Hadamard Product Research Articles

Robust speckle covariance matrix estimation of sea clutter based on spectral symmetry

Speckle covariance matrix estimation plays an important role in adaptive target detection of maritime radars. Spatial heterogeneity of sea clutter incurs insufficient secondary data in estimation, which degrades detection performance. It is an effective way of estimation improvement to exploit the Doppler spectrum knowledge of sea clutter for structural dimension reduction of the speckle covariance matrix. This paper proposes a speckle covariance matrix estimation method based on the spectral symmetry knowledge of sea clutter, indicating that the spectrum of sea clutter is symmetric with respect to the Doppler offset. First of all, the spectral symmetry of sea clutter is analyzed by using the measured data from several opened databases and the results show that most of the data excluding sea spikes have symmetric Doppler spectra. Secondly, the spectral symmetry constrains the speckle covariance matrix into the Hadamard product of a special rank-one Toeplitz matrix and a real positive definite symmetric matrix. The degrees of freedom are reduced to almost half of that of a Hermitian matrix and thus fewer secondary data are required. Thirdly, a robust iterative maximum likelihood estimator is proposed to estimate the speckle covariance matrix with structural constraint and is free of the clutter texture distribution. The performance of the estimator is verified by the measured data and the results show that it is superior to traditional estimators, particularly in fewer secondary data.

Research of electrical impedance tomography based on multilayer artificial neural network optimized by Hadamard product for human-chest models

Electrical impedance tomography (EIT) is a non-radiation, non-invasive visual diagnostic technique. In order to improve the imaging resolution and the removing artifacts capability of the reconstruction algorithms for electrical impedance imaging in human-chest models, the HMANN algorithm was proposed using the Hadamard product to optimize multilayer artificial neural networks (MANN). The reconstructed images of the HMANN algorithm were compared with those of the generalized vector sampled pattern matching (GVSPM) algorithm, truncated singular value decomposition (TSVD) algorithm, backpropagation (BP) neural network algorithm, and traditional MANN algorithm. The simulation results showed that the correlation coefficient of the reconstructed images obtained by the HMANN algorithm was increased by 17.30% in the circular cross-section models compared with the MANN algorithm. It was increased by 13.98% in the lung cross-section models. In the lung cross-section models, some of the correlation coefficients obtained by the HMANN algorithm would decrease. Nevertheless, the HMANN algorithm retained the image information of the MANN algorithm in all models, and the HMANN algorithm had fewer artifacts in the reconstructed images. The distinguishability between the objects and the background was better compared with the traditional MANN algorithm. The algorithm could improve the correlation coefficient of the reconstructed images, and effectively remove the artifacts, which provides a new direction to effectively improve the quality of the reconstructed images for EIT.

Generalized Fractional Integral Operator in a Complex Domain

A new fractional integral operator is used to present a generalized class of analytic functions in a complex domain. The method of definition is based on a Hadamard product of analytic function, which is called convolution product. Then we formulate a convolution integral operator acting on the sub-class of normalized analytic functions. Consequently, we investigate the suggested convolution operator geometrically. Differential subordination inequalities, taking the starlike formula are given. Some consequences of well-known results are illustrated. Keywords: Analytic function, subordination and superordination, univalent function, open unit disk, fractional integral operator, convolution operator, fractional calculus.

Exploring the Interplay between the Hologenome and Complex Traits in Bovine and Porcine Animals Using Genome-Wide Association Analysis.

Genome-wide association studies (GWAS) significantly enhance our ability to identify trait-associated genomic variants by considering the host genome. Moreover, the hologenome refers to the host organism's collective genetic material and its associated microbiome. In this study, we utilized the hologenome framework, called Hologenome-wide association studies (HWAS), to dissect the architecture of complex traits, including milk yield, methane emissions, rumen physiology in cattle, and gut microbial composition in pigs. We employed four statistical models: (1) GWAS, (2) Microbial GWAS (M-GWAS), (3) HWAS-CG (hologenome interaction estimated using COvariance between Random Effects Genome-based restricted maximum likelihood (CORE-GREML)), and (4) HWAS-H (hologenome interaction estimated using the Hadamard product method). We applied Bonferroni correction to interpret the significant associations in the complex traits. The GWAS and M-GWAS detected one and sixteen significant SNPs for milk yield traits, respectively, whereas the HWAS-CG and HWAS-H each identified eight SNPs. Moreover, HWAS-CG revealed four, and the remaining models identified three SNPs each for methane emissions traits. The GWAS and HWAS-CG detected one and three SNPs for rumen physiology traits, respectively. For the pigs' gut microbial composition traits, the GWAS, M-GWAS, HWAS-CG, and HWAS-H identified 14, 16, 13, and 12 SNPs, respectively. We further explored these associations through SNP annotation and by analyzing biological processes and functional pathways. Additionally, we integrated our GWA results with expression quantitative trait locus (eQTL) data using transcriptome-wide association studies (TWAS) and summary-based Mendelian randomization (SMR) methods for a more comprehensive understanding of SNP-trait associations. Our study revealed hologenomic variability in agriculturally important traits, enhancing our understanding of host-microbiome interactions.

