Artificial intelligence has shown great promise in noninvasive recognition of vulnerable coronary plaques. However, practical data issues in multicenter studies, such as inconsistent data distribution and insufficient or missing data labels, could significantly affect the recognition accuracy. Unsupervised domain adaptation (UDA) can be introduced to address this challenge, but several limits still remain. First, many existing UDA models are black boxes, hindering healthcare professionals' ability to interpret and trust the model's decision. Second, some methods use pseudolabel to enhance performance, but often overlook the quality assessment of these pseudolabels, potentially leading to negative knowledge transfer. To this end, based on the interpretable Takagi–Sugeno–Kang fuzzy system (TSK-FS), a novel domain adaptive method is proposed to improve model generalizability for vulnerable coronary plaques recognition in multicenter data. First of all, TSK-FS is employed to construct a shared fuzzy feature space for the source domain and the target domain, aiming to better align data distribution. To make full use of the information of unlabeled target domain data and further reduce the negative knowledge transfer, the enhanced pseudolabel learning mechanism is further introduced by combining the graph-based random walking and label filtering. Moreover, Multicenter data of 910 patients with suspected or diagnosed coronary artery disease were collected from three hospitals for experiments. Experimental results demonstrate that the proposed DA-TSK-PLR-FS achieves the promising generalizability across multicenter datasets

The first-order Takagi-Sugeno-Kang (TSK) fuzzy classifier with a fully combined fuzzy rule base (FuCo-FRB) is a potent and interpretable classifier for multiple input and multiple output (MIMO) tasks. However, FuCo-FRB possess an exponential increase in the number of fuzzy rules, and it poses challenges for efficient identification of the parameter matrix in MIMO tasks. A lightweight TSK fuzzy classifier (LW-TSK-FC) is proposed to achieve the balance of training efficiency and predictive performance especially on MIMO tasks. It has the following advantages: (1) An adaptive weighting method based on directly connected FRB enables the efficient generation of fuzzy rules, meanwhile retaining the distribution characteristic of FuCo-FRB to reduce information loss. (2) The consequent network of first-order TSK is optimized to a novel series structure by using matrix factorization. This new series structure increases the depth of consequent network and enable the implementation of kernel function and least learning machine (LLM), enhancing the calculation efficiency and predictive performance. (3) There are only weight parameters in consequent network of LW-TSK-FC and these parameters can be identified quantitatively by LLM, leading to a great training efficiency. The comparison experiments with other 14 power classifiers on 13 public UCI datasets shown comparable predictive performance and outstanding training and testing efficiency in both MISO and MIMO tasks. The experiments on a real-world clinical task demonstrated the significant capability of LW-TSK-FC on handling imbalanced small data, and can provide the semantic interpretability for reasoning process.

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.

Interpretable artificial intelligence (AI), also known as explainable AI, is indispensable in establishing trustable AI for bench-to-bedside translation, with substantial implications for human well-being. However, the majority of existing research in this area has centered on designing complex and sophisticated methods, regardless of their interpretability. Consequently, the main prerequisite for implementing trustworthy AI in medical domains has not been met. Scientists have developed various explanation methods for interpretable AI. Among these methods, fuzzy rules embedded in a fuzzy inference system (FIS) have emerged as a novel and powerful tool to bridge the communication gap between humans and advanced AI machines. However, there have been few reviews of the use of FISs in medical diagnosis. In addition, the application of fuzzy rules to different kinds of multimodal medical data has received insufficient attention, despite the potential use of fuzzy rules in designing appropriate methodologies for available datasets. This review provides a fundamental understanding of interpretability and fuzzy rules, conducts comparative analyses of the use of fuzzy rules and other explanation methods in handling three major types of multimodal data (i.e., sequence signals, medical images, and tabular data), and offers insights into appropriate fuzzy rule application scenarios and recommendations for future research.

