Multi-view fuzzy clustering has attracted increasing attention owing to its strong clustering performance and inherent ability to effectively model uncertainty. However, most existing methods rely on the unrealistic assumption that all views are fully observed, which rarely holds in practice. Although several methods have been proposed to address incomplete multi-view data, they typically focus only on extracting shared information across views while overlooking view-specific information. Moreover, they often tend to neglect missing views imputation, a key mechanism for handling incomplete data. Furthermore, by separating representation learning from clustering, many existing frameworks yield representations that are not necessarily optimal for clustering, thus compromising robustness. To address these limitations and based on fuzzy clustering, a novel enhanced one step incomplete multi-view clustering method (IMVFCM_DRL) is proposed in this paper. First, to effectively handle incomplete multi-view data, we construct a new representation learning framework that explicitly integrates missing-view imputation. Second, to fully exploit the multi-view information, a dual information learning strategy is introduced to jointly capture both common and view-specific information. Finally, a unified one-step fuzzy clustering framework with weighted structure preservation is developed, ensuring that representation learning and fuzzy clustering are jointly optimized. The experiments conducted on various multi-view datasets demonstrate the effectiveness of IMVFCM_DRL. The codes are available at https://github.com/BBKing49/IMVFCM_DRL.

Large multimodal models (LMMs) have advanced significantly by integrating visual encoders with extensive language models, enabling robust reasoning capabilities. However, compressing LMMs for deployment on edge devices remains a critical challenge. In this work, we propose an adaptive search algorithm that optimizes sparsity and KV cache compression to enhance LMM efficiency. Utilizing the Tree-structured Parzen Estimator, our method dynamically adjusts pruning ratios and KV cache quantization bandwidth across different LMM layers, using model performance as the optimization objective. This approach uniquely combines pruning with key-value cache quantization and incorporates a fast pruning technique that eliminates the need for additional fine-tuning or weight adjustments, achieving efficient compression without compromising accuracy. Comprehensive evaluations on benchmark datasets, including LLaVA-1.5 7B and 13B, demonstrate our method’s superiority over state-of-the-art techniques such as SparseGPT and Wanda across various compression levels. Notably, our framework’s automatic allocation of KV cache compression resources sets a new standard in LMM optimization, delivering memory efficiency without sacrificing much performance. Code is available at https://github.com/tezhang65/optspa.git

MOTIVATION: Spatial clustering is a key analytical technique for exploring spatial transcriptomics data. Recent graph neural network-based methods have shown promise in spatial clustering but face notable challenges. One significant issue is that analyzing the functions and complex mechanisms of organisms from a single scale is difficult and most methods focus exclusively on the single-scale representation of transcriptomic data, potentially limiting the discriminative power of extracted features for spatial domain clustering. Furthermore, classical clustering algorithms are often applied directly to latent representation, making it a worthwhile endeavor to explore a tailored clustering method to further improve the accuracy of spatial domain annotation. RESULTS: To address these limitations, we propose m2ST, a novel dual multi-scale graph clustering method. m2ST first uses a multi-scale masked graph autoencoder to extract representations across different scales from spatial transcriptomic data. To effectively compress and distill meaningful knowledge embedded in the data, m2ST introduces a random masking mechanism for node features and uses a scaled cosine error as the loss function. Additionally, we introduce a tailored multi-scale clustering framework that integrates scale-common and scale-specific information exploration into the clustering process, achieving more robust annotation performance. Shannon entropy is finally utilized to dynamically adjust the importance of different scales. Extensive experiments on multiple spatial transcriptomic datasets demonstrate the superior performance of m2ST compared to existing methods. AVAILABILITY AND IMPLEMENTATION: https://github.com/BBKing49/m2ST.

