Binary Matrix Research Articles

A reinforcement learning recommender system using bi-clustering and Markov Decision Process

Collaborative filtering (CF) recommender systems are static in nature and does not adapt well with changing user preferences. User preferences may change after interaction with a system or after buying a product. Conventional CF clustering algorithms only identifies the distribution of patterns and hidden correlations globally. However, the impossibility of discovering local patterns by these algorithms, headed to the popularization of bi-clustering algorithms. Bi-clustering algorithms can analyze all dataset dimensions simultaneously and consequently, discover local patterns that deliver a better understanding of the underlying hidden correlations. In this paper, we modelled the recommendation problem as a sequential decision-making problem using Markov Decision Processes (MDP). To perform state representation for MDP, we first converted user-item votings matrix to a binary matrix. Then we performed bi-clustering on this binary matrix to determine a subset of similar rows and columns. A bi-cluster merging algorithm is designed to merge similar and overlapping bi-clusters. These bi-clusters are then mapped to a squared grid (SG). RL is applied on this SG to determine best policy to give recommendation to users. Start state is determined using Improved Triangle Similarity (ITR similarity measure. Reward function is computed as grid state overlapping in terms of users and items in current and prospective next state. A thorough comparative analysis was conducted, encompassing a diverse array of methodologies, including RL-based, pure Collaborative Filtering (CF), and clustering methods. The results demonstrate that our proposed method outperforms its competitors in terms of precision, recall, and optimal policy learning.

Convolutional neural network and 2D logistic-adjusted-Chebyshev-based zero-watermarking of color images

Robust zero-watermarking is a protection of copyright approach that is both effective and distortion-free, and it has grown into a core of research on the subject of digital watermarking. This paper proposes a revolutionary zero-watermarking approach for color images using convolutional neural networks (CNN) and a 2D logistic-adjusted Chebyshev map (2D-LACM). In this algorithm, we first extracted deep feature maps from an original color image using the pre-trained VGG19. These feature maps were then fused into a featured image, and the owner's watermark sequence was incorporated using an XOR operation. Finally, 2D-LACM encrypts the copyright watermark and scrambles the binary feature matrix to ensure security. The experimental results show that the proposed algorithm performs well in terms of imperceptibility and robustness. The BER values of the extracted watermarks were below 0.0044 and the NCC values were above 0.9929, while the average PSNR values of the attacked images were 33.1537 dB. Also, it is superior to other algorithms in terms of robustness to conventional image processing and geometric attacks.

Investigation into Na and Cs activity coefficients in high salt solutions to support Cs removal in Hanford tank waste

Abstract The treatment of Hanford tank waste is one of the most technically challenging environmental cleanup activities for the U.S. Department of Energy to date. To expedite the processing of liquid waste stored in underground tanks in southeastern Washington state, it is necessary to remove the significant dose contributor, 137Cs. Toward this effort, ion exchange with crystalline silicotitanate (CST) has been employed as part of the Tank Side Cesium Removal system. The model used to predict Cs exchange onto CST was developed using activity coefficients calculated from the Bromley equation. A series of batch contact tests that varied in [Na] were conducted to look at the impact of Na concentration on Cs distribution. Experimental distribution ratios (K d) were compared to the distribution ratios predicted using three different activity coefficient models: (1) commercially available HSC software, (2) the Bromley equation, and (3) a simplified approach adapted from Marcos-Arroyo et al. Ultimately, the Bromley method underpredicted the effect of ionic strength on the Na activity coefficient (γ Na+), HSC overestimated the impact of ionic strength on the expected performance due to the Cs activity coefficient (γ Cs+), but the simplified approach predicted the experimental K d values quite well in a binary matrix. Expansion of this approach in complex matrices is necessary for application to Hanford tank waste.

Quantum LDPC Codes Based on Cocyclic Block Matrices.

Motivated by a family of binary cocyclic block matrices over GF(2), we proposed a construction method to gain the stabilizer of long-length quantum error-correction codes (QECCs). Stabilizer quantum codes (SQCs) can be obtained by the different rows of the yielded circulant permutation matrices; hence, the quantum codes have the virtue of a fast construction algorithm. The recursive relation of a block matrix is employed in the proposed approach, so that the generator matrix of quantum cocyclic codes with long length can be constructed easily. Furthermore, the obtained quantum codes have the low-density advantage of there being no 4-cycles in the Tanner graph.

A New Binary Biclustering Algorithm Based on Weight Adjacency Difference Matrix for Analyzing Gene Expression Data.

