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Video summarization is an effective way to facilitate video searching and browsing. Most of existing systems employ encoder-decoder based recurrent neural networks, which fail to explicitly diversify the system-generated summary frames while requiring intensive computations. In this paper, we propose an efficient convolutional neural network architecture for video SUMmarization via Global Diverse Attention called SUM-GDA, which adapts attention mechanism in a global perspective to consider pairwise temporal relations of video frames. Particularly, the GDA module has two advantages: 1) it models the relations within paired frames as well as the relations among all pairs, thus capturing the global attention across all frames of one video; 2) it reflects the importance of each frame to the whole video, leading to diverse attention on these frames. Thus, SUM-GDA is beneficial for generating diverse frames to form satisfactory video summary. Extensive experiments on three data sets, i.e., SumMe, TVSum, and VTW, have demonstrated that SUM-GDA and its extension outperform other competing state-of-the-art methods with remarkable improvements. In addition, the proposed models can be run in parallel with significantly less computational costs, which helps the deployment in highly demanding applications., Comment: 12 pages, 8 figures

An adaptive BDF2 implicit time-stepping method is analyzed for the phase field crystal model. The suggested method is proved to preserve a modified energy dissipation law at the discrete levels if the time-step ratios $r_k:=\tau_k/\tau_{k-1}<3.561$, a recent zero-stability restriction of variable-step BDF2 scheme for ordinary differential problems. By using the discrete orthogonal convolution kernels and the corresponding convolution inequalities, an optimal $L^2$ norm error estimate is established under the weak step-ratio restriction $0

A time-fractional Allen-Cahn equation with volume constraint is first proposed by introducing a nonlocal time-dependent Lagrange multiplier. Adaptive linear second-order energy stable schemes are developed for the proposed model by combining invariant energy quadratization and scalar auxiliary variable approaches with the recent L1$^{+}$ formula. The new developed methods are proved to be volume-preserving and unconditionally energy stable on arbitrary nonuniform time meshes. The accelerated algorithm and adaptive time strategy are employed in numerical implement. Numerical results show that the proposed algorithms are computationally efficient in multi-scale simulations, and appropriate for accurately resolving the intrinsically initial singularity of solution and for efficiently capturing the fast dynamics away initial time., Comment: 21 pages, 75 figures, 3 tables

A fourth-order compact scheme is proposed for a fourth-order subdiffusion equation with the first Dirichlet boundary conditions. The fourth-order problem is firstly reduced into a couple of spatially second-order system and we use an averaged operator to construct a fourth-order spatial approximation. This averaged operator is compact since it involves only two grid points for the derivative boundary conditions. The L1 formula on irregular mesh is considered for the Caputo fractional derivative, so we can resolve the initial singularity of solution by putting more grid points near the initial time. The stability and convergence are established by using three theoretical tools: a complementary discrete convolution kernel, a discrete fractional Gronwall inequality and an error convolution structure. Some numerical experiments are reported to demonstrate the accuracy and efficiency of our method., Comment: 20 pages

Adaptive second-order Crank-Nicolson time-stepping methods using the recent scalar auxiliary variable (SAV) approach are developed for the time-fractional Molecular Beam Epitaxial models with Caputo's derivative. Based on the piecewise linear interpolation, the Caputo's fractional derivative is approximated by a novel second-order formula, which is naturally suitable for a general class of nonuniform meshes and essentially preserves the positive semi-definite property of integral kernel. The resulting Crank-Nicolson SAV time-stepping schemes are unconditional energy stable on nonuniform time meshes, and are computationally efficient in multiscale time simulations when combined with adaptive time steps, such as are appropriate for accurately resolving the intrinsically initial singularity of solution and for efficiently capturing fast dynamics away from the initial time. Numerical examples are presented to show the effectiveness of our methods., Comment: 23 pages, 23 figures

Two fast L1 time-stepping methods, including the backward Euler and stabilized semi-implicit schemes, are suggested for the time-fractional Allen-Cahn equation with Caputo's derivative. The time mesh is refined near the initial time to resolve the intrinsically initial singularity of solution, and unequal time-steps are always incorporated into our approaches so that an adaptive time-stepping strategy can be used in long-time simulations. It is shown that the proposed schemes using the fast L1 formula preserve the discrete maximum principle. Sharp error estimates reflecting the time regularity of solution are established by applying the discrete fractional Gr\"{o}nwall inequality and global consistency analysis. Numerical experiments are presented to show the effectiveness of our methods and to confirm our analysis., Comment: 19 pages, 8 figures

