The vulnerability of graph-based recommender systems to spurious correlations has become a significant obstacle to their practical deployment, hindering their robustness in out-of-distribution (OOD) scenarios. While existing approaches offer partial solutions, they are limited by fundamental shortcomings: model-centric approaches reliant on predefined causal graphs often suffer from suboptimal performance due to complex and dynamic environmental influences. These methods typically require identifying an environmental label or performing feature decoupling, but hidden environments are often difficult to model. Furthermore, existing general feature decoupling methods fail to account for the unique structural characteristics of graphs. To overcome these challenges, we advocate for a shift towards explicit, geometrically-grounded disentanglement. Hyperbolic geometry is particularly suited for this task due to its capacity to model the inherent hierarchies of user interests. We introduce C-HyPOD : Causal Hyperbolic Representation Learning with Prototype Orthogonal Disentanglement, a novel framework designed for graph-based OOD recommendation. Unlike traditional methods, C-HyPOD transforms disentanglement into a concrete geometric task. It introduces a global interest space by learning a single set of universal interest prototypes. They provides a superior geometric foundation for ensuring these prototypes are well-separated and semantically distinct. To ensure a complete separation and prevent information leakage, a targeted orthogonality constraint is then applied. This constraint purifies the aggregated causal representation by forcing it to be orthogonal to the spurious representation in the tangent space, thereby eliminating their linear correlation. Extensive experiments on four public datasets demonstrate that C-HyPOD significantly improves OOD robustness and recommendation performance, surpassing state-of-the-art methods.

Recommendation systems alleviate the issue of information overload via modeling user preferences from interaction sequences. Although self-attention based sequential models effectively capture long-range dependencies, they are susceptible to noise amplification in sparse sequences and over-smoothing of item representations, which obscures true user intent and reduces sensitivity to fine-grained behavioral changes. To overcome these challenges, we propose SAFA, a sparse sequential recommendation framework comprising: (1) an adaptive sparse attention mechanism that suppresses noisy interactions while preserving embedding diversity; (2) a frequency-aware encoder that decomposes interaction sequences into low-frequency components for long-term preference modeling and high-frequency components for short-term intent dynamics; and (3) a simplified focal loss that removes the class-balancing term while preserving the focusing factor, emphasizing hard-to-predict samples rather than class priors. Experiments on seven benchmark datasets demonstrate that SAFA consistently achieve state-of-the-art performance with average improvements of up to 3.77%, 4.10% and 4.25% in terms of HR@5, HR@10 and HR@20, respectively, and 4.30%, 4.78% and 4.58% in terms of NDCG@5, NDCG@10 and NDCG@20, respectively, over the best competing model. Ablation studies verify the importance of each component, with notable performance degradation upon removing the sparse attention or frequency-aware encoder. Overall, SAFA enhances sequential recommendation by improving robustness and discriminative learning under noisy and sparse conditions.

Anchor-based multi-view clustering has gained increasing attention for its efficiency in approximating similarity structures and scaling to large datasets. To reduce the burden of manual hyper-parameter tuning, recent studies have introduced parameter-free extensions. However, existing methods still face critical challenges: anchors are typically fixed after initialization, limiting adaptability to heterogeneous data; enforcing a shared anchor set across views suppresses view-specific diversity; and heuristic or self-weighted fusion strategies often lack explicit cross-view alignment, resulting in structural inconsistencies. To address these issues, we propose a Parameter-Free Multi-view Clustering framework with Adaptive Anchors for Large-scale Data (FPMCAA). Unlike existing approaches that decouple anchor construction and graph fusion, FPMCAA integrates adaptive anchor learning, anchor graph construction, and explicit cross-view alignment within a unified optimization model. Anchors are iteratively refined to capture complex distributions, while view-specific graphs are aligned toward a consensus structure without sacrificing inherent diversity. The framework avoids manual hyperparameter tuning and achieves linear computational complexity through efficient alternating optimization. Extensive experiments on benchmark datasets demonstrate that FPMCAA consistently outperforms state-of-the-art methods in clustering performance, robustness, and scalability. The source code of FPMCAA is available athttps://github.com/Xuchen2020/FPMCAA.

