The one‐class classification (OCC) problem has always been a popular topic because it is difficult or expensive to obtain abnormal data in many practical applications. Most of OCC methods focused on monomodal data, such as support vector data description (SVDD) and its variants, while we often face multimodal data in reality. The data come from the same task in multimodal learning, and thus, the inherent structures among all modalities should be hold, which is called the consistency principle. However, each modality contains unique information that can be used to repair the incompleteness of other modalities. It is called the complementarity principle. To follow the above two principles, we designed a multimodal graph–regularized term and a sparse projection matrix–regularized term. The former aims to preserve the within‐modal structural and between‐modal relationships, while the latter aims to richly use the complementarity information hidden in multimodal data. Further, we follow the multimodal subspace (MS) SVDD architecture and use two regularized terms to regularize SVDD. Consequently, a novel OCC method for multimodal data is proposed, called the consistency and complementarity jointly regularized subspace SVDD (CCS‐SVDD). Extensive experimental results demonstrate that our approach is more effective and competitive than other algorithms. The source codes are available at https://github.com/wongchuang/CCS_SVDD .

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.

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.

The recently developed fuzzy style k -plane clustering (S-KPC) algorithm displays promising clustering quality by leveraging both similarities and distinguishable styles between samples on stylistic data. However, S-KPC becomes vulnerable to similar styles that are not easily distinguishable. In this study, a novel f uzzy s tyle f lat-based c lustering (FSFC) algorithm is proposed to overcome this vulnerability. In FSFC, a style flat matrix (SFM) is designed to project samples onto appropriate flats while maintaining the styles of different clusters in a reasonable manner. Based on SFM, the core of FSFC is to learn the potentially intersecting manifold structures of clusters in the projected flat space to make samples with the same style close to the cluster center and simultaneously far away from the other cluster centers. Furthermore, the objective function of FSFC can provide scale flexibility for each flat in the projected flat space. In particular, the optimization problem of FSFC can be decomposed into a series of sub-problems about the flat parameters, which can be locally optimized using the concave-convex procedure (CCCP). Extensive experiments on both synthetic and real-world datasets demonstrate the competitive clustering performance of FSFC. Moreover, FSFC outperforms some state-of-the-art manifold clustering algorithms on six case studies about stylistic data.

Support vector machine (SVM) is an excellent pattern recognition method. Many experiments have shown that SVM can achieve a generalization performance gain by carrying out it in the feature transformation space. Nevertheless, the theoretical foundation behind this phenomenon is presently lack of deep investigation. In the paper, we first give and prove a vital theoretical conclusion that SVM in the feature transformation space can obtain a lower radius-margin bound than one in the feature original space. This means that the performance of SVM can be improved by feature transformation since the radius-margin bound is directly associated with the generalization capacity. Based on this theoretical support, we further propose a novel method called covering-hyperellipsoid-constrained large margin classifier (CHC-LMC). The key characteristic of CHC-LMC is that it jointly learns the minimum bounding hyperellipse and the used classifier by directly minimizing the radius-margin bound in the transformation space, and so embodies the structural risk minimization principle. We develop the linear and nonlinear versions of CHC-LMC and employ an alternate optimization strategy to deal with the corresponding optimization problems. Finally, comprehensive experiments are conducted to verify the validity of CHC-LMC and evaluate the generalization performance by comparing it with the competing methods.

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.

The knowledge-leverage-based Takagi--Sugeno--Kang fuzzy system (KL-TSK-FS) modeling method has shown promising performance for fuzzy modeling tasks where transfer learning is required. However, the knowledge-leverage mechanism of the KL-TSK-FS can be further improved. This is because available training data in the target domain are not utilized for the learning of antecedents and the knowledge transfer mechanism from a source domain to the target domain is still too simple for the learning of consequents when a Takagi--Sugeno--Kang fuzzy system (TSK-FS) model is trained in the target domain. The proposed method, that is, the enhanced KL-TSK-FS (EKL-TSK-FS), has two knowledge-leverage strategies for enhancing the parameter learning of the TSK-FS model for the target domain using available information from the source domain. One strategy is used for the learning of antecedent parameters, while the other is for consequent parameters. It is demonstrated that the proposed EKL-TSK-FS has higher transfer learning abilities than the KL-TSK-FS. In addition, the EKL-TSK-FS has been further extended for the scene of the multisource domain.

Based on the extensive Kuramoto model, synchronization-inspired partitioning clustering algorithm was recently proposed and is attracting more and more attentions, due to the fact that it simulates the synchronization phenomena in clustering where each data object is regarded as a phase oscillator and the dynamic behavior of the objects is simulated over time. In order to circumvent the serious difficulty that its existing version can only be effectively carried out on considerably small/medium datasets, a novel scalable synchronization-inspired partitioning clustering algorithm termed LSSPC, based on the center-constrained minimal enclosing ball and the reduced set density estimator, is proposed for large dataset applications. LSSPC first condenses a large scale dataset into its reduced dataset by using a fast minimal-enclosing-ball based approximation for the reduced set density estimator, thus achieving an asymptotic time complexity that is linear in the size of dataset and a space complexity that is independent of this size. Then it carries out clustering adaptively on the obtained reduced dataset by using Sync with the Davies-Bouldin clustering criterion and a new order parameter which can help us observe the degree of local synchronization. Finally, it finishes clustering by using the proposed algorithm CRD on the remaining objects in the large dataset, which can capture the outliers and isolated clusters effectively. The effectiveness of the proposed clustering algorithm LSSPC for large datasets is theoretically analyzed and experimentally verified by running on artificial and real datasets.