The rapid advancement of medical imaging technologies has led to an exponential increase in medical image data, making efficient retrieval from large-scale datasets critical for improving diagnostic accuracy and speed. However, two key challenges hinder this process: first, the presence of uncertain and subtle lesions in medical images that are often difficult to discern, and second, class imbalance across different case types within medical image databases. These inherent challenges significantly degrade the performance of existing hashing algorithms. In recent years, methods based on the Takagi–Sugeno–Kang fuzzy system (TSK-FS) have shown promising performance in medical image modeling. Inspired by these advances, this article proposes a novel fuzzy hashing network (FHN) based on TSK-FS to enhance retrieval performance by effectively handling both uncertainty and data imbalance in medical imaging. The FHN first introduces a novel fuzzification mechanism that incorporates the concept of a self-attention mechanism to effectively capture the complex underlying features in medical images, thereby enhancing the data discriminability in fuzzy spaces. Meanwhile, a new consequent parameter learning mechanism is developed for defuzzification by introducing the Transformer network, which aims to improve the inference efficiency and generalization capability of the FHN. Based on these two mechanisms, FHN's capability of analyzing and handling uncertain data is significantly enhanced. Furthermore, a novel hash center loss is designed to capture global relationships while emphasizing local structural information, thereby improving the handling of imbalanced data and significantly enhancing retrieval performance.

Multiview anchor graph clustering has been a prominent research area in recent years, leading to the development of several effective and efficient methods. However, three challenges are faced by current multiview anchor graph clustering methods. First, real-world data often exhibit uncertainty and poor discriminability, leading to suboptimal anchor graphs when directly extracted from the original data. Second, most existing methods assume the presence of common information between views and primarily explore it for clustering, thus neglecting view-specific information. Third, further exploration and exploitation of the learned anchor graph to enhance clustering performance remains an open research question. To address these issues, a novel dual anchor graph fuzzy clustering method is proposed in this article. First, a novel matrix factorization-based dual anchor graph learning method is proposed to address the first two issues by extracting highly discriminative hidden representations for each view and subsequently deriving both common and specific anchor graphs from these hidden representations. Then, to address the third issue, a novel anchor graph fuzzy clustering method is developed with cooperative learning to exploit and utilize the common and specific anchor graphs fully. Meanwhile, a fuzzy membership structure preservation mechanism with dual anchor graphs is constructed to enhance clustering performance. Finally, negative Shannon entropy is further introduced to adaptively adjust the view weighing. Extensive experiments on several datasets demonstrate the effectiveness of the proposed method.

Graph data modeling is nontrivial due to the challenges to ensure model interpretability and handle data uncertainty. While methods derived from deep learning models, such as graph neural networks (GNNs), are able to handle graph data, the interpretability is limited. Graph fuzzy systems (GFSs) based on the fuzzy rules and fuzzy inference have been proposed to improve interpretability, but the existing methods are developed for whole graph prediction only and cannot deal with node prediction, which is a more common task in graph data modeling. To tackle the challenges, a novel GFS for node prediction (GFS-node) is investigated in this study. For this purpose, the concepts, framework, and algorithms of GFS-node are systematically developed. First, several related concepts are defined, including the node fuzzy rule base, node fuzzy set, and node consequent processing module (NCPM). A general framework for GFS-node is then presented, where the construction of antecedents and the consequents of fuzzy rules are analyzed. Furthermore, a concrete implementation method of GFS-node is designed. In particular, the kernelKvirtual central nodes clustering (KVCN) algorithm is proposed to develop the algorithm for antecedent generation, and the linear message passing network (LMPN) is adopted to develop the algorithm for consequent generation and learning. Experiments are carried out on multiple benchmark datasets, and the results show that GFS-node combines the advantages of both traditional fuzzy systems and classical GNNs for node prediction.

The rules of a rule-based system provide explanations for its behavior by revealing the relationships between the variables captured. However, ideally, we have AI systems which go beyond explainable AI (XAI), that is, systems which not only explain their behavior, but also communicate their “insights” with respect to the real world. This requires rules to capture causal relationships between variables. In this article, we argue that those systems where the rules reflect causal relationships between variables represent an important class of fuzzy rule-based systems with unique benefits. Specifically, such systems benefit from improved performance and robustness; facilitate global explainability and thus cater to a core ambition for AI: the ability to communicate important relationships among a system's real-world variables to the human users of AI. We establish two causal-rule focused approaches to design fuzzy systems, and show the distinctions in their respective application scenarios for the explanations of the rules obtained by these two methods. The results show that rules which reflect causal relationships are more suitable for XAI than rules which “only” reflect correlations, while also confirming that they offer robustness to over-fitting, in turn supporting strong performance.

