Predicting the trajectory of pedestrians in crowd scenarios is indispensable in self-driving or autonomous mobile robot field because estimating the future locations of pedestrians around is beneficial for policy decision to avoid collision. It is a challenging issue because humans have different walking motions, and the interactions between humans and objects in the current environment, especially between humans themselves, are complex. Previous researchers focused on how to model human-human interactions but neglected the relative importance of interactions. To address this issue, a novel mechanism based on correntropy is introduced. The proposed mechanism not only can measure the relative importance of human-human interactions but also can build personal space for each pedestrian. An interaction module including this data-driven mechanism is further proposed. In the proposed module, the data-driven mechanism can effectively extract the feature representations of dynamic human-human interactions in the scene and calculate the corresponding weights to represent the importance of different interactions. To share such social messages among pedestrians, an interaction-aware architecture based on long short-term memory network for trajectory prediction is designed. Experiments are conducted on two public datasets. Experimental results demonstrate that our model can achieve better performance than several latest methods with good performance.

In this paper, we propose a novel probabilistic variant of iterative closest point (ICP) dubbed as CoBigICP. The method leverages both local geometrical information and global noise characteristics. Locally, the 3D structure of both target and source clouds are incorporated into the objective function through bidirectional correspondence. Globally, error metric of correntropy is introduced as noise model to resist outliers. Importantly, the close resemblance between normal-distributions transform (NDT) and correntropy is revealed. To ease the minimization step, an on-manifold parameterization of the special Euclidean group is proposed. Extensive experiments validate that CoBigICP outperforms several well-known and state-of-the-art methods.

Recent studies have utilized sparse classifications to predict categorical variables from high-dimensional brain activity signals to expose human's intentions and mental states, selecting the relevant features automatically in the model training process. However, existing sparse classification models will likely be prone to the performance degradation which is caused by noise inherent in the brain recordings. To address this issue, we aim to propose a new robust and sparse classification algorithm in this study. To this end, we introduce the correntropy learning framework into the automatic relevance determination based sparse classification model, proposing a new correntropy-based robust sparse logistic regression algorithm. To demonstrate the superior brain activity decoding performance of the proposed algorithm, we evaluate it on a synthetic dataset, an electroencephalogram (EEG) dataset, and a functional magnetic resonance imaging (fMRI) dataset. The extensive experimental results confirm that not only the proposed method can achieve higher classification accuracy in a noisy and high-dimensional classification task, but also it would select those more informative features for the decoding scenarios. Integrating the correntropy learning approach with the automatic relevance determination technique will significantly improve the robustness with respect to the noise, leading to more adequate robust sparse brain decoding algorithm. It provides a more powerful approach in the real-world brain activity decoding and the brain-computer interfaces.

As an algorithm based on deep reinforcement learning, Proximal Policy Optimization (PPO) performs well in many complex tasks and has become one of the most popular RL algorithms in recent years. According to the mechanism of penalty in surrogate objective, PPO can be divided into PPO with KL Divergence (KL-PPO) and PPO with Clip function(Clip-PPO). Clip-PPO is widely used in a variety of practical scenarios and has attracted the attention of many researchers. Therefore, many variations have also been created, making the algorithm better and better. However, as a more theoretical algorithm, KL-PPO was neglected because its performance was not as good as CliP-PPO. In this article, we analyze the asymmetry effect of KL divergence on PPO's objective function , and give the inequality that can indicate when the asymmetry will affect the efficiency of KL-PPO. Proposed PPO with Correntropy Induced Metric algorithm(CIM-PPO) that use the theory of correntropy(a symmetry metric method that was widely used in M-estimation to evaluate two distributions' difference)and applied it in PPO. Then, we designed experiments based on OpenAIgym to test the effectiveness of the new algorithm and compare it with KL-PPO and CliP-PPO.

The goal of tensor completion is to recover a tensor from a subset of its entries, often by exploiting its low-rank property. Among several useful definitions of tensor rank, the low-tubal-rank was shown to give a valuable characterization of the inherent low-rank structure of a tensor. While some low-tubal-rank tensor completion algorithms with favorable performance have been recently proposed, these algorithms utilize second-order statistics to measure the error residual, which may not work well when the observed entries contain large outliers. In this paper, we propose a new objective function for low-tubal-rank tensor completion, which uses correntropy as the error measure to mitigate the effect of the outliers. To efficiently optimize the proposed objective, we leverage a half-quadratic minimization technique whereby the optimization is transformed to a weighted low-tubal-rank tensor factorization problem. Subsequently, we propose two simple and efficient algorithms to obtain the solution and provide their convergence and complexity analysis. Numerical results using both synthetic and real data demonstrate the robust and superior performance of the proposed algorithms.