Biclustering algorithms are essential for processing gene expression data. However, to process the dataset, most biclustering algorithms require preprocessing the data matrix into a binary matrix. Regrettably, this type of preprocessing may introduce noise or cause information loss in the binary matrix, which would reduce the biclustering algorithm's ability to effectively obtain the optimal biclusters. In this paper, we propose a new preprocessing method named Mean-Standard Deviation (MSD) to resolve the problem. Additionally, we introduce a new biclustering algorithm called Weight Adjacency Difference Matrix Biclustering (W-AMBB) to effectively process datasets containing overlapping biclusters. The basic idea is to create a weighted adjacency difference matrix by applying weights to a binary matrix that is derived from the data matrix. This allows us to identify genes with significant associations in sample data by efficiently identifying similar genes that respond to specific conditions. Furthermore, the performance of the W-AMBB algorithm was tested on both synthetic and real datasets and compared with other classical biclustering methods. The experiment results demonstrate that the W-AMBB algorithm is significantly more robust than the compared biclustering methods on the synthetic dataset. Additionally, the results of the GO enrichment analysis show that the W-AMBB method possesses biological significance on real datasets.

Similarity evaluation method of single flow point energy consumption mapping based on Fréchet distance

Abstract Aiming at the problem of inaccurate measurement results caused by factors such as gas leakage during the calibration of the standard meter gas flow standard device of the same type and small diameter, this paper proposes a similarity assessment method of single flow point energy consumption mapping based on Fréchet distance (FD). First, through the statistical analysis of the historical energy consumption data of gas flow standard device, a discrete standard energy consumption mapping is formed. Next, the energy consumption mapping to be tested is standardized and the similarity of the energy consumption mapping is determined by the binary matrix accelerated search of the FD between the energy consumption mapping to be tested and the standard energy consumption mapping. Finally, the similarity threshold is calculated by combining the standard deviation of the FD and the reliability of the gas flowmeter calibration process is evaluated accordingly. The test shows that the method in this paper can effectively determine the reliability of the gas flowmeters calibration results.

Imbalanced least squares regression with adaptive weight learning

Least squares regression (LSR) has demonstrated promising performance in various classification tasks owing to its effectiveness and efficiency. However, there are some deficiencies that seriously hinder its application in imbalanced data scenarios. The first is that LSR strongly relies on a balanced class distribution. A severely imbalanced class distribution may seriously damage the effectiveness of the algorithm. Second, the utilized binary label matrix in the conventional LSR model may be too strict to learn a discriminative transformation matrix for imbalanced learning. To address the above issues, in this paper, an adaptive weight learning mechanism and label relaxation constraint are proposed and incorporated into the framework of LSR to tackle the imbalanced classification problem. The weight of each sample can be adaptively obtained according to the original distribution information of the imbalanced data, in which the importance of minority class samples can be better reflected with larger weights. A new label relaxation matrix consisting of the original label matrix and auxiliary matrix is constructed to widen the margins between different classes. Further, we provide an iterative algorithm with fast convergence to solve the resulting optimization problem. Extensive experimental results on diverse binary-class and multi-class imbalanced datasets show that the proposed method outperforms many other state-of-the-art imbalanced learning approaches.

Enhanced stability and skin permeation of ibuprofen-loaded solid lipid nanoparticles based binary solid lipid matrix: Effect of surfactant and lipid compositions

HypothesisThe type of emulsifier selected has an impact on the physicochemical properties of solid lipid nanoparticles (SLNs). This study was designed to compare the effects of emulsifiers on the physicochemical properties and in vitro skin performance of SLNs prepared from a binary mixture of Softisan® 378 (S378) and cetyl palmitate (CP) to those of SLNs prepared from only CP and S378. ExperimentsSLNs were prepared from CP, S378, or a binary mixture of CP and S378 (1:1 w/w) as the lipid phase and stabilized with Tego®Care 450 (TG450) or poloxamer 188 (P188) containing 1.0% w/w ibuprofen loading. The physicochemical properties including the particle size, polydispersity index (PDI), zeta potential (ZP), encapsulation efficiency (E.E.), crystallinity (%CI), and polymorphism were determined after production and after storage for 180 days under different conditions. In addition, in vitro drug release and permeation through human skin was studied after production and storage at room temperature for 180 days. FindingThe particle sizes of ibuprofen-loaded SLNs (IBSLNs) stabilized with P188 (IBSLN-P188) were smaller than those of SLNs stabilized with TG450 (IBSLN-TG450) (p < 0.05). After 180 days, the particle sizes of the IBSLNs were slightly increased compared to those at the initial time but were <250 nm. The IBSLN-TG450 sample showed a higher %CI than IBSLN-P188 prepared with similar propotions of CP and S378, and ibuprofen crystals were observed in the IBSLN1-TG450 sample after storage at 4 °C for 180 days. Based on the result of the in vitro release study and the in vitro skin permeation test, the addition of S378 into the CP-matrix modified ibuprofen release and skin permeation both permeated ibuprofen through the epidermis and retained ibuprofen in the epidermis. In addition, the storage time affected the release and skin permeation of ibuprofen from the SLNs, which depended on the composition of the IBSLNs.