Unsupervised multi-view representation learning has been extensively studied for mining multi-view data. However, some critical challenges remain. On the one hand, the existing methods cannot explore multi-view data comprehensively since they usually learn a common representation between views, given that multi-view data contains both the common information between views and the specific information within each view. On the other hand, to mine the nonlinear relationship between data, kernel or neural network methods are commonly used for multi-view representation learning. However, these methods are lacking in interpretability. To this end, this paper proposes a new multi-view fuzzy representation learning method based on the interpretable Takagi-Sugeno-Kang (TSK) fuzzy system (MVRL_FS). The method realizes multi-view representation learning from two aspects. First, multi-view data are transformed into a high-dimensional fuzzy feature space, while the common information between views and specific information of each view are explored simultaneously. Second, a new regularization method based on L2,1-norm regression is proposed to mine the consistency information between views, while the geometric structure of the data is preserved through the Laplacian graph. Finally, extensive experiments on many benchmark multi-view datasets are conducted to validate the superiority of the proposed method.

Multiview data are widespread in real-world applications, and multiview clustering is a commonly used technique to effectively mine the data. Most of the existing algorithms perform multiview clustering by mining the commonly hidden space between views. Although this strategy is effective, there are two challenges that still need to be addressed to further improve the performance. First, how to design an efficient hidden space learning method so that the learned hidden spaces contain both shared and specific information of multiview data. Second, how to design an efficient mechanism to make the learned hidden space more suitable for the clustering task. In this study, a novel one-step multiview fuzzy clustering (OMFC-CS) method is proposed to address the two challenges by collaborative learning between the common and specific space information. To tackle the first challenge, we propose a mechanism to extract the common and specific information simultaneously based on matrix factorization. For the second challenge, we design a one-step learning framework to integrate the learning of common and specific spaces and the learning of fuzzy partitions. The integration is achieved in the framework by performing the two learning processes alternately and thereby yielding mutual benefit. Furthermore, the Shannon entropy strategy is introduced to obtain the optimal views weight assignment during clustering. The experimental results based on benchmark multiview datasets demonstrate that the proposed OMFC-CS outperforms many existing methods.

EXplainable Artificial Intelligence (XAI) is of in-creasing importance as researchers and practitioners seek better transparency and verifiability of AI systems. Mamdani fuzzy systems can provide explanations based on their linguistic rules, and thus a potential pathway to XAI. A factual rule based explanation generally refers to the given set of rules executed, or fired, for a given input. However, research has shown that human explanations are often counterfactual (CF), i.e. rather than explaining why a given output was reached, they show why other potential outputs were not. Although several machine learning-based CF explanation generation methods have been proposed in recent years, quasi none of them focus on fuzzy systems. Also, where they do, they focus on correlation, which limits the interpretive value of any CF explanations obtained as humans expect a causal relationship in rules, i.e. we are cause-effect thinkers. In this paper, we propose a new rule generation framework for Mamdani fuzzy classification systems, which we refer to as CF-MABLAR, building on the MARkov BLAnket Rules (MABLAR) framework. CF-MABLAR approximates the causal links between inputs and output(s) of fuzzy systems and generates CF rules by leveraging them. Uniquely, the CF rules obtained not only provide a basic CF explanation, but can also articulate how the given inputs would need to be changed to generate a different output, crucial for lay-user insight, verification and sensitivity-evaluation of XAI systems, for example in decision support around credit risk, cyber security and medical assistance.

Multiview fuzzy systems aim to deal with fuzzy modeling in multiview scenarios effectively and to obtain the interpretable model through multiview learning. However, current studies of multiview fuzzy systems still face several challenges, one of which is how to achieve efficient collaboration between multiple views when there are few labeled data. To address this challenge, this article explores a novel transductive multiview fuzzy modeling method. The dependency on labeled data is reduced by integrating transductive learning into the fuzzy model to simultaneously learn both the model and the labels using a novel learning criterion. Matrix factorization is incorporated to further improve the performance of the fuzzy model. In addition, collaborative learning between multiple views is used to enhance the robustness of the model. The experimental results indicate that the proposed method is highly competitive with other multiview learning methods.

