Recent work by Kilmer and Martin [Linear Algebra Appl., 435 (2011), pp. 641--658] Braman 433 (2010), 1241--1253] provides a setting in which the familiar tools of linear algebra can be extended to better understand third-order tensors. Continuing along this vein, paper investigates further implications including (1) bilinear operator on matrices is nearly an inner product leads definitions for length matrices, angle between two orthogonality (2) use t-linear combinations characterize range...

In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data as an application consider 3-D 4- D (color) video de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, notion rank a related tensor nuclear norm was in [11] to characterize informational structural complexity data. first show that videos with linear camera motion can be represented more efficiently using t-SVD...

The development of energy selective, photon counting X-ray detectors allows for a wide range new possibilities in the area computed tomographic image formation. Under assumption perfect resolution, here we propose tensor-based iterative algorithm that simultaneously reconstructs attenuation distribution each energy. We use multi-linear model rather than more standard "stacked vector" representation order to develop novel regularizers. Specifically, multi-spectral unknown as 3-way tensor...

Summary Variance estimation is a fundamental problem in statistical modelling. In ultrahigh dimensional linear regression where the dimensionality much larger than sample size, traditional variance techniques are not applicable. Recent advances variable selection make this accessible. One of major problems high spurious correlation between unobserved realized noise and some predictors. As result, noises actually predicted when extra irrelevant variables selected, leading to serious...

A tensor is a multidimensional array. First-order tensors and second-order can be viewed as vectors matrices, respectively. Tensors of higher order, with the ability to include more information, appear frequently nowadays in image signal processing, data mining, biomedical engineering, so on. With recent work Kilmer Martin, familiar matrix-based factorizations linear algebra extended straightforward way third-order based on their new multiplication concepts. Our method has an advantage over...

In ultra-high dimensional data analysis, it is extremely challenging to identify important interaction effects, and a top concern in practice computational feasibility. For set with n observations p predictors, the augmented design matrix including all linear order-2 terms of size × (p2 + 3p)/2. When large, say more than tens hundreds, number interactions enormous beyond capacity standard machines software tools for storage analysis. theory, selection consistency hard achieve high settings....

Very long and noisy sequence data arise from biological sciences to social science including high throughput in genomics stock prices econometrics. Often such are collected order identify understand shifts trends, for example, a bull market bear finance or normal number of chromosome copies an excessive genetics. Thus, identifying multiple change points long, possibly very is important problem. In this article, we review both classical new change-point detection strategies. Considering the...

Quadratic regression (QR) models naturally extend linear by considering interaction effects between the covariates. To conduct model selection in QR, it is important to maintain hierarchical structure main and effects. Existing regularization methods generally achieve this goal solving complex optimization problems, which usually demands high computational cost hence are not feasible for high-dimensional data. This article focuses on scalable QR. We first consider two-stage establish...

Surface imperfections in steel materials potentially degrade quality and performance, thereby escalating the risk of accidents engineering applications. Manual inspection, while traditional, is laborious lacks consistency. However, recent advancements machine learning computer vision have paved way for automated defect detection, yielding superior accuracy efficiency. This paper introduces an innovative deep model, GDCP-YOLO, devised multi-category detection. We enhance reference YOLOv8n...

Printed circuit board (PCB) manufacturing processes are becoming increasingly complex, where even minor defects can impair product performance and yield rates. Precisely identifying PCB is critical but remains challenging. Traditional defect detection methods, such as visual inspection automated technologies, have limitations. While be readily identified based on symmetry, the operational aspect proves to quite Deep learning has shown promise in detection; however, current deep models for...

We have developed a novel strategy for simultaneous interpolation and denoising of prestack seismic data. Most surveys fail to cover all possible source-receiver combinations, leading missing data especially in the midpoint-offset domain. This undersampling can complicate certain processing steps such as amplitude-variation-with-offset analysis migration. Data mitigate impact traces. considered 5D multidimensional array or otherwise referred tensor. Using synthetic sets, we first found that...

We leverage machine learning approaches to adapt nanopore sequencing basecallers for nucleotide modification detection. first apply the incremental (IL) technique improve basecalling of modification-rich sequences, which are usually high biological interest. With sequence backbones resolved, we further run anomaly detection (AD) on individual nucleotides determine their status. By this means, our pipeline promises single-molecule, single-nucleotide, and context-free modifications. benchmark...

In this paper we propose novel methods for completion (from limited samples) and de-noising of multilinear (tensor) data as an application consider 3-D 4- D (color) video de-noising. We exploit the recently proposed tensor-Singular Value Decomposition (t-SVD)[11]. Based on t-SVD, notion rank a related tensor nuclear norm was in [11] to characterize informational structural complexity data. first show that videos with linear camera motion can be represented more efficiently using t-SVD...

Single-sided formwork supporting systems (SFSSs) play a crucial role in the urban construction of retaining walls using cast-in-place concrete. By from one side, an SFSS can minimize its spatial footprint, enabling closer placement to boundary lines without compromising structural integrity. However, existing designs struggle achieve balance between mechanical performance and lightweight construction. To address these limitations, innovative instrumented was proposed. It is composed panel...

The MRR terminal in modulating retroreflector (MRR) free-space optical (FSO) communication system is compact and low power consumption, it expected to be equipped on mobile targets with limited payload achieve asymmetric flexible link. However, laser carrier passing through the turbulent atmosphere twice will cause more severe fading signal, severely reduce performance distance. As transmitted wave echo meet at transceiver terminal, they can naturally form homodyne detection improve receiver...

In this paper, we investigate the inconsistency problem arising from observability mismatch that frequently occurs in nonlinear systems such as multi-robot cooperative localization and simultaneous mapping. For a general system, discover theoretically prove unobservable subspace of EKF estimator system is independent state belongs to original system. On basis, establish necessary sufficient conditions for achieving matching. These theoretical findings motivate us introduce linear...

Let Y1, …, Yn be a sequence whose underlying mean is step function with an unknown number of the steps and change points. The detection points, namely positions where changes, important problem in such fields as engineering, economics, climatology bioscience. This has attracted lot attention statistics, variety solutions have been proposed implemented. However, there scant literature on theoretical properties those algorithms. Here, we investigate recently developed algorithm called...