Tensorial and Hadamard product inequalities of Schwarz type for selfadjoint operators in Hilbert spaces

Tensorial and Hadamard product inequalities of Schwarz type for selfadjoint operators in Hilbert spaces

Scalable evaluation of Hadamard products with tensor product basis for entropy-stable high-order methods

Scalable evaluation of Hadamard products with tensor product basis for entropy-stable high-order methods

Properties of a Linear Operator Involving Lambert Series and Rabotnov Function

This work is an attempt to apply Lambert series in the theory of univalent functions. We first consider the Hadamard product of Rabotnov function and Lambert series with coefficients derived from the arithmetic function σn to introduce a normalized linear operator JRα,βz. We then acquire sufficient conditions for JRα,βz to be univalent, starlike and convex, respectively. Furthermore, we discuss the inclusion results in some special classes, namely, spiral-like and convex spiral-like subclasses. In addition, we extend the findings by incorporating two Robin’s inequalities, one of which is analogous to the Riemann hypothesis.

Surface defect detection and semantic segmentation with a novel lightweight deep neural network

Current approaches to defect detection and segmentation make essential use of machine learning methods. To develop lightweight models is one of key tasks for many defect detection and segmentation applications. In this work, we present a lightweight trilateral parallel feature extraction with multi-feature aggregation network (TriMFANet) for surface defect detection and segmentation. In TriMFANet, the top lateral is the feature-rich extraction used to capture detailed information. The other two laterals, efficient semantic feature extraction (ESFE) and reverse ESFE, leverage Hadamard product attention to jointly extract deep-level global feature information. Additionally, the MFA module employs origin-symmetric sigmoid attention to enhance deep feature information and integrates the triple features. We conducted binary defect segmentation tasks on the SD-saliency-900 and RSDDs datasets, achieving outstanding performance in both S α and E ξ . For multi-class defect detection tasks on the NEU-Seg and MSD datasets, we rank first with mIoU scores of 79.0% and 81.2% respectively. Experimental results demonstrate that our lightweight model with only 90 K parameters exhibits excellent performance.

The Hadamard decomposition problem

AbstractWe introduce the Hadamard decomposition problem in the context of data analysis. The problem is to represent exactly or approximately a given matrix as the Hadamard (or element-wise) product of two or more low-rank matrices. The motivation for this problem comes from situations where the input matrix has a multiplicative structure. The Hadamard decomposition has potential for giving more succint but equally accurate representations of matrices when compared with the gold-standard of singular value decomposition (svd). Namely, the Hadamard product of two rank-$$h$$ h matrices can have rank as high as $${h}^2$$ h 2 . We study the computational properties of the Hadamard decomposition problem and give gradient-based algorithms for solving it approximately. We also introduce a mixed model that combines svd and Hadamard decomposition. We present extensive empirical results comparing the approximation accuracy of the Hadamard decomposition with that of the svd using the same number of basis vectors. The results demonstrate that the Hadamard decomposition is competitive with the svd and, for some datasets, it yields a clearly higher approximation accuracy, indicating the presence of multiplicative structure in the data.

Some Applications of Fractional Derivative Operator

Introduction: The aim of this paper is to introduce a new subclass of univalent functions with negative coefficients related to fractional derivative operator in the unit disk We obtain basic properties like coefficient inequality, distortion and covering theorem, radii of starlikeness, convexity and close-to-convexity, extreme points, Hadamard product, and closure theorems for functions belonging to our class

On a Subclass of Meromorphic Functions Defined by a Differential Operator on Hilbert Space

n this article, we introduce and study a new subclass of meromorphic functions associated with a differential operator on Hilbert space. Coefficient estimates, growth and distortion bounds, extreme points, radii results, convex linear combinations, Hadamard product and integral transforms are obtained.

