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The radiation diffusion problem is usually applied to astrophysics and inertial confinement fusion. It seems that the traditional numerical methods such as finite difference method and finite element method is not efficiency to solve the problem because of its nonlinearity and complex computational domain. In this paper, some fast meshfree methods based on radial basis function are proposed to solve the equilibrium radiation diffusion equation. Because the modeling problem has two nonlinear terms, so we use the successive permutation iteration and linearization methods to approximate the nonlinear terms. Firstly, diffusion terms of the one-dimensional (1D) and two-dimensional (2D) equilibrium radiation diffusion equations are linearized by constructing a successive permutation iteration method for fully-implicit discretization. Then, three kinds of different linearization methods (factorization iteration, Picard–Newton iteration and Richtmyer iteration) are proposed and used to linearization of other nonlinear terms. Finally, the linearized equation is solved numerically by Kansa's method with compactly supported radial basis function. The reliability, accuracy and effectiveness of new methods are verified by 1D and 2D numerical experiments. The advantages of presented method are apparent. They require neither domain nor boundary discretization, and no domain integration is required. New methods are easy for implementation and coding. They not only avoid the complexity of generation mesh, but also solve the equilibrium radiation diffusion equation with high accuracy. [ABSTRACT FROM AUTHOR]

Multi-task learning (MTL) is a joint learning paradigm to improve the generalization performance of the tasks. At present, most of MTL methods are all based on one hypothesis that all learning tasks are related and approximate for joint learning. However, this hypothesis may not be held in some scenarios, which may further lead to the problem of negative transfer. Therefore, in this paper, we aim to deal with the negative transfer problem and simultaneously improve the generalization performance in the joint learning. Combining with the subspace learning, we proposed a calibrated multi-task subspace learning method (CMTSL) under the binary group constraint. With the low-rank constraint on subspaces and the binary group indicator, our model can identify "with whom" one task should share and perform the multi-task inference on the high-dimensional parameter space in the meantime. To better approximate the low-rank constraint, we introduce a capped rank function as the tight relaxation term. Last, an iteration based re-weighted algorithm is proposed to solve our model and the convergence analysis is also proved in theory. Experimental results on benchmark datasets demonstrate the superiority of our model. [ABSTRACT FROM AUTHOR]

As graph technology is widely used in unsupervised dimensionality reduction, many methods automatically construct a full connection graph to learn the structure of data, and then preserve critical information on data in subspace. The construction of a full connection graph with heavy computational complexity, however, is separated from the optimization of transformation matrix. In order to solve significant computational burden, we design anchor-based graph and unify the construction of graph and optimization of transformation matrix into a framework called fast unsupervised embedding learning with anchor-based graph (FUAG) which not only can avoid the impact of noises and redundant features in original space, but also can capture local structure of data in subspace precisely. Our method additionally incorporates the discriminant information of data captured by using trace difference form. Meanwhile, it optimizes the anchor-based graph partitioning problem with Constrained Laplacian Rank in order to ensure that the number of connected components is exactly equal to the number of classes. We also impose ℓ 0 norm constraint on each point to avoid trivial solutions and propose an efficient iterative algorithm. Experimental results on both synthetic and real-world datasets demonstrate the promising performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Finding a consensus embedding from multiple views is the mainstream task in multiview graph-based clustering, in which the key problem is to handle the inconsistence among multiple views. In this article, we consider clustering effectiveness and practical applicability collectively, and propose a parameter-free model to alleviate the inconsistence of multiple views cleverly. To be specific, the proposed model considers the diversities of multiple views as two-layers. The first layer considers the inconsistence among different features of each view and the second layer considers linking the preembeddings of multiple views attentively. By this way, a consensus embedding can be learned via kernel method effectively and the whole learning procedure is parameter-free. To solve the optimization problem involved in the proposed model, we propose an alternative algorithm which is efficient and easy to implement in practice. In the experiments, we evaluate the proposed model on synthetic and real datasets and the experimental results demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