An optimization framework for RIS-based energy-efficient multi-cell NOMA systems

Non-orthogonal multiple access (NOMA) is a highly promising multiple access strategy for wideband communication systems due to its high spectral efficiency. However, in multi-cell multi-band systems, interference issues can arise from resource sharing among multiple users, which limits the potential of NOMA. To tackle these issues, in this paper, we study a NOMA system where reconfigurable intelligent surfaces (RIS) are employed across multiple cells with multiple users clusters. Specifically, we propose an optimization framework to maximize the system energy efficiency (EE) through jointly designing the transmission beamformer at each base station, the RIS phase shifts and the corresponding binary selection matrix indicating which elements of the RIS should be used to serve a specific cell. Our optimization framework takes into account the minimum rate requirements of users, the successive interference cancellation (SIC) decoding-based rate constraint, fairness among users as well as the maximum allowed transmission power. The resulting non-convex problem is solved by using an alternating optimization algorithm, wherein semidefinite programming (SDP), successive convex approximation (SCA), and penalty-based difference-of-convex (DC) programming are used to reach a solution. Simulation results show that the proposed system outperforms conventional orthogonal access in terms of EE performance, the achievable rate, and power consumption. Also, the results revealed the critical transmission power level for NOMA beyond which the EE starts decaying. Moreover, the proposed NOMA system shows a limited EE performance compared to the conventional orthogonal access as the number of clusters exceeds a certain limit.

Embedding finite involution semigroups in matrices with transposition

The present article establishes two contrasting results: a finite involution semigroup is embeddable in some semigroup of complex matrices with conjugate transposition if and only if it is an inverse semigroup, while every finite involution semigroup is embeddable in some semigroup of binary matrices with the skew transposition across the secondary diagonal.

Binary Matrix Factorization and Completion via Integer Programming

Binary matrix factorization is an essential tool for identifying discrete patterns in binary data. In this paper, we consider the rank-k binary matrix factorization problem (k-BMF) under Boolean arithmetic: we are given an n × m binary matrix X with possibly missing entries and need to find two binary matrices A and B of dimension n × k and k × m, respectively, which minimize the distance between X and the Boolean product of A and B in the squared Frobenius distance. We present a compact and two exponential size integer programs (IPs) for k-BMF and show that the compact IP has a weak linear programming (LP) relaxation, whereas the exponential size IPs have a stronger equivalent LP relaxation. We introduce a new objective function, which differs from the traditional squared Frobenius objective in attributing a weight to zero entries of the input matrix that is proportional to the number of times the zero is erroneously covered in a rank-k factorization. For one of the exponential size Ips, we describe a computational approach based on column generation. Experimental results on synthetic and real-world data sets suggest that our integer programming approach is competitive against available methods for k-BMF and provides accurate low-error factorizations. Funding: O. Günlük was partially supported by the Office of Naval Research [Grant N00014-21-1-2575]. R. Á. Kovács was supported by a doctoral scholarship from The Alan Turing Institute under the EPSRC [Grant EP/N510129/1] and the Office for National Statistics. R. A. Hauser was supported by The Alan Turing Institute under the EPSRC [Grant EP/N510129/1].

Fuzzy clustering of spatial interval-valued data

In this paper, two fuzzy clustering methods for spatial interval-valued data are proposed, i.e. the fuzzy C-Medoids clustering of spatial interval-valued data with and without entropy regularization. Both methods are based on the Partitioning Around Medoids (PAM) algorithm, inheriting the great advantage of obtaining non-fictitious representative units for each cluster.In both methods, the units are endowed with a relation of contiguity, represented by a symmetric binary matrix. This can be intended both as contiguity in a physical space and as a more abstract notion of contiguity. The performances of the methods are proved by simulation, testing the methods with different contiguity matrices associated to natural clusters of units. In order to show the effectiveness of the methods in empirical studies, three applications are presented: the clustering of municipalities based on interval-valued pollutants levels, the clustering of European fact-checkers based on interval-valued data on the average number of impressions received by their tweets and the clustering of the residential zones of the city of Rome based on the interval of price values.

A Hypothesis for Ad-Hoc Routing Algorithm Improvement

In this article, a new approach to reducing the complexity of routing algorithms is discussed to improve routing in ad hoc networks. To avoid duplicating the routing process for each data transfer, nodes create binary matrices for each base station and update them when the routing is complete. Routing may be made much simpler using the method given here.

