Attention graph: Learning effective visual features for large-scale image classification

In recent years, the research of deep learning has received extensive attention, and many breakthroughs have been made in various fields. On this basis, a neural network with the attention mechanism has become a research hotspot. In this paper, we try to solve the image classification task by implementing channel and spatial attention mechanism which improve the expression ability of neural network model. Different from previous studies, we propose an attention module consisting of channel attention module (CAM) and spatial attention module (SAM). The proposed module derives attention graphs from channel dimension and spatial dimension respectively, then the input features are selectively learned according to the importance of the features. Besides, this module is lightweight and can be easily integrated into image classification algorithms. In the experiment, we combine the deep residual network model with the attention module and the experimental results show that the proposed method brings higher image classification accuracy. The channel attention module adds weight to the signals on different convolution channels to represent the correlation. For different channels, the higher the weight, the higher the correlation which required more attention. The main function of spatial attention is to capture the most informative part in the local feature graph, which is a supplement to channel attention. We evaluate our proposed module based on the ImageNet-1K and Cifar-100 respectively. Through a large number of comparative experiments, our proposed model achieved outstanding performance.

The convergence of a numerical method for total variation flow

We present a convergence analysis for a finite difference scheme for the time dependent partial different equation called gradient flow associated with the Rudin-Osher-Fetami model. We devise an iterative algorithm to compute the solution of the finite difference scheme and prove the convergence of the iterative algorithm. Finally computational experiments are shown to demonstrate the convergence of the finite difference scheme.

Reshuffle minimisation to improve storage yard operations efficiency

There are many ways to measure the efficiency of the storage area management in container terminals. These include minimising the need for container reshuffle especially at the yard level. In this paper, we consider the container reshuffle problem for stacking and retrieving containers. The problem was represented as a binary integer programming model and solved exactly. However, the exact method was not able to return results for large instances. We therefore considered a heuristic approach. A number of heuristics were implemented and compared on static and dynamic reshuffle problems including four new heuristics introduced here. Since heuristics are known to be instance dependent, we proposed a compatibility test to evaluate how well they work when combined to solve a reshuffle problem. Computational results of our methods on realistic instances are reported to be competitive and satisfactory.

Approximation of noisy data using multivariate splines and finite element methods

We compare a recently proposed multivariate spline based on mixed partial derivatives with two other standard splines for the scattered data smoothing problem. The splines are defined as the minimiser of a penalised least squares functional. The penalties are based on partial differential operators, and are integrated using the finite element method. We compare three methods to two problems: to remove the mixture of Gaussian and impulsive noise from an image, and to recover a continuous function from a set of noisy observations.

Modeling and image quality enhancement for dynamic compressive imaging system

Traditional single-pixel imaging systems are aimed mainly at relatively static or slowly changing targets. When there is relative motion between the imaging system and the target, sizable deviations between the measurement values and the real values can occur and result in poor image quality of the reconstructed target. To solve this problem, a novel dynamic compressive imaging system is proposed. In this system, a single-column digital micro-mirror device is used to modulate the target image, and the compressive measurement values are obtained for each column of the image. Based on analysis of the measurement values, a new recovery model of dynamic compressive imaging is given. Differing from traditional reconstruction results, the measurement values of any column of vectors in the target image can be used to reconstruct the vectors of two adjacent columns at the same time. Contingent upon characteristics of the results, a method of image quality enhancement based on an overlapping average algorithm is proposed. Simulation experiments and analysis show that the proposed dynamic compressive imaging can effectively reconstruct the target image; and that when the moving speed of the system changes within a certain range, the system reconstructs a better original image. The system overcomes the impact of dynamically changing speeds, and affords significantly better performance than traditional compressive imaging.