• The proposed model is built on Grassmann manifold. • The proposed model can fully mine the subspace information of views. • The proposed model can get clustering results directly without postprocessing. • The proposed model can ensure the inconsistency of different views. • The proposed model with effectiveness and efficiency can be applied to practice. Multi-view clustering plays an important role in a wide spectrum of applications. In this article, we propose a multi-view clustering approach with adaptive Procrustes on Grassmann manifold (MC-APGM) to overcome the three demerits in existing graph-based multi-view clustering methods, namely, insufficient mining of subspace information of views, a requirement for post-processing, and high computational complexity. Specifically, in the proposed model, the indicator matrix is directly learned from multiple orthogonal spectral embeddings, avoiding the random clustering results caused by post-processing; The orthogonal form of the indicator matrix approximates multiple orthogonal spectral embeddings on the Grassmann manifold, fully uncovering subspace information of views and thus improving clustering performance; Both implicitly and explicitly weighted learning mechanisms are established to capture inconsistencies among different views. Moreover, an efficient algorithm with rigorous convergence guarantee is derived to optimize the proposed model. Finally, experimental results on both toy and real-world datasets demonstrate the effectiveness and efficiency of this proposed method. [ABSTRACT FROM AUTHOR]

This paper introduces a prediction model rooted in sparse representation and transfer learning, with the primary objective of predicting user behavior during rumor propagation. Users' behavior is dynamic, and rumor, rumor-refuting, and rumor-promoting messages interact dynamically, according to the model. Firstly, this paper proposes to compensate for the low performance of propagation prediction models due to data sparsity at the beginning of rumor topics' lifes. Transfer learning is used to compensate for the data sparsity problem at the beginning of the topic. To map the rumor topic space effectively, a low-rank dense vectorization algorithm based on sparse representation is proposed. Finally, to mine the potential impact of multiple types of information on users, a model based on three-party game theory is constructed. It considers the complex interaction between rumor, rumor-refuting, and rumor-promoting information in the propagation of rumor. Additionally, this paper develops a model of dynamic user behavior prediction using Rumor-Attention-Mechanism-Graph-Attention (RAM-GAT) to predict rumor propagation. Experiments demonstrate that our model can effectively mine the interaction influence between multiple types of information. It can accurately predict user behavior when initial data is insufficient. In addition, rumor propagation patterns and trends are revealed. • A user behavior prediction model is proposed. • Sparse representation can be used to express the rumor feature space. • The complex influences that influence user behavior are quantified. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel feature selection approach, named unsupervised feature selection with constrained $\ell _{2,0}$ -norm (row-sparsity constrained) and optimized graph (RSOGFS), which unifies feature selection and similarity matrix construction into a general framework instead of independently performing the two-stage process; thus, the similarity matrix preserving the local manifold structure of data can be determined adaptively. Unlike those sparse learning-based feature selection methods that can only solve the relaxation or approximation problems by introducing sparsity regularization term into the objective function, the proposed method directly tackles the original $\ell _{2,0}$ -norm constrained problem to achieve group feature selection. Two optimization strategies are provided to solve the original sparse constrained problem. The convergence and approximation guarantees for the new algorithms are rigorously proved, and the computational complexity and parameter determination are theoretically analyzed. Experimental results on real-world data sets show that the proposed method for solving a nonconvex problem is superior to the state of the arts for solving the relaxed or approximate convex problems. [ABSTRACT FROM AUTHOR]

Feature selection has been widely used in machine learning for a long time. In this paper, we propose a supervised local sparse discriminative feature selection method named LSDFS to obtain sparse features by imposing ℓ 2 , 0 -norm constraint on transformation matrix. Differently from traditional approaches, our method does not require approximation or relaxation schemes, such as ℓ 2 , p -norm to solve long-standing challenge. Our method is based on the trace difference form of Linear Discriminant Analysis (LDA), which can efficiently obtain discriminative information in low-dimensional space. In order to explore the local structure of data which contains more discriminative information, we adopt a sparse connections graph between anchor points and data points instead of fully-connected graph with time-consuming, and add a decay parameter to avoid trivial solutions, making the model more precisely. Extensive experiments conducted on synthetic datasets and several real-world datasets have demonstrated the advantages of our method. [ABSTRACT FROM AUTHOR]