Active learning can effectively reduce the cost of labeling while enhancing model classification performance. However, prior studies have indicated that imbalanced class distributions adversely impact active learning, leading to diminished model effectiveness. Existing approaches to unbalanced active learning often neglect the multi-class imbalance problem and suffer from low performance and high time consumption. To address these issues, this paper introduces a hybrid active learning with online weighted broad learning system (HAL-OWBLS). Its main advantages include: (1) We optimize the initial labeled instance selection through an approximate query strategy to avoid the cold-start problem and introduce a sample selection strategy based on double uncertainty to enhance the rationality of active learning iterations. (2) A weighted broad learning system (WBLS) is chosen as the classifier, and an improved weighting strategy is adopted for multi-class imbalanced data. (3) We theoretically derive an efficient online updating model for WBLS, which reduces the time cost of active learning iterations by using only newly labeled samples for fast updating. The proposed HAL-OWBLS algorithm has better performance and robustness compared with existing related algorithms on various multi-class imbalanced data sets.

The challenges associated with large-scale user-item interaction graphs have attracted increasing attention in graph-based recommendation systems, primarily due to computational inefficiencies and inadequate information propagation. Existing methods provide partial solutions but suffer from notable limitations: model-centric approaches, such as sampling and aggregation, often struggle with generalization, while data-centric techniques, including graph sparsification and coarsening, lead to information loss and ineffective handling of bipartite graph structures. Recent advances in graph condensation offer a promising direction by reducing graph size while preserving essential information, presenting a novel approach to mitigating these challenges. Inspired by the principles of democracy, we proposeDemoRec, a framework that leverages graph condensation to generate user and item representatives for recommendation tasks. By constructing a compact interaction graph and clustering nodes with shared characteristics from the original graph, DemoRec significantly reduces graph size and computational complexity. Furthermore, it mitigates the over-reliance on high-order information, a critical challenge in large-scale bipartite graphs. Extensive experiments conducted on four public datasets demonstrate the effectiveness of DemoRec, showcasing substantial improvements in recommendation performance, computational efficiency, and robustness compared to SOTA methods.

The processing of continuous data streams in non-stationary environments has gained increasing attention. However, supervised online learning is often limited by label availability. Furthermore, it is crucial to develop a stable and high-performance online method in non-stationary environments. To tackle these issues, we propose a dynamic chunk-based active learning framework (DCAL). This framework includes a dynamic dual-stage query strategy and an enhanced active learning model. Specifically, the proposed query strategy, referred to as DyDQS, evaluates sample value comprehensively by considering local density, uncertainty, and dynamic imbalance ratio. This approach selects samples that are both representative and uncertain, while also enhancing the likelihood of selecting minority class samples. Additionally, we introduce an enhanced active learning model, named eBLS-W, which is based on the broad learning system (BLS). We redesign the update rule of BLS and equip it with a kernel mapping to improve its robustness and performance, enabling it to better handle non-stationary environments. The effectiveness of the DyDQS, eBLS-W, and DCAL was validated through experiments on synthetic datasets with drift and real-world datasets. The results demonstrate that our approach outperforms other advanced methods in terms of robustness and accuracy.

Active learning can significantly reduce the cost of labeling instances while improving model performance. However, similar to other traditional algorithms, active learning encounters the problem of class imbalance and delivers sub-optimal performance. Additionally, existing approaches suffer from poor performance and are time-consuming. To address these issues, we propose an Actively Incrementally Weighted Broad Learning System (AI-WBLS). Firstly, we introduce an active learning framework based on the weighted broad learning system, which employs a double uncertainty sample selection strategy to enhance the value and reasonableness of sample selection in each iteration of active learning. To further improve the model's adaptability during the iterative learning process, an adaptive weighting strategy is designed to adaptively modify the penalty weights according to the changes in the sample labels. Finally, an efficient incremental paradigm is developed to update the model with newly labelled samples instead of re-training, resulting in improved performance and efficiency. Extensive comparative experiments confirm that our approach outperforms other imbalanced active learning methods.

