In multisource clustering tasks, the number of clusters in each source or view may not align with the number of ground-truth clusters. Existing ensemble clustering methods face two notable challenges: (1) developing a new ensemble framework that yields a final clustering result matching the ground-truth cluster count and (2) revealing consistency among all base clustering results. To address these challenges, we propose a novel one-step fuzzy ensemble clustering method (OS-FECM) that incorporates ground-truth cluster number graphs. Initially, OS-FECM establishes a one-step fuzzy ensemble framework that directly integrates all base fuzzy clustering results (i.e., membership matrices) with varying cluster counts, thereby eliminating reliance on the CA matrix typical of existing two-step ensemble frameworks. Furthermore, we construct a ground-truth cluster number graph, which maps the number of clusters in each base clustering result to the ground-truth cluster count in the final ensemble result. This graph reveals the consistency among all base fuzzy clustering results and illustrates the relationships between clusters in the base results and the ground-truth clusters. It is then embedded into the corresponding base fuzzy clustering results to enhance the final ensemble result. Lastly, we employ an alternating optimization method alongside a weighting mechanism to derive the final ensemble clustering result and adaptively assign importance to each base clustering result. Experimental evaluations across various datasets demonstrate that OS-FECM achieves clustering performance that is at least comparable to, if not superior to, that of other comparative methods.

While the classical KNN (k nearest neighbor) shares its avoidance of the consistent distribution assumption between training and testing samples to achieve fast prediction, it still faces two challenges: (a) its generalization ability heavily depends on an appropriate number k of nearest neighbors; (b) its prediction behavior lacks interpretability. In order to address the two challenges, a novel Bayes-decisive linear KNN with adaptive nearest neighbors (i.e., BLA-KNN) is proposed to obtain the following three merits: (a) a diagonal matrix is introduced to adaptively select the nearest neighbors and simultaneously improve the generalization capability of the proposed BLA-KNN method; (b) the proposed BLA-KNN method owns the group effect, which inherits and extends the group property of the sum of squares for total deviations by reflecting the training sample class-aware information in the group effect regularization term; (c) the prediction behavior of the proposed BLA-KNN method can be interpreted from the Bayes-decision-rule perspective. In order to do so, we first use a diagonal matrix to weigh each training sample so as to obtain the importance of the sample, while constraining the importance weights to ensure that the adaptive k value is carried out efficiently. Second, we introduce a class-aware information regularization term in the objective function to obtain the nearest neighbor group effect of the samples. Finally, we introduce linear expression weights related to the distance measure between the testing and training samples in the regularization term to ensure that the interpretation of Bayes-decision-rule can be performed smoothly. We also optimize the proposed objective function using an alternating optimization strategy. We experimentally demonstrate the effectiveness of the proposed BLA-KNN method by comparing it with 7 comparative methods on 15 benchmark datasets.

Motivated by both the commonly used "from wholly coarse to locally fine" cognitive behavior and the recent finding that simple yet interpretable linear regression model should be a basic component of a classifier, a novel hybrid ensemble classifier called hybrid Takagi-Sugeno-Kang fuzzy classifier (H-TSK-FC) and its residual sketch learning (RSL) method are proposed. H-TSK-FC essentially shares the virtues of both deep and wide interpretable fuzzy classifiers and simultaneously has both feature-importance-based and linguistic-based interpretabilities. RSL method is featured as follows: 1) a global linear regression subclassifier on all original features of all training samples is generated quickly by the sparse representation-based linear regression subclassifier training procedure to identify/understand the importance of each feature and partition the output residuals of the incorrectly classified training samples into several residual sketches; 2) by using both the enhanced soft subspace clustering method (ESSC) for the linguistically interpretable antecedents of fuzzy rules and the least learning machine (LLM) for the consequents of fuzzy rules on residual sketches, several interpretable Takagi-Sugeno-Kang (TSK) fuzzy subclassifiers are stacked in parallel through residual sketches and accordingly generated to achieve local refinements; and 3) the final predictions are made to further enhance H-TSK-FC's generalization capability and decide which interpretable prediction route should be used by taking the minimal-distance-based priority for all the constructed subclassifiers. In contrast to existing deep or wide interpretable TSK fuzzy classifiers, benefiting from the use of feature-importance-based interpretability, H-TSK-FC has been experimentally witnessed to have faster running speed and better linguistic interpretability (i.e., fewer rules and/or TSK fuzzy subclassifiers and smaller model complexities) yet keep at least comparable generalization capability.