Stacking-based takagi-sugeno-kang (TSK) fuzzy system ensemble has been successfully applied to imbalanced data classification. However, there still exist many challenges that need to be further addressed. For example, during stacking, augmenting output variables into the input feature space reduces the interpretability of antecedents of fuzzy rules. During sampling for balancing, discovering informative samples usually only relies on training samples, which may reduce generalizability. More importantly, there is no theory to support the reliability of stacking. To address the aforementioned challenges, in this study, we propose a deep reconciled and self-paced TSK fuzzy system ensemble framework termed D-RSP-TSKE for imbalanced data classification. Compared with the existing ensemble frameworks, its superiorities can be exhibited from the following three aspects. First, in the first layer, we use random undersampling to generate a class-balanced training set to train an initial zero-order TSK fuzzy classifier. Based on the TSK fuzzy classifier, then we define classifier-specific and testing-compatible sample sensitivity to discover informative (high-sensitive) samples and design a reconciled and self-paced sampling approach to balance the minority class for the training of the following layers. Second, to improve the interpretability of antecedents of fuzzy rules, we propose to transfer the output variables from antecedents to consequents through equivalent mathematical transformations while keeping the final output unchanged. These transferred output variables are interpreted as the dynamic fuzzy rule confidence. Third, furthermore, we engage in a comprehensive theoretical examination of our stacking-based ensemble to elucidate the underlying mechanisms that enable the stacking strategy to consistently deliver superior performance. We conduct tests and comparisons on 7 artificial datasets and 30 real-world datasets to evaluate D-RSP-TSKE. The experimental results demonstrate the effectiveness and interpretability of D-RSP-TSKE for imbalanced data classification.

Radiomics, dosiomics and contouromics have been combined to predict adaptive radiotherapy eligibility in nasopharyngeal carcinoma. However, the commonly-used feature concatenation ignores the complementary or consistency relationship across different omics feature spaces. Also, the number of features increases with the concatenation of omics, leading to the curse of dimensionality and potential overfitting. To address the issues, in this study, multi-omics collaborative learning MOCL is developed. In MOCL, a priori knowledge-driven consistency regularization associated with Shannon entropy is designed to automatically explore the weighting consistency across different omics feature spaces. In addition, a label soften strategy is adopted to enlarge the margins between different classes, rendering more freedom for the models to fit the soft label matrix. To avoid overfitting, we design a regularized term deduced from manifold learning to keep samples in the label space as close as possible if they are in the same manifold in the feature space. Experimental results on 311 nasopharyngeal carcinoma patients collected from the Hong Kong Queen Elizabeth Hospital demonstrate the promising performance of MOCL.

The accurate prediction of adaptive radiation therapy (ART) for nasopharyngeal carcinoma (NPC) patients before radiation therapy (RT) is crucial for minimizing toxicity and enhancing patient survival rates. Owing to the complexity of the tumor micro-environment, a single high-resolution image offers only limited insight. Furthermore, the traditional softmax-based loss falls short in quantifying a model’s discriminative power. To address these challenges, we introduce a supervised multi-view contrastive learning approach with an additive margin (MMCon). For each patient, we consider four medical images to form multi-view positive pairs, which supply supplementary information and bolster the representation of medical images. We employ supervised contrastive learning to determine the embedding space, ensuring that NPC samples from the same patient or with the same labels stay in close proximity while NPC samples with different labels are distant. To enhance the discriminative ability of the loss function, we incorporate a margin into the contrastive learning process. Experimental results show that this novel learning objective effectively identifies an embedding space with superior discriminative abilities for NPC images.

Social data analytics is often taken as the most commonly used method for community discovery, product recommendations, knowledge graph, and so on. In this study, social data are firstly represented in different feature spaces by using various feature extraction algorithms. Then we build a transfer learning model to leverage knowledge from multiple feature spaces. During modeling, since the assumption that the training and the testing data have the same distribution is always true, we give a theorem and its proof which asserts the necessary and sufficient condition for achieving a minimum testing error. We also theoretically demonstrate that maximizing the classification error consistency across different feature spaces can improve the classification performance. Additionally, the cluster assumption derived from semi-supervised learning is introduced to enhance knowledge transfer. Finally, aTagaki-Sugeno-Kang (TSK)fuzzy system-based learning algorithm is proposed, which can generate interpretable fuzzy rules. Experimental results not only demonstrate the promising social data classification performance of our proposed approach but also show its interpretability which is missing in many other models.

With the development of sensors, more and more multimodal data are accumulated, especially in biomedical and bioinformatics fields. Therefore, multimodal data analysis becomes very important and urgent. In this study, we combine multi-kernel learning and transfer learning, and propose a feature-level multi-modality fusion model with insufficient training samples. To be specific, we firstly extend kernel Ridge regression to its multi-kernel version under the lp-norm constraint to explore complementary patterns contained in multimodal data. Then we use marginal probability distribution adaption to minimize the distribution differences between the source domain and the target domain to solve the problem of insufficient training samples. Based on epilepsy EEG data provided by the University of Bonn, we construct 12 multi-modality & transfer scenarios to evaluate our model. Experimental results show that compared with baselines, our model performs better on most scenarios.