Feature mining is a challenging work in the field of multivariate time series (MTS) data mining. Traditional methods suffer from three major issues. 1) Learned shapelets may seriously diverge from original subsequences since learning methods do not restrain the learned ones similar to raw sequences, which reduces interpretability. 2) Existing rule mining methods just generate association rules based on feature combination of different variables without considering temporal relations among features, which could not adequately express the essential characteristics of MTS data. 3) Most deep learning methods only mine global and high-level features of MTS data, which affects interpretability. To address these issues, we propose a temporal association rule mining method based on Generative Adversarial Network (GAN) called TAR-GAN. First, a shapelet mining method based on GAN (SGAN) is advanced to discover dataset-level and sample-level shapelets of all variables in MTS data. Second, a Temporal Graph based Rule Mining method (TGRM) is introduced to discover temporal association rules based on the temporal relationships among shapelets of different variables. Meanwhile, a Fast Convolution-based Similarity Measure methods(FCSM) is introduced to measure the similarity between MTS samples and temporal association rules. Furthermore, an adversarial training strategy is introduced to ensure the effectiveness and stability of generated temporal association rules, which could reflect the essential characteristics of MTS data. Extensive experiments on 12 datasets show the effectiveness and efficiency of our method.

Recently, rule-based classification on multivariate time series (MTS) data has gained lots of attention, which could improve the interpretability of classification. However, state-of-the-art approaches suffer from three major issues. 1) few existing studies consider temporal relations among features in a rule, which could not adequately express the essential characteristics of MTS data. 2) due to the concept drift and time warping of MTS data, traditional methods could not mine essential characteristics of MTS data. 3) existing online learning algorithms could not effectively update shapelet-based temporal association rules of MTS data due to its temporal relationships among features of different variables. To handle these issues, we propose an online learning method for temporal association rule on dynamically collected MTS data (OTARL). First, a new type of rule named temporal association rule is defined and mined to represent temporal relationships among features in a rule. Second, an online learning mechanism with a probability correlation-based evaluation criterion is proposed to realize the online learning of temporal association rules on dynamically collected MTS data. Finally, an ensemble classification approach based on maximum-likelihood estimation is advanced to further enhance the classification performance. We conduct experiments on ten real-world datasets to verify the effectiveness and efficiency of our approach.

Feature selection is a highly regarded research area in the field of data mining, as it significantly enhances the efficiency and performance of high-dimensional data analysis by eliminating redundant and irrelevant features. Despite the ease of data acquisition, labeling data remains a laborious and expensive task. To leverage the abundance of unlabeled data, researchers have proposed various feature selection methods that operate with limited labels, including semi-supervised feature selection and unsupervised feature selection. However, a comprehensive review encompassing a thorough overview of feature selection algorithms with limited labels is lacking. To bridge this gap, this paper conducts a comprehensive exploration of feature selection methods specifically tailored to limited-label scenarios. These methods are systematically classified into two primary categories: semi-supervised and unsupervised feature selection. Additionally, by introducing a novel taxonomy and discussing future challenges, this survey aims to provide researchers with a comprehensive and in-depth understanding of feature selection in limited-label scenarios. Moreover, it aims to offer valuable insights that can guide further research and development in this domain.

Incomplete multi-view clustering (IMVC) presents a significant challenge due to the need for effectively exploring complementary and consistent information within the context of missing views. One promising strategy to tackle this challenge is to recover missing views by inferring the missing samples. However, such approaches often fail to fully utilize discriminative structural information or adequately address consistency, as it requires such information to be known or learnable in advance, which contradicts the incomplete data setting. In this study, we propose a novel approach calledLatentStructure-Aware view recovery (LaSA) for the IMVC task. Our objective is to recover missing views through discriminative latent representations by leveraging structural information. Specifically, our method offers a unified closed-form formulation that simultaneously performs missing data inference and latent representation learning, using a learned intrinsic graph as structural information. This formulation, incorporating graph structure information, enhances the inference of missing data while facilitating discriminative feature learning. Even when intrinsic graph is initially unknown due to incomplete data, our formulation allows for effective view recovery and intrinsic graph learning through an iterative optimization process. To further enhance performance, we introduce an iterative consistency diffusion process, which effectively leverages the consistency and complementary information across multiple views. Extensive experiments demonstrate the effectiveness of the proposed method compared to state-of-the-art approaches.

