Class imbalance has been extensively studied in single-view scenarios; however, addressing this challenge in multi-view contexts remains an open problem, with even scarcer research focusing on trustworthy solutions. In this paper, we tackle a particularly challenging class imbalance problem in multi-view scenarios: long-tailed classification. We propose TMLC, a Trusted Multi-view Long-tailed Classification framework, which makes contributions on two critical aspects: opinion aggregation and pseudo-data generation. Specifically, inspired by Social Identity Theory, we design a group consensus opinion aggregation mechanism that guides decision-making toward the direction favored by the majority of the group. In terms of pseudo-data generation, we introduce a novel distance metric to adapt SMOTE for multi-view scenarios and develop an uncertainty-guided data generation module that produces high-quality pseudo-data, effectively mitigating the adverse effects of class imbalance. Extensive experiments on long-tailed multi-view datasets demonstrate that our model is capable of achieving superior performance.

Recently, multi-view learning has witnessed a considerable interest on the research of trusted decision-making. Previous methods are mainly inspired from an important paper published by Han et al. in 2021, which formulates a Trusted Multi-view Classification (TMC) framework that aggregates evidence from different views based on Dempster's combination rule. All these methods only consider inter-view aggregation, yet lacking exploitation of intra-view information. In this paper, we propose a generalized trusted multi-view classification framework with hierarchical opinion aggregation. This hierarchical framework includes a two-phase aggregation process: the intra-view and inter-view aggregation hierarchies. In the intra aggregation, we assume that each view is comprised of common information shared with other views, as well as its specific information. We then aggregate both the common and specific information. This aggregation phase is useful to eliminate the feature noise inherent to view itself, thereby improving the view quality. In the inter-view aggregation, we design an attention mechanism at the evidence level to facilitate opinion aggregation from different views. To the best of our knowledge, this is one of the pioneering efforts to formulate a hierarchical aggregation framework in the trusted multi-view learning domain. Extensive experiments show that our model outperforms some state-of-art trust-related baselines. One can access the source code onhttps://github.com/lshi91/GTMC-HOA.

Incomplete multi-view clustering (IMVC) aims to leverage complementary information from multi-view data with missing instances to enhance clustering performance. Many existing IMVC methods exhibit limitations in effectively exploiting hidden information and addressing distribution differences between views and modules. To address these challenges, we present a novel IMVC framework that leverages the proposed stack feature-based matrix completion to impute the missing instances, enhancing the exploitation of underlying information. We also incorporate graph consensus to integrate graph structures learned from both completed and observed data. Additionally, we introduce correntropy-induced metric as a flexible measurement to adaptively assign different constraints to various views and modules. Furthermore, we derive an efficient iterative algorithm based on Fenchel conjugate and accelerated block coordinate update (BCU) to solve the joint learning problem. Experimental results on eight benchmark datasets demonstrate the superior performance of our method compared to state-of-the-art IMVC methods across various metrics.

Due to the effectiveness in learning the subspace structures, low-rank representation (LRR) and its variations have been widely applied in various fields, such as computer vision and pattern recognition. However, in real applications, it is a challenge to handle the complex noises. To address this problem, we propose a novel robust LRR method based on kernel risk-sensitive loss (KRSL) with high-order manifold constraint, called RHLRR, in which the KRSL is introduced to deal with the noises and the multiple hypergraph regularization term is used as a high order manifold constraint to effectively capture the locality, similarity and the intrinsic geometric information in data. Besides, an iterative algorithm based on the half-quadratic (HQ) and the accelerated block coordinate update (BCU) is developed. The experimental results demonstrate that the proposed method can outperform other state-of-the-art LRR variants.

Multiview subspace clustering, which aims to cluster the given data points with information from multiple sources or features into their underlying subspaces, has a wide range of applications in the communities of data mining and pattern recognition. Compared with the single-view subspace clustering, it is challenging to efficiently learn the structure of the representation matrix from each view and make use of the extra information embedded in multiple views. To address the two problems, a novel correntropy-based multiview subspace clustering (CMVSC) method is proposed in this article. The objective function of our model mainly includes two parts. The first part utilizes the Frobenius norm to efficiently estimate the dense connections between the points lying in the same subspace instead of following the standard compressive sensing approach. In the second part, the correntropy-induced metric (CIM) is introduced to characterize the noise in each view and utilize the information embedded in different views from an information-theoretic perspective. Furthermore, an efficient iterative algorithm based on the half-quadratic technique (HQ) and the alternating direction method of multipliers (ADMM) is developed to optimize the proposed joint learning problem, and extensive experimental results on six real-world multiview benchmarks demonstrate that the proposed methods can outperform several state-of-the-art multiview subspace clustering methods.

Recently, maximum correntropy criterion (MCC) has been widely and successfully used in robust signal processing and machine learning, in which the correntropy is maximized instead of minimizing the popular mean square error (MSE) to improve the robustness with respect to outliers or impulsive noises. A lot of efforts have been devoted to derive different adaptive algorithms under MCC, but to date, little insight has been gained as to how the MCC solution will be influenced by outliers. In this paper, we investigate this problem and our focus is mainly on the parameter estimation of a simple linear errors-in-variables (EIVs) model with scalar variables. Under some conditions, we derive an upper bound on the absolute value of the estimation error and show that the MCC solution can get very close to the true value of the unknown parameter even with arbitrarily large outliers in both the input and output variables. Illustrative examples are provided to verify and clarify the theory.

