A d ynamically w eighted d irected n etwork (DWDN) is frequently encountered in various big data-related applications like a terminal interaction pattern analysis system (TIPAS) concerned in this study. It consists of large-scale dynamic interactions among numerous nodes. As the involved nodes increase drastically, it becomes impossible to observe their full interactions at each time slot, making a resultant DWDN H igh D imensional and I ncomplete (HDI). An HDI DWDN, in spite of its incompleteness, contains rich knowledge regarding involved nodes’ various behavior patterns. To extract such knowledge from an HDI DWDN, this paper proposes a novel A lternating direction method of multipliers (ADMM)-based N onnegative L atent-factorization of T ensors (ANLT) model. It adopts three-fold ideas: a) building a data density-oriented augmented Lagrangian function for efficiently handling an HDI tensor's incompleteness and nonnegativity; b) splitting the optimization task in each iteration into an elaborately designed subtask series where each one is solved based on the previously solved ones following the ADMM principle to achieve fast convergence; and c) theoretically proving that its convergence is guaranteed with its efficient learning scheme. Experimental results on six DWDNs from real applications demonstrate that the proposed ANLT outperforms state-of-the-art models significantly in both computational efficiency and prediction accuracy for missing links of an HDI DWDN. Hence, this study proposes a novel and efficient approach to large-scale DWDN representation.

In this work, tapered/etched multicore fiber (MCF) probes are spliced with multimode fiber (MMF) to fabricate the sensor structure. To improve sensitivity, gold nanoparticles (AuNPs) and molybdenum disulfide nanoparticles (MoS ₂ -NPs) are used to immobilize both probes. Synthesized AuNPs and molybdenum disulfide (MoS ₂ )-nanoparticles (NPs) have peak absorption wavelengths of 519 and 330 nm, respectively. High-resolution transmission electron microscopy is used to examine the morphology of the NPs. The scanning electron microscope (SEM) is used to characterize the NP-immobilized optical fiber sensor structures, and SEM-EDX is used to verify the NP-coating over fiber structure. The functionalization of the acetylcholinesterase enzyme over the NP-immobilized probe increases the specificity of the sensor later on. Finally, the developed sensor probes are tested by detecting various acetylcholine concentrations. In addition, performance analyses, such as reusability, reproducibility, and selectivity (in the presence of ascorbic acid, glucose, dopamine, and uric acid), are carried out, and proposed biosensors are experimentally evaluated. The developed tapered fiber sensor with a sensitivity of 0.062 nm/ $\mu \text{M}$ can detect even very low concentrations, such as 14.28 $\mu \text{M}$ , over a wide detection range of 0–1000 $\mu \text{M}$ .

Low-rank minimization aims to recover a matrix of minimum rank subject to linear system constraint. It can be found in various data analysis and machine learning areas, such as recommender systems, video denoising, and signal processing. Nuclear norm minimization is a dominating approach to handle it. However, such a method ignores the difference among singular values of target matrix. To address this issue, nonconvex low-rank regularizers have been widely used. Unfortunately, existing methods suffer from different drawbacks, such as inefficiency and inaccuracy. To alleviate such problems, this article proposes a flexible model with a novel nonconvex regularizer. Such a model not only promotes low rankness but also can be solved much faster and more accurate. With it, the original low-rank problem can be equivalently transformed into the resulting optimization problem under the rank restricted isometry property (rank-RIP) condition. Subsequently, Nesterov’s rule and inexact proximal strategies are adopted to achieve a novel algorithm highly efficient in solving this problem at a convergence rate of $O(1/K)$ , with $K$ being the iterate count. Besides, the asymptotic convergence rate is also analyzed rigorously by adopting the Kurdyka- ojasiewicz (KL) inequality. Furthermore, we apply the proposed optimization model to typical low-rank problems, including matrix completion, robust principal component analysis (RPCA), and tensor completion. Exhaustively empirical studies regarding data analysis tasks, i.e., synthetic data analysis, image recovery, personalized recommendation, and background subtraction, indicate that the proposed model outperforms state-of-the-art models in both accuracy and efficiency.

In recent years, a large number of studies have shown that low rank matrix learning (LRML) has become a popular approach in machine learning and computer vision with many important applications, such as image inpainting, subspace clustering, and recommendation system. The latest LRML methods resort to using some surrogate functions as convex or nonconvex relaxation of the rank function. However, most of these methods ignore the difference between different rank components and can only yield suboptimal solutions. To alleviate this problem, in this paper we propose a novel nonconvex regularizer called capped reweighting norm minimization (CRNM), which not only considers the different contributions of different rank components, but also adaptively truncates sequential singular values. With it, a general LRML model is obtained. Meanwhile, under some mild conditions, the global optimum of CRNM regularized least squares subproblem can be easily obtained in closed-form. Through the analysis of the theoretical properties of CRNM, we develop a high computational efficiency optimization method with convergence guarantee to solve the general LRML model. More importantly, by using the Kurdyka-Łojasiewicz (KŁ) inequality, its local and global convergence properties are established. Finally, we show that the proposed nonconvex regularizer as well as the optimization approach are suitable for different low rank tasks, such as matrix completion and subspace clustering. Extensive experimental results demonstrate that the constructed models and methods provide significant advantages over several state-of-the-art low rank matrix leaning models and methods.