Imbalanced data biases the classifier towards the majority class. Accompanied with high-dimensional characteristics, classification performance is further degraded. Existing researches for skewed data mainly involve resampling, cost-sensitive learning, and classifier ensemble. However, these approaches have some limitations: 1) resampling suffers from noisy and redundant features in high-dimensional skewed data; 2) cost-sensitive learning is hard to construct an optimal cost matrix for sample misclassification; 3) ensemble with random feature subspace easily leads to information loss; 4) ensemble with sample subspace on small-size data easily leads to insufficient description of sample space and suffers from negative impacts of high-dimensional data. This paper proposes an improved contraction-expansion subspace ensemble (ICESE) for high-dimensional imbalanced data classification. First, a contraction-expansion subspace optimization (CESO) is designed to perform subspace selection and transformation, which is beneficial for enhancing the discrimination and diversity of subspace. Then, to strengthen classification capabilities, a CESO-based multilayer optimization structure is developed to construct the improved subspace. Finally, to mitigate the effects of skewed data, ICESE performs a resampling scheme on the improved subspace for constructing a rebalanced subset to base classifier. Experimental results on 24 high-dimensional imbalanced data sets demonstrate that our ICESE outperforms different mainstream ensemble systems in terms of F-score and G-mean.

Imbalanced data poses a substantial challenge to conventional classification methods, which often disproportionately favor samples from the majority class. To mitigate this issue, various oversampling techniques have been deployed, but opportunities for optimizing data distributions remain underexplored. By exploiting the ability of metric learning to refine the sample distribution, we propose a novel approach, Imbalance Large Margin Nearest Neighbor (ILMNN). Initially, ILMNN is applied to establish a latent feature space, pulling intra-class samples closer and distancing inter-class samples, thereby amplifying the efficacy of oversampling techniques. Subsequently, we allocate varying weights to samples contingent upon their local distribution and relative class frequency, thereby equalizing contributions from minority and majority class samples. Lastly, we employ Kullback-Leibler (KL) divergence as a safeguard to maintain distributional similarity to the original dataset, mitigating severe intra-class imbalances. Comparative experiments on various class-imbalanced datasets verify that our ILMNN approach yields superior results.

Broad learning system (BLS) is a simple yet efficient learning algorithm that only needs to train a three-layer feedforward neural network. Although various BLS variants have been designed for supervised learning, none have been used for unsupervised learning. This paper proposes BLS-AE, a novel data clustering scheme that seamlessly combines BLS and auto-encoder. Then, graph regularization is introduced into BLS-AE to increase the capability of learning intrinsic structures in data and adaptation to various data simultaneously, which is termed BLSg-AE. Moreover, different concatenation styles of feature and enhancement nodes are investigated for reusing the learned features, followed by designing two special strategies (i.e., pruning optimization and incremental learning) to reduce the parameter scale significantly and improve performance, which is termed xBLSg-AE. To address the performance instability issue caused by random subspace in a single xBLSg-AE, the x-cascade broad learning system graph regularization multi-auto-encoder (xBLSg-MAE) algorithm is proposed. Extensive experiments are conducted on multiple real data sets to demonstrate that the proposed methods are more effective and robust than competing approaches.