The sparse channel estimation problem is drawing increasing attention in broadband wireless communication. Sparsity nature in structure and noise is one of the most important issues in such problems. Researchers have devised several sparsity penalty terms such as zero-attracting (ZA) and correntropy induced metric (CIM) to exploit potential sparse structure information and improve sparse channel estimate accuracy. To combat impulsive (sparse) noises, several adaptive filtering algorithms based on the maximum correntropy criterion (MCC) have been developed, which can achieve excellent performance, especially in heavy-tailed noises. Recently, the concept of mixture correntropy and the maximum mixture correntropy criterion (MMCC) were proposed to further promote the robustness of the MCC against impulsive noises. In this paper, a new robust and sparse adaptive filtering algorithm is developed to estimate the sparse channels with impulsive noises by combining the MMCC and CIM penalty. Thanks to the desirable property of the mixture correntropy, the proposed method behaves quite well with excellent convergence performance. Simulation results show that the new method can outperform several existing methods in sparse channel estimation including the MCC based methods.

Comparing with traditional learning criteria, such as mean square error, the minimum error entropy (MEE) criterion is superior in nonlinear and non-Gaussian signal processing and machine learning. The argument of the logarithm in Renyi's entropy estimator, called information potential (IP), is a popular MEE cost in information theoretic learning. The computational complexity of IP is, however, quadratic in terms of sample number due to double summation. This creates the computational bottlenecks, especially for large-scale data sets. To address this problem, in this paper, we propose an efficient quantization approach to reduce the computational burden of IP, which decreases the complexity from O(N2) to O(MN) with M ≪ N. The new learning criterion is called the quantized MEE (QMEE). Some basic properties of QMEE are presented. Illustrative examples with linear-in-parameter models are provided to verify the excellent performance of QMEE.

Traditional locality preserving projection (LPP) is an excellent linear dimensionality reduction method that can preserve the local structure of the data. The objective function of LPP is based on L2-norm criterion, which results in obvious sensitivity to the outliers. In order to solve this problem, researchers proposed some LPP variants based on the L1-norm (LPP-L1) and the maximum correntropy criterion (LPP-MCC). In this paper, we propose a more robust version of LPP, called LPP-KRSL, whose objective function is based on the kernel risk-sensitive loss (KRSL). The objective function can be efficiently solved via a half-quadratic optimization procedure. The experimental results on both synthetic and real-world data demonstrate that LPP-KRSL is more robust and effective than other LPP methods.

Correntropy is a second order statistical measure in kernel space, which has been successfully applied in robust learning and signal processing. In this paper, we define a nonsecond order statistical measure in kernel space, called the kernel mean- power error (KMPE), including the correntropic loss (C-Loss) as a special case. Some basic properties of KMPE are presented. In particular, we apply the KMPE to extreme learning machine (ELM) and principal component analysis (PCA), and develop two robust learning algorithms, namely ELM-KMPE and PCA-KMPE. Experimental results on synthetic and benchmark data show that the developed algorithms can achieve better performance when compared with some existing methods.

The minimum error entropy (MEE) is an important and highly effective optimization criterion in information theoretic learning (ITL). For regression problems, MEE aims at minimizing the entropy of the prediction error such that the estimated model preserves the information of the data generating system as much as possible. In many real world applications, the MEE estimator can outperform significantly the well-known minimum mean square error (MMSE) estimator and show strong robustness to noises especially when data are contaminated by non-Gaussian (multimodal, heavy tailed, discrete valued, and so on) noises. In this brief, we present some theoretical results on the robustness of MEE. For a one-parameter linear errors-in-variables (EIV) model and under some conditions, we derive a region that contains the MEE solution, which suggests that the MEE estimate can be very close to the true value of the unknown parameter even in presence of arbitrarily large outliers in both input and output variables. Theoretical prediction is verified by an illustrative example.

Currently, colorectal cancer (CRC) already becomes one of the most common cancers worldwide. Though the prognosis of CRC patients is dramatically improved due to the new advanced treatments and medical improvements, the 5-year survival rate for the CRC patient is still low. Thus, we hypothesize that CRC may result from the complicated reasons related to both genetic and environmental factors. For this reason, this study collects such big CRC data with information of genetic variations and environmental exposure for the CRC patients and cancer-free controls that are employed to train and test the predictive CRC model. Our results demonstrate that (1) the explored genetic and environmental biomarkers are validated to cause the CRC by the manually reviewed experimental evidences, (2) the model can efficiently predict the risk of CRC after parameter optimization by the big CRC-related data, (3) our innovated generalized kernel recursive maximum correntropy(GKRMC) algorithm has high predictive power. Finally, we discuss why the GKRMC can outperform the classical regression algorithms and the related future study.

The steady-state excess mean square error (EMSE) of the adaptive filtering under the maximum correntropy criterion (MCC) has been studied. For Gaussian noise case, we establish a fixed-point equation to solve the exact value of the steady-state EMSE, while for non-Gaussian noise case, we derive an approximate analytical expression for the steady-state EMSE, based on a Taylor expansion approach. Simulation results agree with the theoretical calculations quite well.