Stemming from information-theoretic learning, the correntropy criterion and its applications to machine learning tasks have been extensively explored and studied. Its application to regression problems leads to the robustness enhanced regression paradigm -- namely, correntropy based regression. Having drawn a great variety of successful real-world applications, its theoretical properties have also been investigated recently in a series of studies from a statistical learning viewpoint. The resulting big picture is that correntropy based regression regresses towards the conditional mode function or the conditional mean function robustly under certain conditions. Continuing this trend and going further, in the present study, we report some new insights into this problem. First, we show that under the additive noise regression model, such a regression paradigm can be deduced from minimum distance estimation, implying that the resulting estimator is essentially a minimum distance estimator and thus possesses robustness properties. Second, we show that the regression paradigm, in fact, provides a unified approach to regression problems in that it approaches the conditional mean, the conditional mode, as well as the conditional median functions under certain conditions. Third, we present some new results when it is utilized to learn the conditional mean function by developing its error bounds and exponential convergence rates under conditional $(1+\epsilon)$-moment assumptions. The saturation effect on the established convergence rates, which was observed under $(1+\epsilon)$-moment assumptions, still occurs, indicating the inherent bias of the regression estimator. These novel insights deepen our understanding of correntropy based regression, help cement the theoretic correntropy framework, and also enable us to investigate learning schemes induced by general bounded nonconvex loss functions.

As an effective and efficient discriminative learning method, Broad Learning System (BLS) has received increasing attention due to its outstanding performance in various regression and classification problems. However, the standard BLS is derived under the minimum mean square error (MMSE) criterion, which is, of course, not always a good choice due to its sensitivity to outliers. To enhance the robustness of BLS, we propose in this work to adopt the maximum correntropy criterion (MCC) to train the output weights, obtaining a correntropy based broad learning system (C-BLS). Thanks to the inherent superiorities of MCC, the proposed C-BLS is expected to achieve excellent robustness to outliers while maintaining the original performance of the standard BLS in Gaussian or noise-free environment. In addition, three alternative incremental learning algorithms, derived from a weighted regularized least-squares solution rather than pseudoinverse formula, for C-BLS are developed.With the incremental learning algorithms, the system can be updated quickly without the entire retraining process from the beginning, when some new samples arrive or the network deems to be expanded. Experiments on various regression and classification datasets are reported to demonstrate the desirable performance of the new methods.

In recent years, correntropy has been seccessfully applied to robust adaptive filtering to eliminate adverse effects of impulsive noises or outliers. Correntropy is generally defined as the expectation of a Gaussian kernel between two random variables. This definition is reasonable when the error between the two random variables is symmetrically distributed around zero. For the case of asymmetric error distribution, the symmetric Gaussian kernel is however inappropriate and cannot adapt to the error distribution well. To address this problem, in this letter we propose a new variant of correntropy, named asymmetric correntropy, which uses an asymmetric Gaussian model as the kernel function. In addition, a robust adaptive filtering algorithm based on asymmetric correntropy is developed and its steadystate convergence performance is analyzed. Simulations are provided to confirm the theoretical results and good performance of the proposed algorithm.

As a novel similarity measure that is defined as the expectation of a kernel function between two random variables, correntropy has been successfully applied in robust machine learning and signal processing to combat large outliers. The kernel function in correntropy is usually a zero-mean Gaussian kernel. In a recent work, the concept of mixture correntropy (MC) was proposed to improve the learning performance, where the kernel function is a mixture Gaussian kernel, namely a linear combination of several zero-mean Gaussian kernels with different widths. In both correntropy and mixture correntropy, the center of the kernel function is, however, always located at zero. In the present work, to further improve the learning performance, we propose the concept of multi-kernel correntropy (MKC), in which each component of the mixture Gaussian kernel can be centered at a different location. The properties of the MKC are investigated and an efficient approach is proposed to determine the free parameters in MKC. Experimental results show that the learning algorithms under the maximum multi-kernel correntropy criterion (MMKCC) can outperform those under the original maximum correntropy criterion (MCC) and the maximum mixture correntropy criterion (MMCC).

Correntropy is a local similarity measure defined in kernel space and the maximum correntropy criterion (MCC) has been successfully applied in many areas of signal processing and machine learning in recent years. The kernel function in correntropy is usually restricted to the Gaussian function with center located at zero. However, zero-mean Gaussian function may not be a good choice for many practical applications. In this study, we propose an extended version of correntropy, whose center can locate at any position. Accordingly, we propose a new optimization criterion called maximum correntropy criterion with variable center (MCC-VC). We also propose an efficient approach to optimize the kernel width and center location in MCC-VC. Simulation results of regression with linear in parameters (LIP) models confirm the desirable performance of the new method.