Due to the advantages of fast training speed and competitive performance, Broad Learning System (BLS) has been widely used for classification tasks across various domains. However, the random weight generation mechanism in BLS makes the model unstable, and the performance of BLS may be limited when dealing with some complex datasets. On the other hand, the instability of BLS brings diversity to ensemble learning, and ensemble methods can also reduce the variance and bias of the single BLS. Therefore, we propose an ensemble learning algorithm based on BLS, which includes three modules. To improve the stability and generalization ability of BLS, we utilize BLS as the base classifier in an AdaBoost framework first. Taking advantage of the incremental learning mechanism of BLS, we then propose a selective ensemble method to raise the accuracy and diversity of the BLS ensemble method. In addition, based on the former selective Adaboost framework, we suggest a hierarchical ensemble algorithm, which combines sample and feature dimensions to further improve the fitting ability of the ensemble BLS. Extensive experiments have demonstrated that the proposed method performs better than the original BLS and other state-of-the-art models, proving the effectiveness and versatility of our proposed approaches.

Cluster ensemble improves the robustness and stability of clustering performances by utilizing multiple solutions. Although traditional cluster ensemble methods have achieved promising performances, they are not adaptive enough to cope with data sets that have multiple levels of complexities. Besides, these methods may contain noisy and redundancy members which have negative effects. To mitigate the above issues, in this paper, we propose a multi-objective filter refinement scheme (MOFRS). First, we perform various clustering methods on different representations of data to generate diverse solutions. Second, we propose a solution filter to select a proper method and reduce the number of initial partitions for a given data set. Third, four stability indices are designed to split instances into stable and unstable groups. Fourth, objective functions based on diversity and quality are utilized to quantify the goodness of base clustering solutions. Finally, we design an improvement oriented multi-objective evolutionary algorithm to optimize these objective functions. Extensive experimental results conducted on 27 real-world data sets show that MOFRS outperforms most cluster ensemble selection methods, and achieves statistically significant improvements, compared with full ensemble methods.

Ensemble clustering has an advantage in producing a more promising and robust clustering result by combining multiple partitions strategically. The quality of both base partitions and co-association matrix plays an essential role in improving the consensus partition. However, the current ensemble clustering methods have several limitations: 1) The noise in high-dimensional feature space is ignored; 2) The independent base partition generation process does not pay attention to ambiguous samples; 3) The co-association matrix and the weights of base partitions commonly lack of theoretical optimization. In order to address these issues, we propose an adaptive ensemble clustering framework with boosting BLS-based autoencoder (BoostAEC). In the generation step, a boosting BLS-based autoencoder (BoostBLSAE) is designed to generate base partitions sequentially, which learns compressed feature subspaces for ambiguous samples and adaptively evaluates the corresponding weights of reliability. In the integration step, we construct a fuzzy membership function to capture the inter-cluster correlation and explicitly propose a consensus objective function to optimize the unified co-association matrix by considering the weighted base partitions. Extensive experiments on various real-world datasets demonstrate the superior performance of BoostAEC to the state-of-the-art ensemble clustering methods.

High-dimensional small-size data seriously affects the performance of classifiers. By combining classifiers, ensemble learning obtains higher accuracy and more robust predictions. However, these classifier ensemble methods suffer from several limitations: 1) ensemble with sample space suffers from noise and redundant features; 2) constructing sample subspace on small-size data leads to an insufficient description of sample space; 3) ensemble with feature space leads to information loss, which will degrade performance of classifiers. To overcome the above limitations, a new classifier ensemble method based on subspace enhancement (CESE) is proposed for high-dimensional data classification. First, a superior subspace enhancement scheme (SSE) is designed to effectively implement feature selection and transformation for high-dimensional data, followed by generating multiple superior feature subspaces with diversity and discrimination, which enhances the representative ability of features. Second, we develop a mixed space enhancement process (MSE) based on multiscale rotation reconstruction and various subspace enhanced features of SSE. Furthermore, to improve the capacity of our method, we design various feature combination strategies for enhanced features from both SSE and MSE. Comparative results on 33 high-dimensional data sets indicate that our approach CESE outperforms different mainstream integrated system