Solving mathematical word problems (MWPs) automatically is challenging, primarily due to the semantic gap between human-readable words and machine-understandable logics. Despite the long history dated back to the1960s, MWPs have regained intensive attention in the past few years with the advancement of Artificial Intelligence (AI). Solving MWPs successfully is considered as a milestone towards general AI. Many systems have claimed promising results in self-crafted and small-scale datasets. However, when applied on large and diverse datasets, none of the proposed methods in the literature achieves high precision, revealing that current MWP solvers still have much room for improvement. This motivated us to present a comprehensive survey to deliver a clear and complete picture of automatic math problem solvers. In this survey, we emphasize on algebraic word problems, summarize their extracted features and proposed techniques to bridge the semantic gap and compare their performance in the publicly accessible datasets. We also cover automatic solvers for other types of math problems such as geometric problems that require the understanding of diagrams. Finally, we identify several emerging research directions for the readers with interests in MWPs., Comment: 18 pages, 5 figures

Low-rank learning has attracted much attention recently due to its efficacy in a rich variety of real-world tasks, e.g., subspace segmentation and image categorization. Most low-rank methods are incapable of capturing low-dimensional subspace for supervised learning tasks, e.g., classification and regression. This paper aims to learn both the discriminant low-rank representation (LRR) and the robust projecting subspace in a supervised manner. To achieve this goal, we cast the problem into a constrained rank minimization framework by adopting the least squares regularization. Naturally, the data label structure tends to resemble that of the corresponding low-dimensional representation, which is derived from the robust subspace projection of clean data by low-rank learning. Moreover, the low-dimensional representation of original data can be paired with some informative structure by imposing an appropriate constraint, e.g., Laplacian regularizer. Therefore, we propose a novel constrained LRR method. The objective function is formulated as a constrained nuclear norm minimization problem, which can be solved by the inexact augmented Lagrange multiplier algorithm. Extensive experiments on image classification, human pose estimation, and robust face recovery have confirmed the superiority of our method., Comment: 14 pages, 7 figures, accepted to appear in IEEE Transactions on Cybernetics

As compared to simple actions, activities are much more complex, but semantically consistent with a human's real life. Techniques for action recognition from sensor generated data are mature. However, there has been relatively little work on bridging the gap between actions and activities. To this end, this paper presents a novel approach for complex activity recognition comprising of two components. The first component is temporal pattern mining, which provides a mid-level feature representation for activities, encodes temporal relatedness among actions, and captures the intrinsic properties of activities. The second component is adaptive Multi-Task Learning, which captures relatedness among activities and selects discriminant features. Extensive experiments on a real-world dataset demonstrate the effectiveness of our work., Comment: IJCAI 2015

Many aesthetic models in computer vision suffer from two shortcomings: 1) the low descriptiveness and interpretability of those hand-crafted aesthetic criteria (i.e., nonindicative of region-level aesthetics), and 2) the difficulty of engineering aesthetic features adaptively and automatically toward different image sets. To remedy these problems, we develop a deep architecture to learn aesthetically-relevant visual attributes from Flickr1, which are localized by multiple textual attributes in a weakly-supervised setting. More specifically, using a bag-ofwords (BoW) representation of the frequent Flickr image tags, a sparsity-constrained subspace algorithm discovers a compact set of textual attributes (e.g., landscape and sunset) for each image. Then, a weakly-supervised learning algorithm projects the textual attributes at image-level to the highly-responsive image patches at pixel-level. These patches indicate where humans look at appealing regions with respect to each textual attribute, which are employed to learn the visual attributes. Psychological and anatomical studies have shown that humans perceive visual concepts hierarchically. Hence, we normalize these patches and feed them into a five-layer convolutional neural network (CNN) to mimick the hierarchy of human perceiving the visual attributes. We apply the learned deep features on image retargeting, aesthetics ranking, and retrieval. Both subjective and objective experimental results thoroughly demonstrate the competitiveness of our approach.

Aerial image categorization plays an indispensable role in remote sensing and artificial intelligence. In this paper, we propose a new aerial image categorization framework, focusing on organizing the local patches of each aerial image into multiple discriminative subgraphs. The subgraphs reflect both the geometric property and the color distribution of an aerial image. First, each aerial image is decomposed into a collection of regions in terms of their color intensities. Thereby region connected graph (RCG), which models the connection between the spatial neighboring regions, is constructed to encode the spatial context of an aerial image. Second, a subgraph mining technique is adopted to discover the frequent structures in the RCGs constructed from the training aerial images. Thereafter, a set of refined structures are selected among the frequent ones toward being highly discriminative and low redundant. Lastly, given a new aerial image, its sub-RCGs corresponding to the refined structures are extracted. They are further quantized into a discriminative vector for SVM classification. Thorough experimental results validate the effectiveness of the proposed method. In addition, the visualized mined subgraphs show that the discriminative topologies of each aerial image are discovered.