On Uniformly Starlike Functions with Respect to Symmetrical Points Involving the Mittag-Leffler Function and the Lambert Series

The aim of this paper is to define the linear operator based on the generalized Mittag-Leffler function and the Lambert series. By using this operator, we introduce a new subclass of β-uniformly starlike functions ΤJ(αi). Further, we obtain coefficient estimates, convex linear combinations, and radii of close-to-convexity, starlikeness, and convexity for functions f∈ΤJ(αi). In addition, we investigate the inclusion conditions of the Hadamard product and the integral transform. Finally, we determine the second Hankel inequality for functions belonging to this subclass.

NTSM: a non-salient target segmentation model for oral mucosal diseases

BackgroundOral mucosal diseases are similar to the surrounding normal tissues, i.e., their many non-salient features, which poses a challenge for accurate segmentation lesions. Additionally, high-precision large models generate too many parameters, which puts pressure on storage and makes it difficult to deploy on portable devices.MethodsTo address these issues, we design a non-salient target segmentation model (NTSM) to improve segmentation performance while reducing the number of parameters. The NTSM includes a difference association (DA) module and multiple feature hierarchy pyramid attention (FHPA) modules. The DA module enhances feature differences at different levels to learn local context information and extend the segmentation mask to potentially similar areas. It also learns logical semantic relationship information through different receptive fields to determine the actual lesions and further elevates the segmentation performance of non-salient lesions. The FHPA module extracts pathological information from different views by performing the hadamard product attention (HPA) operation on input features, which reduces the number of parameters.ResultsThe experimental results on the oral mucosal diseases (OMD) dataset and international skin imaging collaboration (ISIC) dataset demonstrate that our model outperforms existing state-of-the-art methods. Compared with the nnU-Net backbone, our model has 43.20% fewer parameters while still achieving a 3.14% increase in the Dice score.ConclusionsOur model has high segmentation accuracy on non-salient areas of oral mucosal diseases and can effectively reduce resource consumption.

The range of combined matrices and doubly quasi-stochastic matrices of order 3

The combined matrix of a nonsingular matrix A is the matrix C(A)=A∘A−t, where ∘ means the Hadamard (entrywise) product. Since the sum of the entries of each row and each column of C(A) is one, when the combined matrix is a real matrix, it is a doubly quasi-stochastic matrix. In this work, doubly quasi-stochastic combined matrices are studied. The characterization of all real matrices such that their combined matrix is doubly quasi-stochastic of order 3 is obtained, and the study of the class of totally positive matrices is given.

Context Disentangling and Prototype Inheriting for Robust Visual Grounding.

Visual grounding (VG) aims to locate a specific target in an image based on a given language query. The discriminative information from context is important for distinguishing the target from other objects, particularly for the targets that have the same category as others. However, most previous methods underestimate such information. Moreover, they are usually designed for the standard scene (without any novel object), which limits their generalization to the open-vocabulary scene. In this paper, we propose a novel framework with context disentangling and prototype inheriting for robust visual grounding to handle both scenes. Specifically, the context disentangling disentangles the referent and context features, which achieves better discrimination between them. The prototype inheriting inherits the prototypes discovered from the disentangled visual features by a prototype bank to fully utilize the seen data, especially for the open-vocabulary scene. The fused features, obtained by leveraging Hadamard product on disentangled linguistic and visual features of prototypes to avoid sharp adjusting the importance between the two types of features, are then attached with a special token and feed to a vision Transformer encoder for bounding box regression. Extensive experiments are conducted on both standard and open-vocabulary scenes. The performance comparisons indicate that our method outperforms the state-of-the-art methods in both scenarios.

Prioritising Actions for Improving Classroom Air Quality Based on the Analytic Hierarchy Process: Case Studies in China and the UK

The air quality in classrooms significantly impacts school children’s health and learning performance. It has been reported worldwide that classroom air quality does not meet the required standard and actions are pledged for improvement. However, it poses a challenge for decision-making in terms of prioritising taking-up measures. The aim of this study is to propose a method of identifying the action measures for improving classroom air quality and prioritising them. Case studies in the UK and China were conducted, and the key measures were identified through literature studies, open-ended questionnaire surveys, and workshop discussions, which are classified into three categories: B1, policy; B2, technology; and B3, information sharing. The analytical hierarchy process (AHP) is applied in the prioritisation of the action measures. A total of 138 teachers and parents from China and the UK participated in this case study. The genetic algorithm-optimised Hadamard product (GAOHP) method is applied to justify the consistency ratio (CR) within the required threshold value in order to ensure the consistency of the subjective perception and the accuracy of comparative weights. The results show that item B2, technology, is the most desired measure by both Chinese and British parents and teachers, despite the deviation from the optimal choice in China and the UK. Among the proposed action measures, the UK respondents strongly expected air purifiers with natural ventilation as opposed to their Chinese counterparts preferring to share the real-time status of classroom air quality. Our work will provide strong support for the subsequent selection of indoor air quality improvement strategies for schools.