With effective performance and fast training speed, broad learning system (BLS) has been widely developed in recent years, which provides a new way for network training. However, the randomly generated feature nodes and enhancement nodes in the BLS network may have redundant and inefficient features, which will affect the subsequent classification performance. In response to the above issues, we propose a series of self-encoding networks based on BLS from the perspective of unsupervised feature extraction. These include the single hidden layer autoencoder built on the basis of BLS(BLS-AE), the stacked BLS-based autoencoder (ST-BLS), the sparse BLS-based autoencoder (SP-BLS), and the stacked sparse BLS-based autoencoder(SS-BLS). The proposed BLS-based self-encoding networks retain the advantage of efficient BLS model training, and overcome the time-consuming defect of iterative parameter optimization in traditional self-encoding networks. In addition, the higher-level abstract features of the input data can be learned through the progressive encoding and decoding process. Combining$L_1$regularization to train the parameters can further enhance the robustness of the extracted features. Extensive comparative experiments on real-world data sets demonstrate the superiority of the proposed methods in terms of both effectiveness and efficiency.

Broad learning system (BLS) is a novel and efficient model, which facilitates representation learning and classification by concatenating feature nodes and enhancement nodes. In spite of the efficient properties, BLS is still suboptimal when facing with imbalance problem. Besides, outliers and noises in imbalanced data remain a challenge for BLS. To address the above issues, in this paper we first propose a weighted BLS, which assigns a weight to each training sample, and adopt a general weighting scheme, which augments the weight of samples from the minority class. To further explore the prior distribution of original data, we design a density based weight generation mechanism to guide the specific weight matrix generation and propose the adaptive weighted broad learning system (AWBLS). This mechanism considers the inter-class and intra-class distance simultaneously in the density calculation. Finally, we propose the incremental weighted ensemble broad learning system (IWEB) by utilizing a progressive mechanism to further improve the stability and robustness of AWBLS. Extensive comparative experiments on 38 real-world data sets verfy that IWEB outperforms most of the imbalance ensemble classification methods.

In this paper, we propose two GAN-based enhanced deep subspace clustering approaches: deep subspace clustering via dual adversarial generative networks (DSC-DAG) and self-supervised deep subspace clustering with adversarial generative networks ($S^2 DSC-AG$). In DSC-DAG, the distributions of both the inputs and corresponding latent representations are learning via adversarial training simultaneously. Besides, there are two kinds of synthetical representations to facilitate the fine-tuning of the encoder module: the combinations of latent representations with certain random combination coefficients and the representations of real-like inputs derived from noise variables. In$S^DSC-AG$, a self-supervised information learning module substitutes for adversarial learning in the latent space, since both of them play the same role in learning discriminative latent representations. We analyze the connections between these methods and demonstrate their equivalences. We conduct extensive experiments on multiple real-world data sets against state-of-the-art subspace clustering methods in terms of accuracy, normalized mutual information and purity. Experimental results demonstrate the effectiveness and superiority of our proposed methods.

Classifying high-dimensional small-size data is challenging in the field of pattern recognition. Traditional ensemble learning methods have several limitations: 1) sample-space based methods are easily affected by noise and redundant features; 2) feature-space based methods cannot excavate the essential characteristics of features; 3) feature subspaces cause information loss, which leads to a decline in accuracy; 4) most selective ensemble methods only consider the diversity and performance of sub-classifiers and ignore the impact on integration systems. To address the above limitations, we propose an adaptive classifier ensemble learning method (AdaSPEL) based on spatial perception for high-dimensional data. First, we design a local-space perception method for feature transformation, which encourages both high performance and diversity of the ensemble members. Second, we design a cross-space perception method based on the distribution of samples to obtain the cross-space enhanced features to provide a macro analysis for the characteristics of data. Furthermore, an adaptive selective ensemble method based on local and global evaluation mechanisms is proposed, which considers the impact of sub-classifiers on integrated systems. Experimental results on 33 high-dimensional data sets verify that our method outperforms mainstream ensemble learning methods based on feature space and sample space, and neural network-based algorithms.