Optimal parameter selection in Weeks’ method for numerical Laplace transform inversion based on machine learning

The Weeks method for the numerical inversion of the Laplace transform utilizes a Möbius transformation which is parameterized by two real quantities, σ and b. Proper selection of these parameters depends highly on the Laplace space function F( s) and is generally a nontrivial task. In this paper, a convolutional neural network is trained to determine optimal values for these parameters for the specific case of the matrix exponential. The matrix exponential eA is estimated by numerically inverting the corresponding resolvent matrix [Formula: see text] via the Weeks method at [Formula: see text] pairs provided by the network. For illustration, classes of square real matrices of size three to six are studied. For these small matrices, the Cayley-Hamilton theorem and rational approximations can be utilized to obtain values to compare with the results from the network derived estimates. The network learned by minimizing the error of the matrix exponentials from the Weeks method over a large data set spanning [Formula: see text] pairs. Network training using the Jacobi identity as a metric was found to yield a self-contained approach that does not require a truth matrix exponential for comparison.

A Laplace transform finite difference scheme for the Fisher-KPP equation

This paper proposes a numerical approach to the solution of the Fisher-KPP reaction-diffusion equation in which the space variable is developed using a purely finite difference scheme and the time development is obtained using a hybrid Laplace Transform Finite Difference Method (LTFDM). The travelling wave solutions usually associated with the Fisher-KPP equation are, in general, not deemed suitable for treatment using Fourier or Laplace transform numerical methods. However, we were able to obtain accurate results when some degree of time discretisation is inbuilt into the process. While this means that the advantage of using the Laplace transform to obtain solutions for any time t is not fully exploited, the method does allow for considerably larger time steps than is otherwise possible for finite-difference methods.

A bat optimization algorithm with moderate orientation and perturbation of trend

In order to improve the convergence speed and optimization accuracy of the bat algorithm, a bat optimization algorithm with moderate optimal orientation and random perturbation of trend is proposed. The algorithm introduces the nonlinear variation factor into the velocity update formula of the global search stage to maintain a high diversity of bat populations, thereby enhanced the global exploration ability of the algorithm. At the same time, in the local search stage, the position update equation is changed, and a strategy that towards optimal value modestly is used to improve the ability of the algorithm to local search for deep mining. Finally, the adaptive decreasing random perturbation is performed on each bat individual that have been updated in position at each generation, which can improve the ability of the algorithm to jump out of the local extremum, and to balance the early global search extensiveness and the later local search accuracy. The simulating results show that the improved algorithm has a faster optimization speed and higher optimization accuracy.

Non-negative sparse Laplacian regularized latent multi-view subspace clustering

Recently, in the area of artificial intelligence and machine learning, subspace clustering of multi-view data is a research hotspot. The goal is to divide data samples from different sources into different groups. We proposed a new subspace clustering method for multi-view data which termed as Non-negative Sparse Laplacian regularized Latent Multi-view Subspace Clustering (NSL2MSC) in this paper. The method proposed in this paper learns the latent space representation of multi view data samples, and performs the data reconstruction on the latent space. The algorithm can cluster data in the latent representation space and use the relationship of different views. However, the traditional representation-based method does not consider the non-linear geometry inside the data, and may lose the local and similar information between the data in the learning process. By using the graph regularization method, we can not only capture the global low dimensional structural features of data, but also fully capture the nonlinear geometric structure information of data. The experimental results show that the proposed method is effective and its performance is better than most of the existing alternatives.

A parallel in time/spectral collocation combined with finite difference method for the time fractional differential equations

In this article, we consider the numerical solution for the time fractional differential equations (TFDEs). We propose a parallel in time method, combined with a spectral collocation scheme and the finite difference scheme for the TFDEs. The parallel in time method follows the same sprit as the domain decomposition that consists in breaking the domain of computation into subdomains and solving iteratively the sub-problems over each subdomain in a parallel way. Concretely, the iterative scheme falls in the category of the predictor-corrector scheme, where the predictor is solved by finite difference method in a sequential way, while the corrector is solved by computing the difference between spectral collocation and finite difference method in a parallel way. The solution of the iterative method converges to the solution of the spectral method with high accuracy. Some numerical tests are performed to confirm the efficiency of the method in three areas: (i) convergence behaviors with respect to the discretization parameters are tested; (ii) the overall CPU time in parallel machine is compared with that for solving the original problem by spectral method in a single processor; (iii) for the fixed precision, while the parallel elements grow larger, the iteration number of the parallel method always keep constant, which plays the key role in the efficiency of the time parallel method.