In this study, an online transfer TSK fuzzy classifier O-T-TSK-FC is proposed for recognizing epilepsy signals. Compared with most of the existing transfer learning models, O-T-TSK-FC enjoys its merits from the following three aspects: 1) Since different patients often response to the same neuronal firing stimulation in different neural manners, the labeled data in the source domain cannot accurately represent the primary EEG data in the target domain. Therefore, we design an objective function which can integrate with subject-specific data in the target domain to induce the target predictive function. 2) A new regularization used for knowledge transfer is proposed from the perspective of error consensus, and its rationality is explained from the perspective of probability density estimation. 3) Clustering is used to partition source domains so as to reduce the computation of O-T-TSK-FC without affecting its performance. Based on the EEG signals collected from Bonn University, six different online scenarios for transfer learning are constructed. Experimental results on them show that O-T-TSK-FC performs better than benchmarking algorithms and robustly.

Most of the medoid-based fuzzy clustering algorithms only use one similarity matrix to organize objects into groups. The similarity matrix is often constructed by equally employing all features which may ignore the contribution differences existing among the features. In this study, we also propose a medoid-based fuzzy clustering algorithm feature pattern-driven similarity matrices-reduction based fuzzy clustering (FP-SMR-FC) which is different from the existing ones in the following two aspects. First, multiple similarity matrices are constructed to represent the similarity between objects. Additionally, a feature pattern-driven Shannon entropy which combines nondeterminacy information contained in the similarity matrices and statistical information contained in the features together is used to learn the weight of each similarity matrix. Second, during the clustering processes of FP-SMR-FC, a new schema for eliminating some of the similarity matrices with very few contributions is developed for similarity matrices reduction. The comparison studies in terms of time complexity and clustering accuracy for FP-SMR-FC with various medoid-based clustering algorithms on real-life data sets are done. In addition, FP-SMR-FC is applied to head pose estimation of human behavior analysis. Comparisons, indeed, demonstrate the promising performance of FP-SMR-FC in practice.

Industry 4.0 places special emphasis on the use of intelligent models to discover patterns in data. In this article, we propose a novel Takagi-Sugeno-Kang (TSK) fuzzy system with low model complexity for multiview data pattern discovery. Compared with the classic TSK fuzzy systems, the proposed one has three merits: First, we introduce a transformation matrix to relax the strict binary label matrix of the training set so that the margins between classes become more discriminative. Second, we introduce two kinds of sparsity regularizations, i.e., cross-rule and cross-view, to reduce indiscriminative fuzzy rules and consequent parameters so that the model complexity is significantly reduced. Third, we introduce the alternating direction method of multipliers to optimize the objective function so that we have compact closed-form solutions in each iteration. Extensive experiments on different kinds of multiview image datasets indicate the promising performance for data pattern discovery with low model complexity.

In the field of intelligent transportation, transfer learning (TL) is often used to recognize EEG-based drowsy driving for a new subject with few subject-specific calibration data. However, most of existing TL-based models are offline, non-transparent, and in which features are only represented from one view (usually only one algorithm is used to extract features). In this paper, we consider an online multi-view regression model with high interpretability. By taking the 1-order TSK fuzzy system as the basic regression component and injecting the nature of the multi-view settings into the existing transfer learning framework and enforcing the consistencies across different views, we propose an online multi-view & transfer TSK fuzzy system for driver drowsiness estimation. In this novel model, features in both the source domain and the target domain are represented from multi-view perspectives such that more pattern information can be utilized during model training. Also, comparing with offline training, the proposed online fuzzy system meets the practical requirements more competently. An experiment on a driving dataset demonstrates that the proposed fuzzy system has smaller drowsiness estimation errors and higher interpretability than introduced benchmarking models.

Using unsupervised learning methods for clinical diagnosis is very meaningful. In this study, we propose an unsupervised multi-view & multi-medoid variant-entropy-based fuzzy clustering (M 2 VEFC) method for epilepsy EEG signals detecting. Comparing with existing related studies, M 2 VEFC has four main merits and contributions: (1) Features in original EEG data are represented from different perspectives that can provide more pattern information for epilepsy signals detecting. (2) During multi-view modeling, multi-medoids are used to capture the structure of clusters in each view. Furthermore, we assume that the medoids in a cluster observed from different views should keep invariant, which is taken as one of the collaborative learning mechanisms in this study. (3) A variant entropy is designed as another collaborative learning mechanism in which view weight learning is controlled by a user-free parameter. The parameter is derived from the distribution of samples in each view such that the learned weights have more discrimination. (4) M 2 VEFC does not need original data as its input—it only needs a similarity matrix and feature statistical information. Therefore, the original data are not exposed to users and hence the privacy is protected. We use several different kinds of feature extraction techniques to extract several groups of features as multi-view data from original EEG data to test the proposed method M 2 VEFC. Experimental results indicate M 2 VEFC achieves a promising performance that is better than benchmarking models.