The goal of multiple clusterings is to discover multiple independent ways of organizing a dataset into clusters. Current approaches to this problem just focus on one-way clustering. In many real-world applications, though, it's meaningful and desirable to explore alternative two-way clustering (or co-clusterings), where both samples and features are clustered. To tackle this challenge and unexplored problem, in this paper we introduce an approach, called Multiple Co-Clusterings (MultiCC), to discover non-redundant alternative co-clusterings. MultiCC makes use of matrix tri-factorization to optimize the sample-wise and feature-wise co-clustering indicator matrices, and introduces two non-redundancy terms to enforce diversity among co-clusterings. We then combine the objective of matrix tri-factorization and two non-redundancy terms into a unified objective function and introduce an iterative solution to optimize the function. Experimental results show that MultiCC outperforms existing multiple clustering methods, and it can find interesting co-clusters which cannot be discovered by current solutions.

Traditional cluster ensemble approaches have several limitations. (1) Few make use of prior knowledge provided by experts. (2) It is difficult to achieve good performance in high-dimensional datasets. (3) All of the weight values of the ensemble members are equal, which ignores different contributions from different ensemble members. (4) Not all pairwise constraints contribute to the final result. In the face of this situation, we propose double weighting semi-supervised ensemble clustering based on selected constraint projection(DCECP) which applies constraint weighting and ensemble member weighting to address these limitations. Specifically, DCECP first adopts the random subspace technique in combination with the constraint projection procedure to handle high-dimensional datasets. Second, it treats prior knowledge of experts as pairwise constraints, and assigns different subsets of pairwise constraints to different ensemble members. An adaptive ensemble member weighting process is designed to associate different weight values with different ensemble members. Third, the weighted normalized cut algorithm is adopted to summarize clustering solutions and generate the final result. Finally, nonparametric statistical tests are used to compare multiple algorithms on real-world datasets. Our experiments on 15 high-dimensional datasets show that DCECP performs better than most clustering algorithms.

Conventional semi-supervised clustering approaches have several shortcomings, such as (1) not fully utilizing all useful must-link and cannot-link constraints, (2) not considering how to deal with high dimensional data with noise, and (3) not fully addressing the need to use an adaptive process to further improve the performance of the algorithm. In this paper, we first propose the transitive closure based constraint propagation approach, which makes use of the transitive closure operator and the affinity propagation to address the first limitation. Then, the random subspace based semi-supervised clustering ensemble framework with a set of proposed confidence factors is designed to address the second limitation and provide more stable, robust, and accurate results. Next, the adaptive semi-supervised clustering ensemble framework is proposed to address the third limitation, which adopts a newly designed adaptive process to search for the optimal subspace set. Finally, we adopt a set of nonparametric tests to compare different semi-supervised clustering ensemble approaches over multiple datasets. The experimental results on 20 real high dimensional cancer datasets with noisy genes and 10 datasets from UCI datasets and KEEL datasets show that (1) The proposed approaches work well on most of the real-world datasets. (2) It outperforms other state-of-the-art approaches on 12 out of 20 cancer datasets, and 8 out of 10 UCI machine learning datasets.

Cluster ensemble, as one of the important research directions in the ensemble learning area, is gaining more and more attention, due to its powerful capability to integrate multiple clustering solutions and provide a more accurate, stable and robust result. Cluster ensemble has a lot of useful applications in a large number of areas. Although most of traditional cluster ensemble approaches obtain good results, few of them consider how to achieve good performance for noisy datasets. Some noisy datasets have a number of noisy attributes which may degrade the performance of conventional cluster ensemble approaches. Some noisy datasets which contain noisy samples will affect the final results. Other noisy datasets may be sensitive to distance functions.

Recently, cluster ensemble approaches have gained more and more attention [1]–[2], due to useful applications in the areas of pattern recognition, data mining, bioinformatics, and so on. When compared with traditional single clustering algorithms, cluster ensemble approaches are able to integrate multiple clustering solutions obtained from different data sources into a unified solution, and provide a more robust, stable and accurate final result.

