International Journal of Wavelets, Multiresolution and Information Processing

Sufficient dimension reduction (SDR) plays an essential role in high-dimensional regression analysis, and most existing SDR methods suffer when data are subject to censoring. This paper tries to extend distance covariance (dCov) to SDR for survival data. Unlike most methods requiring strict constraints on predictors and survival time, the method based on dCov only relies on very mild conditions and works well when many predictors are categorical or discrete. The difficulty of SDR for survival data is that we cannot completely observe the real survival time, which may introduce a substantial bias. When the censoring time is independent of survival time, we show that the dCov-SDR method can estimate the SDR directions with a surrogate response. Furthermore, under other censoring assumptions, we extend the dCov-SDR method by proposing a new consistent empirical version of dCov for survival data. We discuss the inherent properties of our method, and under regularity conditions, statistical consistency is established for our estimators. Both simulations and real data analysis demonstrate the promising performance of the proposed method.

We study a class of almost diagonal matrices compatible with the mixed-norm $\alpha$-modulation spaces $M_{p,q}^{s,\alpha }({ℝ}^n)$, $\alpha \in [0,1]$, introduced recently by Cleanthous and Georgiadis. The class of almost diagonal matrices is shown to be closed under matrix multiplication and we connect the theory to the continuous case by identifying a suitable notion of molecules for the mixed-norm $\alpha$-modulation spaces. It is shown that the “change of frame” matrix for a pair of time-frequency frames for the mixed-norm $\alpha$-modulation consisting of suitable molecules is almost diagonal. As examples of applications, we use the almost diagonal matrices to construct compactly supported frames for the mixed-norm $\alpha$-modulation spaces, and to obtain a straightforward boundedness result for Fourier multipliers on the mixed-norm $\alpha$-modulation spaces.

Oral cancer becomes the most disastrous ailment that affects the oral cavity parts of the mouth. Oral cancer diagnosis is the main challenge in the medical field. It becomes expensive and less capable of classifying oral cancer. In some cases, it may cause unnecessary morbidity and mortality. Recently, the detection of malignant and premalignant oral lesions has been a critical process owing to their low image resolution and lower acquisition time. Thus, a novel hybrid deep learning with meta-heuristic-based optimization is proposed. The pre-processing occurs by median filtering and Contrast Limited Adaptive Histogram Equalization (CLAHE). The CLAHE method is utilized to reduce unwanted noise. Finally, the classification is done by a proposed hybrid-based deep learning model termed as Recurrent Deep Belief Network (RDBN), in which the Deep Belief Network (DBN) is incorporated with the Recurrent Neural Network (RNN). Here, the RDBN helps to increase the performance classification. Furthermore, the hyperparameters of the RDBN model, such as learning rate, epochs and hidden neurons, are tuned using the proposed Hybrid Beetle-Barnacle Swarm Optimization (HBBSO) algorithm, where the Barnacles Mating Optimizer (BMO) is superimposed with Beetle Swarm Optimization (BSO) algorithms. In the given proposed model, the selected features are extracted by the optimization algorithms. Here, the parameters are fine-tuned to get the better optimal solution. From the experimental outcome, the developed model has acquired 5.2% better than PSO-RDBN, 5.6% improved than GWO-RDBN, 3.2% enhanced than BSO-RDBN and 3.5% superior to BMO-RDBN regarding accuracy. Thus, the proposed model achieves higher results for detecting oral cancer with enhanced classification performance than the existing approaches.

In this paper we define, using the Stirling numbers of the second kind, the Gompertz wavelets and show their basic properties. In particular, we prove that the admissibility condition holds for them. We also compute the normalizing factors in the space of the square-integrable functions $L^2(ℝ)$ and present an explicit formula for them in terms of the Bernoulli numbers. Then, after implementing the second-order Gompertz wavelets in the Matlab Wavelet Toolbox, we perform numerical experiments demonstrating the practical applicability and effectiveness of the wavelets.

Unsupervised feature selection has emerged as a significant and challenging issue in multi-view learning due to the need to process a large amount of unlabeled and high-dimensional multi-view data. Although numerous methods have been developed to this point, the majority of them are offline and have substantial computational and memory costs. Unlike previous work, we propose an Online Unsupervised Multi-View Feature Selection with Adaptive Neighbors (OUMVFSAN) method by exploring view-specific feature selection matrices and weights to handle the multi-view streaming data. Specifically, the proposed OUMVFSAN method naturally performs information fusion of different views guided through a consensus clustering indicator matrix to make feature selection matrices select more valuable features. Moreover, through processing multi-view streaming data by a buffering technique, OUMVFSAN reduces the computational and storage cost without sacrificing performance. We demonstrate the effectiveness and efficiency of the proposed OUMVFSAN with extensive experiments on eight multi-view datasets. It is worth noting that OUMVFSAN performs better than many state-of-the-art online and offline unsupervised multi-view feature selection methods.

In this paper, the boundedness and compactness of the Hankel wavelet multiplier associated with the unitary representation on $L^p$ space for $1\le p\le \infty$, are obtained by using the Hankel transform technique. The application of Hankel wavelet multipliers in form of the Landau–Pollak–Slepian operator is given. With the help of the Hankel wavelet multiplier, the Sobolev space associated with the Hankel transform is constructed and its various properties are studied.

