International Journal of Wavelets, Multiresolution and Information Processing

Stochastic optimization on large-scale machine learning problems has been developed dramatically since stochastic gradient methods with variance reduction technique were introduced. Several stochastic second-order methods, which approximate curvature information by the Hessian in stochastic setting, have been proposed for improvements. In this paper, we introduce a Stochastic Sub-Sampled Newton method with Variance Reduction (S2NMVR), which incorporates the sub-sampled Newton method and stochastic variance-reduced gradient. For many machine learning problems, the linear time Hessian-vector production provides evidence to the computational efficiency of S2NMVR. We then develop two variations of S2NMVR that preserve the estimation of Hessian inverse and decrease the computational cost of Hessian-vector product for nonlinear problems.

Many multi-object tracking methods have been proposed to solve the computer vision problem which has been attracting significant attentions because of the significant appearance changes caused by deformation, abrupt motion, background clutter and occlusion. In this paper, hybrid deformable convolution neural networks with frame-pair input and deformable layers for multi-object tracking are presented. The object tracking method trained using two successive frames can predict the centers of searching windows as the locations of tracked targets to improve the accuracy and robustness of object tracking. Histogram of Oriented Gradient and CNN features are extracted as appearance features to measure similarities between objects. Kalman filter and Hungarian algorithm are used to create tracklets association which indicates the location and the trajectories of tracked targets. To solve the problem of object transformation, we construct a novel sampling strategy for off-line training with the idea of augmenting the special sampling locations in the convolution layers and pooling layers with additional offsets. Experiments on the popular challenging datasets show that the proposed tracking system performs on par with recently developed generic multi-object tracking methods, but effective for dense geometric transformation objects and with much less memory. In addition, the proposed tracking system can run in a speed of over 75 (24) fps with a GPU (CPU), much faster than most deep networks-based trackers.

Recently, quasi-Monte Carlo (QMC) rules for multivariate integration in some weighted Sobolev spaces of functions defined over unit cubes ${[0,1]}^m$, products of $m$ copies of the simplex ${𝕋}^d\subset {ℝ}^d$ and products of $m$ copies of the unit sphere ${𝕊}^d\subset {ℝ}^{d+1}$ have been well-studied in the literature. In this paper, we consider QMC tractability of integrals of functions defined over product of $m$ copies of the ball ${𝔹}^d\subset {ℝ}^d$. The space is a tensor product of $m$ reproducing kernel Hilbert spaces defined by positive and uniformly bounded weights ${\gamma }_{m,j}$ for $j=1,2,\dots ,m$. We obtain matching necessary and sufficient conditions in terms of this weights for various notions of QMC tractability, including strong polynomial tractability, polynomial tractability, quasi-polynomial tractability, uniformly weak tractability and $(s,t)$-weak tractability.

In blind image deconvolution, priors are often leveraged to constrain the solution space, so as to alleviate the under-determinacy. Priors which are trained separately from the task of deconvolution tend to be unstable. We propose the Golf Optimizer, a novel but simple form of network that learns deep priors from data with better propagation behavior. Like playing golf, our method first estimates an aggressive propagation towards optimum using one network, and recurrently applies a residual CNN to learn the gradient of prior for delicate correction on restoration. Experiments show that our network achieves competitive performance on GoPro dataset, and our model is extremely lightweight compared with the state-of-the-art works.

The rolling guidance filtering (RGF) has a good characteristic which can smooth texture and preserve the edges, and non-subsampled shearlet transform (NSST) has the features of translation invariance and direction selection based on which a new infrared and visible image fusion method is proposed. Firstly, the rolling guidance filter is used to decompose infrared and visible images into the base and detail layers. Then, the NSST is utilized on the base layer to get the high-frequency coefficients and low-frequency coefficients. The fusion of low-frequency coefficients uses visual saliency map as a fusion rule, and the coefficients of the high-frequency subbands use gradient domain guided filtering (GDGF) and improved Laplacian sum to fuse coefficients. Finally, the fusion of the detail layers combines phase congruency and gradient domain guided filtering as the fusion rule. As a result, the proposed method can not only extract the infrared targets, but also fully preserves the background information of the visible images. Experimental results indicate that our method can achieve a superior performance compared with other fusion methods in both subjective and objective assessments.

Handwriting recognition is a very active research in the machine learning community. In this paper, we tackled two important applications: handwritten digit recognition and Signature verification using convolution neural network (CNN). Signature is one of the most popular personal attributes for authentication. It is basic, shabby and adequate to individuals, official associations and courts. This paper focuses on offline signature verification (SV). It is a kind of a classification problem, which classifies the signature as genuine, or forgery. We use CNN in two types of datasets: the MNIST database, and UTSIG database. In order to obtain better accuracy, we propose to preprocess the data in the wavelet domain and in the Gabor filter combining the outputs of both CNN. This combination resulted in higher recognition accuracy compared to other techniques.

Modal regression aims at learning the conditional mode function, which is different from the traditional least-squares for approximating the conditional mean function. Due to its robust to complex noise and outliers, modal regression has attracted increasing attention recently in statistics and machine learning community. However, most of the previous modal regression models are limited to learning framework with data-independent hypothesis spaces. Usually, the data-dependent hypothesis spaces can provide much flexibility and adaptivity for many learning problems. By employing data-dependent hypothesis spaces, we propose a new regularized modal regression and establish its generalization error analysis. Data experiments demonstrate the competitive performance of the proposed model over the related least-squares regression.