Traditional cluster ensemble approaches have three limitations: (1) They do not make use of prior knowledge of the datasets given by experts. (2) Most of the conventional cluster ensemble methods cannot obtain satisfactory results when handling high dimensional data. (3) All the ensemble members are considered, even the ones without positive contributions. In order to address the limitations of conventional cluster ensemble approaches, we first propose an incremental semi-supervised clustering ensemble framework (ISSCE) which makes use of the advantage of the random subspace technique, the constraint propagation approach, the proposed incremental ensemble member selection process, and the normalized cut algorithm to perform high dimensional data clustering. The random subspace technique is effective for handling high dimensional data, while the constraint propagation approach is useful for incorporating prior knowledge. The incremental ensemble member selection process is newly designed to judiciously remove redundant ensemble members based on a newly proposed local cost function and a global cost function, and the normalized cut algorithm is adopted to serve as the consensus function for providing more stable, robust, and accurate results. Then, a measure is proposed to quantify the similarity between two sets of attributes, and is used for computing the local cost function in ISSCE. Next, we analyze the time complexity of ISSCE theoretically. Finally, a set of nonparametric tests are adopted to compare multiple semisupervised clustering ensemble approaches over different datasets. The experiments on 18 real-world datasets, which include six UCI datasets and 12 cancer gene expression profiles, confirm that ISSCE works well on datasets with very high dimensionality, and outperforms the state-of-the-art semi-supervised clustering ensemble approaches.

Cluster ensemble is one of the main branches in the ensemble learning area which is an important research focus in recent years. The objective of cluster ensemble is to combine multiple clustering solutions in a suitable way to improve the quality of the clustering result. In this paper, we design a new noise immune cluster ensemble framework named as AP2CE to tackle the challenges raised by noisy datasets. AP2CE not only takes advantage of the affinity propagation algorithm (AP) and the normalized cut algorithm (Ncut), but also possesses the characteristics of cluster ensemble. Compared with traditional cluster ensemble approaches, AP2CE is characterized by several properties. (1) It adopts multiple distance functions instead of a single Euclidean distance function to avoid the noise related to the distance function. (2) AP2CE applies AP to prune noisy attributes and generate a set of new datasets in the subspaces consists of representative attributes obtained by AP. (3) It avoids the explicit specification of the number of clusters. (4) AP2CE adopts the normalized cut algorithm as the consensus function to partition the consensus matrix and obtain the final result. In order to improve the performance of AP2CE, the adaptive AP2CE is designed, which makes use of an adaptive process to optimize a newly designed objective function. The experiments on both synthetic and real datasets show that (1) AP2CE works well on most of the datasets, in particular the noisy datasets; (2) AP2CE is a better choice for most of the datasets when compared with other cluster ensemble approaches; (3) AP2CE has the capability to provide more accurate, stable and robust results.

Advances in biotechnology have made available multitudes of heterogeneous proteomic and genomic data. Integrating these heterogeneous data sources, to automatically infer the function of proteins, is a fundamental challenge in computational biology. Several approaches represent each data source with a kernel (similarity) function. The resulting kernels are then integrated to determine a composite kernel, which is used for developing a function prediction model. Proteins are also found to have multiple roles and functions. As such, several approaches cast the protein function prediction problem within a multi-label learning framework. In our work we develop an approach that takes advantage of several unlabeled proteins, along with multiple data sources and multiple functions of proteins. We develop a graph-based transductive multi-label classifier (TMC) that is evaluated on a composite kernel, and also propose a method for data integration using the ensemble framework, called transductive multi-label ensemble classifier (TMEC). The TMEC approach trains a graph-based multi-label classifier for each individual kernel, and then combines the predictions of the individual models. Our contribution is the use of a bi-relational directed graph that captures relationships between pairs of proteins, between pairs of functions, and between proteins and functions. We evaluate the ability of TMC and TMEC to predict the functions of proteins by using two yeast datasets. We show that our approach performs better than recently proposed protein function prediction methods on composite and multiple kernels.