A traffic flow prediction method based on constrained dynamic graph convolutional recurrent networks

To enhance the efficiency of predicting future traffic flow trends within a transportation network, we propose a traffic flow prediction approach based on Constrained Dynamic Graph Convolutional Recurrent Network (C-DGCRN). Firstly, we employ matrix linear constraint and low-rank constraint optimization techniques to assist the Dynamic Graph Convolutional Recurrent Network (DGCRN) in extracting relevant internal correlations within the transportation network, leading to the formation of an affinity matrix. Secondly, we utilize the Hadamard product operation to effectively transfer weights from the affinity matrix to DGCRN, further enhancing its predictive accuracy. The experiments conducted an error assessment on the Metro Traffic Los Angeles and Performance Measurement System-Bay Area datasets. The Mean Absolute Error, Root Mean Square Error, and Mean Absolute Percentage Error of C-DGCRN were 2.66, 5.06, and 6.83, respectively. Compared to state-of-the-art methods like Adaptive Graph Convolutional Recurrent Network, C-DGCRN showed a reduction of 7%, 9%, and 11% in these metrics.

Adaptive weighted ensemble clustering via kernel learning and local information preservation

Ensemble clustering refers to learning a robust and accurate consensus result from a collection of base clustering results. Despite extensive research on this topic, it remains challenging due to the absence of raw features and real labels of samples. Current ensemble clustering methods based on co-association (CA) matrix have received much attention from researchers. However, the information contained in the CA matrix is difficult to fully exploit within its inherent representation space. To address this issue and further unveil the underlying patterns and nonlinear relationships within the CA matrix, this paper proposes a novel Adaptive Weighted method based on Kernel learning and local information preservation for Ensemble Clustering, termed AWKEC. Unlike other ensemble clustering studies, AWKEC introduces kernel ideas to ensemble clustering to learn consistent sample relationships across multiple kernel spaces. Moreover, considering the properties of the CA matrix, highly reliable local information is preserved and embedded into the learned similarity coefficient matrices via Hadamard product. The experimental results, conducted on 13 datasets and compared to 10 representative comparative methods, validate the effectiveness of the proposed AWKEC.

Hadamard Product of Monomial Ideals and the Hadamard Package

In this paper, we generalize and study the concept of Hadamard product of ideals of projective varieties to the case of monomial ideals. We have a research direction similar to the one of the join of monomial ideals contained in a paper of Sturmfels and Sullivant. In the second part of the paper, we give a brief tutorial on the Hadamard.m2 package of Macaulay2.

Refinements and Reverses of Tensorial and Hadamard Product Inequalities for Selfadjoint Operators in Hilbert Spaces Related to Young's Result

Let $H$ be a Hilbert space. In this paper we show among others that, if the selfadjoint operators $A$ and $B$ satisfy the condition $0$ $<$ $m\leq A,$ $B\leq M,$ for some constants $m,$ $M,$ then \begin{align*} 0& \leq \frac{m}{M^{2}}\nu \left( 1-\nu \right) \left( \frac{A^{2}\otimes 1+1\otimes B^{2}}{2}-A\otimes B\right) \\ & \leq \left( 1-\nu \right) A\otimes 1+\nu 1\otimes B-A^{1-\nu }\otimes B^{\nu } \\ & \leq \frac{M}{m^{2}}\nu \left( 1-\nu \right) \left( \frac{A^{2}\otimes 1+1\otimes B^{2}}{2}-A\otimes B\right) \end{align*} for all $\nu \in \left[ 0,1\right] .$ We also have the inequalities for Hadamard product \begin{align*} 0& \leq \frac{m}{M^{2}}\nu \left( 1-\nu \right) \left( \frac{A^{2}+B^{2}}{2}% \circ 1-A\circ B\right) \\ & \leq \left[ \left( 1-\nu \right) A+\nu B\right] \circ 1-A^{1-\nu }\circ B^{\nu } \\ & \leq \frac{M}{m^{2}}\nu \left( 1-\nu \right) \left( \frac{A^{2}+B^{2}}{2}% \circ 1-A\circ B\right) \end{align*} for all $\nu \in \left[ 0,1\right] .$