For the wide variety of emerging data in our daily life, realizing exemplar-based clustering effectively and understanding its clustering behavior appropriately become more desirable. In this paper, based on a new look at the Bayesian framework of data clustering, two new concepts are introduced and they correspond to a Bayesian information transmission system and its transmission learning. Facilitated by the new concepts, an exemplar-based transmission learning machine for clustering (ETLMC) is accordingly developed. As an attempt to explain the exemplar-based clustering behavior in a physics-based manner, ETLMC is well justified by revealing that the exemplar masses transfer between data objects during the clustering process can be governed by the proposed gravity enrichment effect rooted at Newton's law of gravity. Practically, ETLMC is distinctive in its easy implementation in terms of its global analytical solution, its fast exemplar finding for large scale data with arbitrary shapes, its easy parameter settings and its stable and efficient clustering results. Extensive experiments on synthetic and real datasets demonstrate the effectiveness of ETLMC, in contrast to a number of existing state-of-the-art clustering algorithms.

Multiview and multiexemplar fuzzy clustering aims at effectively integrating the fuzzy membership matrix of each individual view to search for a final partition of objects in which each cluster may well be represented by one and even multiple exemplars. However, how to integrate the corresponding fuzzy membership matrix of each view such that enhanced clustering performance can be theoretically guaranteed still keeps an open topic. In this study, with the proposed exemplar invariant assumption that an exemplar of a cluster in one view is always an exemplar of that cluster in each other view, we demonstrate that multiview & multiexemplar fuzzy clustering has a theoretical guarantee of enhanced clustering performance. Based on the above-mentioned theoretical result, we develop a novel multiview & multiexemplar fuzzy clustering approach (M2FC). The key features of the proposed approach are: first, embed a quadratic penalization term into its objective function to minimize the discrepancy of exemplars across different views such that the exemplar invariant assumption can be met as much as possible; and second, optimize the proposed objective function of the proposed approach by applying the Lagrangian multiplier method and Karush-Kuhn-Tuchker conditions to assure nonnegative fuzzy memberships. Extensive experimental results show that M2FC outperforms the existing state-of-the-art multiview approaches in most cases.

As a fundamental step in various data analysis, exemplar-based clustering aims at clustering data by identifying representative samples as exemplars of the obtained groups. In this paper, a new fast exemplar-based clustering approach is proposed for a dataset with an arbitrary shape and number of clusters. The proposed approach begins with the reduced set of a dataset, which is a condensation of the dataset obtained by the well-developed kernel density estimators reduced set density estimator or fast reduced set density estimator, and then enters into its two advantageous stages: 1) fast exemplar finding (FEF) and 2) fast cluster assignment. The idea of the proposed approach has its basis in three assumptions: 1) exemplars should come from high-density samples; 2) exemplars should be either the components of the reduced set or their neighbors with high similarities; and 3) clusters can be diffused by surrounding both exemplars and its labeled reduced set. We theoretically analyze the proposed FEF from the perspective of the generalization performance of clustering and demonstrate the power of the proposed approach on several benchmarking datasets.

In many practical applications of classifiers, not only high accuracy but also high interpretability is required. Among a wide variety of existing classifiers, Takagi–Sugeno–Kang (TSK) fuzzy classifiers may be one of the best choices for achieving a good balance between interpretability and accuracy. In order to further improve their accuracy without losing their interpretability, we propose a highly interpretable deep TSK fuzzy classifier HID-TSK-FC (deep shared-linguistic-rule-based TSK fuzzy classifier) based on the concept of shared linguistic fuzzy rules. The proposed classifier has two characteristics: One is a stacked hierarchical structure of component TSK fuzzy classifiers for high accuracy, and the other is the use of interpretable linguistic rules with the same set of linguistic labels for all inputs. High interpretability is achieved at each layer by using the same set of linguistic values for all inputs, including the outputs from the previous layers in the stacked hierarchical structure. We show that a linguistic rule with the outputs from the previous layers as its inputs is equivalent to a fuzzy rule with a nonlinear consequent or a linear consequent with a certainty factor. We also show that HID-TSK-FC is mathematically equivalent to a novel TSK fuzzy classifier with shared interpretable linguistic fuzzy rules. Promising performance of HID-TSK-FC is demonstrated through extensive computational experiments on benchmark datasets and a real-world application case.