The aim of this paper is to establish several versions of Paley–Wiener-type theorems for the canonical Fourier–Bessel transform, which is a Bessel type of linear canonical transform indexed by a matrix parameter m $\in SL(2,ℝ)$.

In various fields of information examination, for example, AI, profoundly getting the hang of missing information is a typical issue. Missing qualities should be tended to since they can adversely affect the exactness and adequacy of prescient models. This research investigates how data discretization affects deep learning methods for filling the missing values in datasets with continuous features. They provide a unique method for imputing missing values using deep neural networks (DNNs) called extravagant expectation maximization-deep neural network (EEM-DNN). This approach discretizes continuous features into separate intervals initially. This is justified by treating the issue of missing value imputation as a classification work, with the missing values being considered a distinct class. A DNN, designed explicitly for imputation, is then trained using the discretized data. The expectation maximization concepts are incorporated into the network architecture, and as a result, the network iteratively improves its imputation predictions. They run comprehensive experiments on several datasets from different fields to gauge the efficacy of the suggested strategy. The effectiveness of EEM-DNN is compared to that of other imputation approaches, such as traditional imputation techniques and deep learning methods without data discretization. Our findings show that data discretization significantly enhances imputation accuracy. In terms of imputation accuracy and prediction performance on downstream tasks, the EEM-DNN method regularly performs better than alternative methods. It also examines if various discretization techniques affect the overall imputation process. They find that the trade-off between bias and variance in imputed data depends on the discretization method selected. This highlights the significance of choosing a suitable discretization approach depending on the unique properties of the dataset.

In this paper, we investigate the $L_p$-saturation of linear combinations of Szász–Mirakjan–Kantorovich operators. The main difficulty is how to tackle the differential operators deduced by Szász–Mirakjan–Kantorovich operators. We firstly investigate the regularity of these differential operators. By virtue of the regularity, the saturation theorem for linear combinations of Szász–Mirakjan–Kantorovich operators is ultimately obtained. Namely, the $L_p$-saturation class of these combinations is characterized.

The properties of activation functions profoundly affect the approximation performance of neural networks. It is always one of the most important tasks to find proper activation functions in approximation by neural networks for some specific purpose. In this paper, we introduce a new activation function which is generated by the Joukowski transformation, and construct some new neural network operators activated by the new activation function. We show that the new neural network operators can be used to approximate the continuous functions on some compact sets. In fact, we give the approximation rate by using the modulus of continuity of the objective function (see Theorem 1). Finally, we provide some specific numerical examples to verify the fitting effects of the neural network operators with different parameters for continuous functions.

An important process for underwater acoustic signal is noise reduction. In ocean exploration and the military, the minimization of noise in the underwater environment is essential to provide a significant impact in our society. While considering the different acoustic channels and complexity of marine environment, the noise reduction process in acoustic signals is always difficult. Owing to these complexities, an advanced noise reduction mechanism for underwater acoustic signal denoising is performed using adaptive deep learning method is developed. The proposed model involves finding and analyzing the noises present in the underwater acoustic signal, which is helpful for underwater target detection, recognition and acoustic communication quality. Here, a Advanced Recurrent Neural Network with Novel Loss Function (ARRNN-NLF) is implemented for reducing noises in underwater acoustic signals. Hence, the input signal is given to the reduction process where the ARRNN-NLF network is utilized for densification. The high-order nonlinear features from the original signal are extracted and converted into subvectors with fixed lengths based on temporal dimension. Finally, the denoised signal is obtained from the developed ARRNN with a minimum loss between the predicted and target output. Here, the parameters from ARRNN-NLF are optimized by the Enhanced Osprey Optimization Algorithm (EOOA) for enhancing the denoising model. The resultant results are evaluated by diverse conventional denoising models to prove efficiency.

Respiratory diseases have a significant impact on modern society, posing considerable public health risks. With the emergence of the COVID-19 pandemic, addressing respiratory issues has become increasingly urgent and important. Recently, artificial intelligence-based methods utilizing the acoustic recordings of suspected patients have shown promise in the diagnosis of various respiratory diseases, enabling localized treatment and containment of their spread. As the existing methods cannot efficiently extract subtle differences between the sound samples, thereby limiting their generalization ability. To improve the diagnosis accuracy, this paper proposes a novel multi-channel, multi-modal deep learning architecture based on the attention mechanism. The proposed framework combines a deep convolutional neural network (DCNN) with a bidirectional long short-term memory (BLSTM) network, and also utilizes the attention scheme to extract temporal and spectral features from different modalities of speech data (e.g. coughs, counting sounds and sustained vowel articulation). The proposed method effectively classifies COVID-19 patients, asthma patients and healthy individuals, with a test accuracy of 89.27 ± 0.1%, and an F1 score of 85.42 ± 0.2%. The experimental results validate the feasibility of our method, and also indicate that it is competitive with the existing deep networks.

In this paper, we characterize the convergence of the multivariate cascade algorithm with an $s\times s$ dilation matrix $M$ and a nonnegative finite mask, which generalizes the result obtained recently. Moreover, we present two examples, which demonstrate the power and applicability of our main result.