International Journal of Wavelets, Multiresolution and Information Processing

Aquila optimizer (AO) is an efficient meta-heuristic optimization method, which mimics the hunting style of Aquila in nature. However, the AO algorithm may suffer from immature convergence during the exploitation stage. In this paper, two strategies are elegantly employed into conventional AO, such as random opposition-based learning and nonlinear flexible jumping factor, which can efficiently enhance the performance of conventional AO. Experiments on $17$ benchmark functions and image segmentation demonstrate the effectiveness of the proposed algorithm. Comparison with several state-of-the-art meta-heuristic optimization techniques indicates the efficacy of the developed method.

The wastewater treatment process is characterized by uncertainty, non-linearity, time delay and complexity, and is susceptible to many dynamic factors. Since some key water quality parameters are not available in real time, a Long Short-Term Memory (LSTM) network water quality prediction model based on sparrow search algorithm (SSA-LSTM) and attention mechanism is proposed to solve the problem. In this model, we take historical data as input, constructs models to learn the feature of internal dynamic changes, introduces the attention mechanism, assigns different weights to the hidden state of the LSTM network by mapping weightings with the learning parameter matrix, and uses the SSA to select the optimal hyperparameters for prediction. As high-latitude feature vectors are subject to the curse of dimension, a PCA-LSTM model is further proposed to apply the Principal Component Analysis (PCA) method to the SSA-LSTM model to reduce the dimensionality of the original data. The SSA-LSTM model without the PCA method (NPCA-LSTM) and the PCA-LSTM model are applied to predict wastewater quality and the PCA-LSTM model shows higher predictive ability.

Federated learning (FL) is an important approach to cooperate with multiple devices for learning without exchanging data between devices and central server. However, due to bandwidth and other reasons, the communication efficiency should be considered when the volume of information transmitted is limited. In this paper, we utilize the tool of lattice quantization form quantization theory and the variable intercommunication interval to improve communication efficiency. Meanwhile, to make strong privacy guarantee, we incorporate the notion of differential privacy (DP) to the FL framework with local SGD algorithm. By adding calibrated noises, we propose a universal lattice quantization for differentially private federated averaging algorithm (ULQ-DP-FedAvg). We provide tight privacy bound by using some privacy techniques. We also analyze the convergence bound of ULQ-DP-FedAvg based on bits rate constraints and the growing inter-communication interval as well as the data are non-independent identically distribution (Non-IID). It turns out that the algorithm converges and preserves that the privacy has scarcely influenced on the convergence rate. The effectiveness of our algorithm is demonstrated by synthetic and real datasets.

The null space property (NSP), which relies merely on the null space of the sensing matrix column space, has drawn numerous interests in sparse signal recovery. This paper studies NSP of the weighted ${\ell }_r-{\ell }_1$ ($r\in (0,1]$) minimization. Several versions of NSP of the weighted ${\ell }_r-{\ell }_1$ minimization including the weighted ${\ell }_r-{\ell }_1$ NSP, the weighted ${\ell }_r-{\ell }_1$ stable NSP, the weighted ${\ell }_r-{\ell }_1$ robust NSP and the ${\ell }_q$ weighted ${\ell }_r-{\ell }_1$ robust NSP for $1\le q\le 2$, are proposed, as well as the associating considerable results are derived. Under these NSPs, sufficient conditions for the recovery of (sparse) signals with the weighted ${\ell }_r-{\ell }_1$ minimization are established. Furthermore, we show that to some extent, the weighted ${\ell }_r-{\ell }_1$ stable NSP is weaker than the restricted isometric property (RIP). And the RIP condition we obtained is better than that of Zhou (2022).

We study nonstationary frames of matrix-valued Gabor systems and wavelet systems in the matrix-valued function space $L^2(ℝ,{ℂ}^{l\times l})$. First, we show that a diagonal matrix-valued window function constitutes a frame for $L^2(ℝ,{ℂ}^{l\times l})$ whenever each diagonal entry constitutes a frame for the space $L^2(ℝ)$. This is not true for arbitrary nonzero matrix-valued function. Using this, we prove the existence of nonstationary matrix-valued Gabor frames associated with the Weyl–Heisenberg group in terms of density of real numbers. We give a representation of the frame operator of matrix-valued nonstationary Gabor system. A necessary condition with explicit frame bounds for nonstationary matrix-valued Gabor frames associated with the Weyl–Heisenberg group is given. We discuss matrix-valued frame preserving maps in terms of adjointablity, with respect to the matrix-valued inner product, of bounded linear operators acting on $L^2(ℝ,{ℂ}^{l\times l})$. It is shown that the image of a matrix-valued Gabor frame under bounded, linear and invertible operator on $L^2(ℝ,{ℂ}^{l\times l})$ may not be a frame for $L^2(ℝ,{ℂ}^{l\times l})$. In this direction, we give sufficient conditions on bounded linear operators which can preserve frame conditions. Finally, we give necessary and sufficient condition for the existence of nonstationary matrix-valued wavelet frames associated with the extended affine group.