This paper presents a simple multiple kernel learning framework for complicated data modeling, where randomized multi-scale Gaussian kernels are employed as base kernels and a $l_1$-norm regularizer is integrated as a sparsity constraint for the solution. The randomly pre-chosen scales provide random basis functions with diversity approximation ability and lead to extremely low computational complexity in finding the optimal solution. The random parameter appearing in the probability distribution and the regularizing factor are decided by the training data with cross validation techniques and the combination weights are solved by a well-posed linear system. Comparison experiments on one function approximation and three real-world regression problems of six learning algorithms are carried out. The way that multi-scale kernels fit the objective function is illustrated, the sparsity and the system robustness analysis with respect to the regularizing factor are given.

This work focuses on image sparse recovery problem. First, we construct a new kind of pseudo-directional multilevel system, which forms a tight frame in $L^2(R^2)$. Different from the widely used directional multilevel transforms curvelts and shearlets, whose subbands are neat and nonsensitive to the energy distribution of signals in Fourier domain, the proposed multilevel system is designed to have subbands with specific shape, the shape is oriented by the energy distribution. Thus, we can obtain more sparse structure of signals and low computation for the multilevel transform. Moreover, to detect directional singularities of signals effectively, a local directional gradient operator is introduced to catch the signal variation along different directions, it can be seen as the generalized gradient. Then we proposed a simple but efficient method for image sparse recovery, the split Bregman algorithm is employed to solve the proposed convex model which guarantees the global optimal solution. Some contrast experiments suggest that the sparse recovery by the proposed method performs well in artifacts’ suppressing and details’ extraction.

To efficiently improve the accuracy of hyperspectral image (HSI) classification, the spatial information is usually fused with spectral information so that the classification performance can be enhanced. In this paper, we propose a new classification method called wavelet transform-based smooth ordering (WTSO). WTSO consists of three main components: wavelet transform for feature extraction, spectral–spatial based similarity measurement, smooth ordering based 1D embedding, and construction of final classifier using interpolation scheme. Specifically, wavelet transform is first imposed to decompose the HSI signal into approximate coefficients (ACs) and details coefficients (DCs). Then, to measure the similar level of pairwise samples, a novel metric is defined on the ACs, where the spatial information serves as the prior knowledge. Next, according to the measurement results, smooth ordering is applied so that the samples are aligned in a 1D space (called 1D embedding). Finally, since the reordering samples are smooth, the labels of test samples can be recovered using the simple 1D interpolation method. In the last step, in order to reduce the bias and improve accuracy, the final classifier is constructed using multiple 1D embeddings. The use of wavelet transform in WTSO can also reduce the high dimensionality of HSI data. By converting the hight-dimensional samples into a 1D ordering sequence, WTSO can reduce the computational cost, and simultaneously perform classification for the test samples. Note that in WTSO, the smooth ordering based 1D embedding and interpolation are executed in an iterative manner. And they will be terminated after finite steps. The proposed method is experimentally demonstrated on two real HSI datasets: IndianPines and University of Pavia, achieving promising results.

Logistics information tends to be large-scale and complicated, and must be handled by intelligent means to promote the sustainable and healthy development of the logistics industry. The key issue currently facing is the optimization of the logistics distribution path. First, analyze the current research status of Internet of Things (IoT) and the basic application of Particle Swarm Optimization (PSO); Then according to the development needs of logistics industry analyze the connection and restriction of optimal path planning. With this as a constraint, the optimization model is built with the goal of comprehensive cost; Then studied how to design and implement the logistics information system based on the IoT. The paper focuses on the design of information mechanism to ensure information security and the intelligent mechanism design to improve distribution efficiency. Finally, an optimization model of logistics distribution path based on IoT is established. The improved PSO algorithm is used to optimize and compare it with the traditional PSO algorithm. It is concluded that based on the logistics distribution model of the IoT, intelligent logistics is formed, so that goods and articles, goods and trucks, goods and people can all be contacted, and the distribution route can be rationally planned.

The medical image fusion process integrates the information of multiple source images into a single image. This fused image can provide more comprehensive information and is helpful in clinical diagnosis and treatment. In this paper, a new medical image fusion algorithm is proposed. Firstly, the original image is decomposed into a low-frequency sub-band and a series of high-frequency sub-bands by using nonsubsampled shearlet transform (NSST). For the low-frequency sub-band, kirsch operator is used to extract the directional feature maps from eight directions and novel sum-modified-Laplacian (NSML) method is used to calculate the significant information of each directional feature map, and then, combining a sigmod function and the significant information updated by gradient domain guided image filtering (GDGF), calculate the fusion weight coefficients of the directional feature maps. The fused feature map is obtained by summing the convolutions of the weight coefficients and the directional feature maps. The final fused low-frequency sub-band is obtained by the linear combination of the eight fused directional feature maps. The modified pulse coupled neural network (MPCNN) model is used to calculate the firing times of each high-frequency sub-band coefficient, and the fused high-frequency sub-bands are selected according to the firing times. Finally, the inverse NSST acts on the fused low-frequency sub-band and the fused high-frequency sub-bands to obtain the fused image. The experimental results show that the proposed medical image fusion algorithm expresses some advantages over the classical medical image fusion algorithms in objective and subjective evaluation.