Multiview clustering is an important topic in multiview learning, where the cooperation of different views is used to improve clustering performance. Although multiview clustering has made considerable progress, most existing methods only utilize the information of the original visible views, or only consider some hidden space information shared by different views. Two of the challenges are: 1) insufficient exploitation of cooperative learning between visible and hidden information despite some preliminary attempts, and 2) inadequate consideration of topological information for improving multiview clustering. To meet the challenges, we propose the cooperation enhanced multiview fuzzy clustering method (CE-MVFC) in this article. First, we characterize multiview data with two hidden views, which are obtained by adaptive multiview non-negative matrix factorization (NMF) and fuzzy partition information of each sample in different clusters. Then, we integrated the hidden views and the original visible views to realize visible-hidden cooperation learning. Furthermore, we establish a similarity matrix for each visible view and the hidden view obtained through NMF to describe the data topology in these views. Based on the spatial topological relationship of the samples and the representation of hidden view obtained by fuzzy partition, the network least absolute shrinkage and selection operator is constructed to constrain multiview learning. Finally, we develop the multiview clustering method by exploiting the visible-hidden information cooperation and the spatial topological information constraints. Experiments on benchmark multiview datasets are conducted to demonstrate the highly competitive performance of the proposed CE-MVFC against the state-of-the-art methods.

Advancement of technology has made available data of different modalities that can be integrated effectively through multiple view learning for modeling real-world problems. Although multiple view learning has achieved great success in many applications, it still faces several challenges. One of them is how to reduce the negative impact of the missing views in incomplete multiple view datasets by fully exploiting the information available. Another challenge is how to enhance the interpretability of the multiple view model for scenarios with high transparency requirement. To address these challenges, this article proposes a novel modeling method for incomplete multiple view fuzzy system. Based on fuzzy interpretable rules, the method integrates missing view imputation and hidden view learning as one single process to yield a model of high interpretability, where cooperative learning is used to mine the complementary information between the visible views and the hidden view. The proposed method has four advantages when compared with existing approaches: 1) the method is more interpretable, attributed to the fuzzy interpretable rules that it is based on, 2) missing view imputation is integrated into the modeling to make it more efficient than the existing two-step strategy, 3) the method not only imputes missing views, but also mines the hidden view shared by the multiple visible views, and 4) cooperative learning is used to mine the complementary information, which significantly reduces the negative impact of missing views. Experiments on real datasets demonstrate the advantages of the proposed method.

Multi-view data are becoming common in real-world applications and many multi-view clustering algorithms have thus been proposed. The existing algorithms usually focus on the cooperation of different visible views in the original space but neglect the influence of the hidden information among these visible views, or they only consider the hidden information among the views. The algorithms are therefore not efficient since the available information is not fully exploited, particularly the otherness information in different views and the consistency information among them. In practice, the otherness and consistency information in multi-view data are both very useful for effective clustering analyses. In this study, a Multi-View clustering algorithm with the Cooperation of Visible and Hidden views, i.e., MV-Co-VH, is proposed. The MV-Co-VH algorithm first projects the multiple views from different visible spaces to the common hidden space by using non-negative matrix factorization to obtain the common hidden view data. Collaborative learning is then implemented in the clustering procedure based on the visible views and the shared hidden view. The experimental results of extensive experiments on UCI multi-view datasets and real-world image multi-view datasets show that the clustering performance of the proposed algorithm is competitive with or even better than that of the existing algorithms.

An important property of fuzzy systems is the interpretability provided by their rules. However, if a fuzzy system is derived through machine learning algorithms, its interpretability is often greatly diminished as membership functions and rules are adjusted to minimize error in respect to a data set. To address part of this challenge, we propose a novel two-step fuzzy rule generation framework leveraging the concept of the Markov blanket, i.e., the set of variables which are causally related to a target variable – such as a system’s output. By estimating the Markov blanket for a given application, we restrict rule learning to (only) the variables which are causally linked to the system output, thus minimising the generation of spurious rules (based on spurious correlations of variables). This decreases the complexity of fuzzy systems and maintains a causal link between rules’ antecedents and consequent(s) – as expected by humans when viewing rules. The proposed framework can improve the interpretability of fuzzy rule based systems which are tuned using machine learning techniques, while also providing performance advantages as are commonly associated with feature selection techniques. Experiment results show that even the initial implementation of the framework proposed here can generate more concise and interpretable rule bases without compromising performance.