Deep metric learning aims to learn a non-linear function that maps raw-data to a discriminative lower-dimensional embedding space, where semantically similar samples have larger similarity than dissimilar ones. Most existing approaches process each raw-data in two steps, by mapping the raw-data to a higher-dimensional feature space via a fixed backbone, followed by mapping the higher-dimensional feature space to a lower-dimensional embedding space via a linear layer. This paradigm, however, inevitably leads to a Generalization Bottleneck (GB) problem. Specifically, GB refers to a limitation that the generalization capacity of lower-dimensional embedding space is inferior to the higher-dimensional feature space in the test stage. To mitigate the capacity gap between feature space and embedding space, we propose to introduce a fully-learnable module, dubbed Relational Knowledge Preserving (RKP), that improves the generalization capacity of lower-dimensional embedding space by transferring the mutual similarity of instances. Our proposed RKP module can be integrated into a general deep metric learning approach. And, experiments conducted on different benchmarks show that it can significantly improve the performance of original model. [ABSTRACT FROM AUTHOR]

Hashing, a widely-studied tool to the approximate nearest neighbor search, aims to embed samples as compact binary representations. Current approaches to this issue generally seek a low-dimensional Hamming Space where representations are discrete and have smaller intra-class distance and larger inter-class distance. As a result, the performance is often limited by the discrete constraint. In this work, we propose to seek an angularly discriminative Embedding Space where representations are continuous and have smaller intra-class angular margin and larger inter-class angular margin. For our goal is to learn continuous representations rather than discrete hash codes, the problems caused by discrete constraint can be avoided. Besides, in order to further reduce the gap between Embedding Space and Hamming Space, we introduce an additional coordinate-constraint for representations. Our method is simple yet effective. Extensive experiments on the image retrieval task show that it achieves encouraging results on four benchmark datasets. Furthermore, the success of our proposed method demonstrates that leveraging the progress made in representation learning to improve hashing is promising in future. [ABSTRACT FROM AUTHOR]

Linear Discriminant Analysis (LDA) is one of most important methods in dimensionality reduction domain, which is limited with Gaussian assumption. Because of the complexity of real data, data often presents non-Gaussian distribution that points in same class can be divided into several sub-clusters and center point is not enough to describe the distribution of data. In order to solve non-Gaussian data, LDA-based methods consider local structure information through measuring each pairwise distance of full connection graph. However, the strategy of establishing fully-connected graph is at expense of high computational complexity and limits it practical and industrial applications. We propose a Fast Local Representation Learning (FLRL) method which leverages anchor points to establish anchor-based graph and uses similarity matrix to depict the relationships of each pairwise connections. Notably, to avoid the affect of noises and redundant features in original space, anchor points and similarity matrix are updated alternately in subspace that local structure of data will be more precise to learn. Extensive pattern classification and image retrieval experiments on several synthetic datasets, well-known datasets and deep features datasets demonstrate the advantages of our method over the state-of-the-art methods. Our source code available on : https://github.com/superzcy/FLRL. [ABSTRACT FROM AUTHOR]

Matrix completion from very limited information is an important machine learning topic, and has received extensive attention in various scientific applications. Matrix completion aims at finding a low-rank matrix to approximate the incomplete data matrix. However, noise in the data matrix may degrade the performance of the existing matrix completion algorithms, especially if there are different types of noise. In this paper, we proposed a robust matrix completion method with column outliers and sparse noise. The incomplete matrix is iteratively divided into low-rank and sparse parts. The ℓ 2 , 1 -norm based objective function makes the recovered matrix keeps a low-rank structure and lets the algorithm robust to column outliers, while the regularization term based on ℓ 1 -norm can alleviate the influence of sparse noise. Besides, a vector completion algorithm has been proposed to help us estimate the missing entries of the out-of-sample vectors. Moreover, the proposed model can be optimized by an efficient iterative re-weighted method, without introducing any additional parameters, while the adaptive weights obtained in the optimization process can help us detect column outliers. Both theoretical analysis and experiments based on synthetic datasets and real world datasets are implemented to validate the performance of the proposed method. [ABSTRACT FROM AUTHOR]