Data loss is a common problem in intelligent transportation systems (ITSs). And the tensor‐based interpolation algorithm has obvious superiority in multidimensional data interpolation. In this paper, a Bayesian robust tensor decomposition method (MBRTF) based on the Markov chain Monte Carlo (MCMC) algorithm is proposed. The underlying low CANDECOMP/PARAFAC (CP) rank tensor captures the global information, and the sparse tensor captures local information (also regarded as anomalous data), which achieves a reliable prediction of missing terms. The low CP rank tensor is modeled by linear interrelationships among multiple latent factors, and the sparsity of the columns on the latent factors is achieved through a hierarchical prior approach, while the sparse tensor is modeled by a hierarchical view of the Student‐ t distribution. It is a challenge for traditional tensor‐based interpolation methods to maintain a stable performance under different missing rates and nonrandom missing (NM) scenarios. The MBRTF algorithm is an effective multiple interpolation algorithm that not only derives unbiased point estimates but also provides a robust method for the uncertainty measures of these missing values.

The identification of important nodes (vertexes) in multilayer networks has aroused many scholars’ attention and various centrality methods have deen developed. However, the current centralities ignore the impact of community structure on node importance. In this article, we define a community-based centrality for finding key vertexes in multilayer networks, referred to as the CBCM. We first construct a multilayer network model with interlayer edges, which is represented by a fourth-order tensor. Based on the fourth-order tensor, we develop a centrality, called PR_BIS, to measure the importance of vertexes and network layers in multilayer networks, simultaneously. CBCM determines the importance of a vertex in each network layer by combining the following three factors: the PageRank centrality score of the vertex, the importance of the community where the vertex is located, and the ability of the vertex within a community to affect vertexes in other communities within two steps. Based on the importance of all the network layers measured by PR_BIS centrality, we perform weighted fusion for the importance of a vertex in all network layers to obtain the importance of the vertex in multilayer networks. Finally, numerical experiments are performed on several multilayer networks to verify the effectiveness and superiority of CBCM and PR_BIS.

Abstract The nuclear norm minimization (NNM) is a special non‐convex rank minimization convex relaxation scheme for image denoising and object detection that requires denoising and background subtraction. Considering excessive shrinkage of rank components and equal treatment of different rank components, NNM is extended to the weighted Schatten‐ p norm minimization (WSNM) with weights assigned to different singular values. In this paper, a multi‐channel weighted truncated WSNM model based on the WSNM optimization framework is proposed for RGB colour image denoising. On the basis of different noise intensities and non‐local self‐similar patches of each channel of the colour image itself, the proposed model is improved significantly by the optimization methods of superposition and truncation. Meanwhile, it can be generalized to the tensor space and employed to the infrared imaging target detection based on the spatial‐temporal tensor model for the first time. And the efficient alternating direction multiplier‐based algorithms are developed to solve the proposed model and the accuracy of the algorithm is effectively improved by choosing an adaptive threshold. Extensive experiments on real infrared data verified the proposed method state‐of‐the‐arts and effectiveness.

The objective of motion capture (mocap) data completion is to recover missing measurement of the body markers from mocap. It becomes increasingly challenging as the missing ratio and duration of mocap data grow. Traditional approaches usually recast this problem as a low-rank matrix approximation problem based on the nuclear norm. However, the nuclear norm defined as the sum of all the singular values of a matrix is not a good approximation to the rank of mocap data. This paper proposes a novel approach to solve mocap data completion problem by adopting a new matrix norm, called truncated nuclear norm. An efficient iterative algorithm is designed to solve this problem based on the augmented Lagrange multiplier. The convergence of the proposed method is proved mathematically under mild conditions. To demonstrate the effectiveness of the proposed method, various comparative experiments are performed on synthetic data and mocap data. Compared to other methods, the proposed method is more efficient and accurate.

Due to the well-known limitations of diffusion tensor imaging, high angular resolution diffusion imaging (HARDI) is used to characterize non-Gaussian diffusion processes. One approach to analyzing HARDI data is to model the apparent diffusion coefficient (ADC) with higher order diffusion tensors. The diffusivity function is positive semidefinite. In the literature, some methods have been proposed to preserve positive semidefiniteness of second order and fourth order diffusion tensors. None of them can work for arbitrarily high order diffusion tensors. In this paper, we propose a comprehensive model to approximate the ADC profile by a positive semidefinite diffusion tensor of either second or higher order. We call this the positive semidefinite diffusion tensor (PSDT) model. PSDT is a convex optimization problem with a convex quadratic objective function constrained by the nonnegativity requirement on the smallest Z-eigenvalue of the diffusivity function. The smallest Z-eigenvalue is a computable measure of the extent of positive definiteness of the diffusivity function. We also propose some other invariants for the ADC profile analysis. Experiment results show that higher order tensors could improve the estimation of anisotropic diffusion and that the PSDT model can depict the characterization of diffusion anisotropy which is consistent with known neuroanatomy.