As an important branch in the field of soft computing, TSK fuzzy systems have been diversely applied to supervised learning in recent years. However, real-world data may contain label noise, which has a negative impact on supervised learning. Label noise samples change the distribution of samples in each class, mislead learning algorithms and make classification problems more complicated. There are various sources of label noise, such as wrong assignment of labels during the data collection, contamination during the data storage, and so on. Thus, it is usually costly and time-consuming to obtain data with no label noise. When dealing with label noise data, existing TSK fuzzy system algorithms still have room for improvement. This article proposes a robust TSK fuzzy system based on semisupervised learning for label noise data (RTSK-FS-SS). By introducing an intuitionistic fuzzy set method, the proposed algorithm can detect label noise samples. An improved learning vector quantization is further adopted to overcome the challenge that traditional unsupervised learning-based antecedent part generation processes unable to make full use of the label information of training samples. Finally, we discard the label of suspicious samples and a consequent parameter learning method based on semisupervised learning is proposed. The proposed algorithm is validated using extensive experiments.

The superior interpretability and uncertainty modeling ability of Takagi-Sugeno-Kang fuzzy system (TSK FS) make it possible to describe complex nonlinear systems intuitively and efficiently. However, classical TSK FS usually adopts the whole feature space of the data for model construction, which can result in lengthy rules for high-dimensional data and lead to degeneration in interpretability. Furthermore, for highly nonlinear modeling task, it is usually necessary to use a large number of rules which further weaken the clarity and interpretability of TSK FS. To address these issues, an enhanced soft subspace clustering (ESSC) and sparse learning (SL) based concise zero-order TSK FS construction method, called ESSC-SL-CTSK-FS, is proposed in this paper by integrating the techniques of ESSC and SL. In this method, ESSC is used to generate the antecedents and various sparse subspaces for different fuzzy rules, whereas SL is used to optimize the consequent parameters of the fuzzy rules based on which the number of fuzzy rules can be effectively reduced. Finally, the proposed ESSC-SL-CTSK-FS method is used to construct concise zero-order TSK FS that can explain the scenes in high-dimensional data modeling more clearly and easily. Experiments are conducted on various real-world datasets to confirm the advantages.

Multiview datasets are frequently encountered in learning tasks, such as web data mining and multimedia information analysis. Given a multiview dataset, traditional learning algorithms usually decompose it into several single-view datasets, from each of which a single-view model is learned. In contrast, a multiview learning algorithm can achieve better performance by cooperative learning on the multiview data. However, existing multiview approaches mainly focus on the views that are visible and ignore the hidden information behind the visible views, which usually contains some intrinsic information of the multiview data, or vice versa. To address this problem, this paper proposes a multiview fuzzy logic system which utilizes both the hidden information shared by the multiple visible views and the information of each visible view. Extensive experiments were conducted to validate its effectiveness.

Embedded networked sensor systems are deeply coupled with the physical world, and the deployed systems are usually difficult to debug. Therefore, it is especially important to thoroughly test and profile the systems before deploying to the real world. Traditional debugging methods are incompetent for detailed tracing on resource constrained devices due to their intrusiveness. This paper proposes a low-cost Hardware Assisted Tracing testBED (HATBED) to enable non-intrusive tracing and profiling for embedded networked sensor systems independent of operating systems and applications. We hope HATBED will foster research on comprehensive testing and profiling of embedded networked systems based on modern 32-bit architecture.

Fuzzy Extreme Learning Machine (F-ELM) constructs a fuzzy neural networks by embedding fuzzy membership functions and rules into the hidden layer of extreme learning machine (ELM), that is, it can be interpreted as a fuzzy system with the structure of neural network. Although F-ELM has shown the characteristics of fast learning of model parameters, it has poor robustness to small and noisy datasets since its parameters connecting hidden layer with output layer are optimized by least square(LS). In order to overcome this challenge, a Ridge Regression based Extreme Learning Fuzzy System (RR-EL-FS) is presented in this study, which has introduced the strategy of ridge regression into F-ELM to enhance the robustness. The experimental results also validate that the performance of RR-EL-FS is better than F-ELM and some related methods to small and noisy datasets.