Due to its strong performance in handling uncertain and ambiguous data, the fuzzy k -nearest-neighbor method (FKNN) has realized substantial success in a wide variety of applications. However, its classification performance would be heavily deteriorated if the number k of nearest neighbors was unsuitably fixed for each testing sample. This study examines the feasibility of using only one fixed k value for FKNN on each testing sample. A novel FKNN-based classification method, namely, fuzzy KNN method with adaptive nearest neighbors (A-FKNN), is devised for learning a distinct optimal k value for each testing sample. In the training stage, after applying a sparse representation method on all training samples for reconstruction, A-FKNN learns the optimal k value for each training sample and builds a decision tree (namely, A-FKNN tree) from all training samples with new labels (the learned optimal k values instead of the original labels), in which each leaf node stores the corresponding optimal k value. In the testing stage, A-FKNN identifies the optimal k value for each testing sample by searching the A-FKNN tree and runs FKNN with the optimal k value for each testing sample. Moreover, a fast version of A-FKNN, namely, FA-FKNN, is designed by building the FA-FKNN decision tree, which stores the optimal k value with only a subset of training samples in each leaf node. Experimental results on 32 UCI datasets demonstrate that both A-FKNN and FA-FKNN outperform the compared methods in terms of classification accuracy, and FA-FKNN has a shorter running time.

While fuzzy random forest (FRF) as a fuzzy implementation of random forest has earned its strong ambiguity/uncertainty handling capability on a rich variety of considerably low dimensional datasets, this article revisits FRF and attempts to enhance its generalization capability and computational speed on high dimensional datasets. For the first issue, in addition to the original use of randomness in FRF, a doubly randomness is newly introduced into the generation of both the candidate attributes and the best splitting attributes in FRF. For the computational speed issue, while the proposed new fuzzy information gain (NFG) measure does not apply to all candidate attributes, the remaining NFG values can be quickly retrieved by copying from the dynamically generated dictionary. As a result, a new method called enhanced fuzzy random forest (E-FRF) is proposed and justified theoretically from the consistency perspective. Our extensive experimental results indicate that the proposed method E-FRF has at least comparable performance to the comparative methods, and is an advantageous alternative to FRF in terms of both testing accuracy and running speed in most of the adopted high dimensional datasets.

As an exemplar-based clustering method, the well-known density peaks clustering (DPC) heavily depends on the computation of kernel-based density peaks, which incurs two issues: first, whether kernel-based density can facilitate a large variety of data well, including cases where ambiguity and uncertainty of the assignment of the data points to their clusters may exist, and second, whether the concept of density peaks can be interpreted and manipulated from the perspective of soft partitions (e.g., fuzzy partitions) to achieve enhanced clustering performance. In this article, in order to provide flexible adaptability for tackling ambiguity and uncertainty in clustering, a new concept of fuzzy peaks is proposed to express the density of a data point as the fuzzy-operator-based coupling of the fuzzy distances between a data point and its neighbors. As a fuzzy variant of DPC, a novel fuzzy density peaks clustering (FDPC) method FDPC based on fuzzy operators (especially S-norm operators) is accordingly devised along with the same algorithmic framework of DPC. With an appropriate choice of a fuzzy operator with its associated tunable parameter for a clustering task, FDPC can indeed inherit the advantage of fuzzy partitions and simultaneously provide flexibility in enhancing clustering performance. The experimental results on both synthetic and real data sets demonstrate that the proposed method outperforms or at least remains comparable to the comparative methods in clustering performance by choosing appropriate parameters in most cases.

When spectral clustering analysis is applied, a similarity matrix of data plays a vital role in both clustering performance and stability of clustering results. In order to enhance the clustering performance and maintain the stability of the clustering results, a new method to jointly learn the similarity matrix and the clustering structure, called the joint learning method (FSCM) of spectral clustering structure and fuzzy similarity matrix of data, is proposed in this paper. In FSCM, the capability of a double-index fuzzy C-means clustering algorithm is used to determine an appropriate fuzzy similarity between any pair of data points. A fuzzy similarity matrix of data is also determined by adaptively assigning fuzzy neighbors of data points so the spectral clustering structure of data can be found and the clustering stability of FSCM can be assured. Experimental results on synthetic and real datasets demonstrate the effectiveness of the proposed method.