apparent outliers demonstrate the effectiveness of the proposed algorithms.

Update summarization is to summarize a document collection B given that the users have already read another document collection A, which has time stamp prior to that of B. An important and challenging issue in update summarization is that contents in B already covered by A should be excluded from the update summary. In this paper, we propose a graph-based regularization framework MarginRank for update summarization. MarginRank extends the cost function of Zhou's Manifold Ranking with suppression terms, suppression of A on B, to fulfil the assumption that users have read A. MarginRank ranks sentences in B in a way that the top ranked sentences are most important and at the same time cover different contents from A. Experiments on the benchmark data sets TAC 2008 and 2009 show the effectiveness of the proposed method.

Novelty, coverage and balance are important requirements in topic-focused summarization, which to a large extent determine the quality of a summary. In this paper, we propose a novel method that incorporates these requirements into a sentence ranking probability model. It differs from the existing methods in that the novelty, coverage and balance requirements are all modeled w.r.t. a given topic, so that summaries are highly relevant to the topic and at the same time comply with topic-aware novelty, coverage and balance. Experimental results on the DUC 2005, 2006 and 2007 benchmark data sets demonstrate the effectiveness of our method.

In this paper, we propose the Interval-valued Matrix Factorization (IMF) framework. Matrix Factorization (MF) is a fundamental building block of data mining. MF techniques, such as Nonnegative Matrix Factorization (NMF) and Probabilistic Matrix Factorization (PMF), are widely used in applications of data mining. For example, NMF has shown its advantage in Face Analysis (FA) while PMF has been successfully applied to Collaborative Filtering (CF). In this paper, we analyze the data approximation in FA as well as CF applications and construct interval-valued matrices to capture these approximation phenomenons. We adapt basic NMF and PMF models to the interval-valued matrices and propose Interval-valued NMF (I-NMF) as well as Interval-valued PMF (I-PMF). We conduct extensive experiments to show that proposed I-NMF and I-PMF significantly outperform their single-valued counterparts in FA and CF applications.