Hierarchical classification (HC) assigns each object with multiple labels organized into a hierarchical structure. The existing deep learning-based HC methods usually predict an instance starting from the root node until a leaf node is reached. However, in the real world, images impaired by noise, occlusion, blur, or low resolution may not provide sufficient information for the classification at subordinate levels. To address this issue, we propose a novel Semantic Guided level-category Hybrid Prediction Network (SGHPN) that can jointly perform the level and category prediction in an end-to-end manner. SGHPN comprises two modules: a visual transformer that extracts feature vectors from the input images, and a semantic guided cross-attention module that uses categories word embeddings as queries to guide learning category-specific representations. In order to evaluate the proposed method, we construct two new datasets in which images are at a broad range of quality and thus are labeled to different levels (depths) in the hierarchy according to their individual quality. Experimental results demonstrate the effectiveness of our proposed HC method.

Convolutional Neural Network (CNN) has shown remarkable success in the area of machine vision. The purpose of this research is to enhance the classification for the few-shot learning datasets by developing a robust feature extraction system using an optimized CNN model. The aforementioned goal is attained in the following way by developing two classification models, (1) CNN optimized using Two-Dimensional Discrete Wavelet Transform (2D-DWT) injection using Principal Component Analysis (PCA), and Grey Wolf Optimizer (GWO), and (2) CNN optimized using 2D-DWT injection using PCA and Multi-Verse Optimizer (MVO) algorithm. This optimization process enhances the rate of face recognition for the small training dataset by extracting maximum features. Experiments on the AT&T (ORL), LFW, and Extended Yale-FACE-B databases show that the technique improves results significantly, with recognition rates increasing to 100% for training accuracy on all datasets and 100%, 98%, 97% on ORL, LFW, and Extended Yale-FACE-B datasets, respectively, for testing accuracy.

This work aims to address two issues that often exist in least square regression (LSR) models for classification tasks, which are (1) learning a compact projection matrix for feature selection and (2) adopting relaxed regression targets. To this end, we first propose a sparse regularized LSR framework for feature selection by introducing the ${\ell }_{2,1}$ regularizer. Second, we utilize two different strategies to relax the strict regression targets based on the sparse framework. One way is to exploit the $𝜀$-dragging technique. Another strategy is to directly learn the labels from the inputs and constrain the distance between true and false classes simultaneously. Hence, more feasible regression schemes are constructed, and the models will be more flexible. Further, efficient iterative methods are derived to optimize the proposed models. Various experiments on image databases intend to manifest our proposed models have outstanding recognition capability compared with many state-of-the-art classifiers.

Infrared images have several applications such as security, health, passenger monitoring, and so on. The quality of infrared image gets affected by noise, blurring effect, and low illumination environment. Due to the low contrast, blurring, and hazy effects in infrared images, state-of-the-art techniques are frequently unable to achieve appropriate edge details. Thus, an edge detection algorithm is proposed using a modified Von Neumann neighborhood kernel and taxicab geometry-based shortest path method. It has been found to perform in a better manner compared to earlier studies in a similar field. The objective of the proposed method is to produce sharp, less noisy and robust edge lines. First, pre-processing of the image is done for edge-preserving smoothing of an infrared image using a smoothing parameter. Second, image segmentation is done based on a two-level threshold value computed by a modified Von Neumann-based kernel. Then, Fourier transform of the segmented image is done to remove spike noise followed by the inverse Fourier transform to produce the final edge lines. The simulation experiment results show that the proposed method is found to yield robust and sharp edge lines compared to other state-of-the-art methods both numerically and visually. Moreover, the whole process takes less computation time.

As we know, feedforward neural networks (FNNs) with sigmoidal activation function are universal approximators. Theoretically, for any continuous function defined on a compact set, there exists an FNN such that the FNN can approximate the function with arbitrary accuracy, which constitutes a theoretical guarantee that FNN can be used as an efficient learning machine. This paper addresses the construction and approximation for FNNs. We construct an FNN with sigmoidal activation function and estimate its approximation error. In particular, an inverse theorem of the approximation is established, which implies the equivalence characterization theorem of the approximation and reveals the relationship between the topological structure of the FNN and its approximation ability. As keys in this study, the concepts of modulus of continuity of function, K-functional, and their relationship are utilized, and two Bernstein-type inequalities are established.