Solitons and quasi-Grammians of the generalized lattice Heisenberg magnet model

In this paper, we study the discrete Darboux and standard binary Darboux transformation for the generalized lattice Heisenberg magnet model. We calculate the quasi-Grammian solutions by the iteration of standard binary Darboux transformation. Furthermore, we derive the explicit matrix solutions for the binary Darboux matrix and then reduce them to the elementary Darboux matrix and plot the dynamics of solutions.

Dual objective bounded abstaining model to control performance for safety-critical applications

Abstaining models have been widely used in safety-critical fields to avoid uncertain classification and reduce misclassification costs. Previous abstaining models have two main disadvantages. First, the costs of classification and rejection need to be set. Unfortunately, it is difficult to obtain or estimate costs in practical applications. When costs change, the trained model will be no longer applicable. Second, a single indicator, such as the error rate or AUC, is optimized, which has poor robustness for different application requirements. To solve such problems, a dual objective bounded abstaining (DOBA) model is proposed. DOBA optimizes the binary confusion matrix with rejection by minimizing the false positive and negative rates under class-specific reject constraints. The DOBA model is solved using an evolutionary multi-objective optimization algorithm. The requirement-oriented abstaining classifier can be selected from a set of Pareto-optimal solutions. Extensive experiments prove the effectiveness and superiority of DOBA compared to other abstaining models.

On binary matrix properties

The so-called matrix properties of finitely complete categories are a special type of exactness properties that can be encoded as extended matrices of integers. The relation of entailment of matrix properties gives an interesting preorder on the set of such matrices, which can be investigated independently of the category-theoretic considerations. In this paper, we conduct such investigation and obtain several results dealing with binary matrices, i.e., when the only integer entries in the matrix are 0 or 1. Central to these results is a complete description of the preorder in the case of a special type of binary matrices, which we call diagonal matrices, and which include matrices that define Mal’tsev, majority and arithmetical categories.

Graphs with the unique path property: Structure, cycles, factors, and constructions

AbstractIn a directed graph with the unique path property, there is a unique directed path of a given length between any ordered pair of its vertices. Such graphs, their paths, cycles, factors, and other properties, were extensively studied during the years, mainly in the context of de Bruijn graphs, forming the most important family of such graphs. Such a graph is equivalent to a binary matrix for which , where is the all‐ones matrix. In this paper, some new results on the structural properties of such graphs, which are not necessarily de Bruijn graphs, are proved. We mainly concentrate on such graphs for which each vertex has in‐degree two and out‐degree two. The minimum number and the maximum number of vertices which are reached from a given vertex using all paths of length smaller than are considered. We provide an exact formula for the number of factors in these graphs and show that this number depends only on the number of alternating cycles in the graph, where in an alternating cycle every two consecutive edges have opposite directions in the cycle. Constructions of such graphs using several methods are presented. In particular, we present a new construction which provides a large set of such graphs with long alternating cycles. We define the integral graph and the derivative graph and implement these definitions on this family of graphs. Various properties from the point of view of the de Bruijn graph and the theory of nonsingular shift‐registers sequences are also considered. Finally, generalizations for graphs in which the in‐degree and the out‐degree of each vertex are greater than two are also discussed.

Visually meaningful image encryption scheme using multi-parameter fractal theory and block synchronous sorting diffusion

Traditional visually meaningful image encryption (VMIE) works by embedding a secret image (SI) into a visually meaningful carrier image (CAI), thus achieving the dual protection of both data information and appearance features. However, the current VMIE algorithm still suffers from problems of reconstruction quality and transmission efficiency. To address these issues, this paper proposes an innovative VMIE algorithm that utilizes a newly designed two-dimensional hyperchaotic map, multi-parameter fractal matrix (MPFM) theory and compressive sensing. The proposed algorithm achieves dual protection of both the semantic information and appearance image data. First, a newly designed 2D infinite triangle folding map (2D-ITFM) is presented to generate a binary key-controlled measurement matrix to measure and compress a plain image (PI) to generate measured image (MI) and decrease the amount of transmission information. Next, based on the hyperchaotic map 2D-ITFM and MPFM, we present the inter-block scrambling (IBS) algorithm and intra-block synchronous sorting diffusion (IBSSD) algorithm, which are used to process the MI and generate SI. Then, the matrix encoding embedding (MEE) technique is utilized to hide the SI into the CAI to produce a visually secure cipher image (CII). Finally, the experimental results demonstrate that our scheme is effective in improving the anti-attack ability while guaranteeing good imperceptibility and reconstruction performance. This scheme can be employed in the field of information security communication.

Graph theory applications in congenital heart disease

Graph theory can be used to address problems with complex network structures. Congenital heart diseases (CHDs) involve complex abnormal connections between chambers, vessels, and organs. We proposed a new method to represent CHDs based on graph theory, wherein vertices were defined as the spaces through which blood flows and edges were defined by the blood flow between the spaces and direction of the blood flow. The CHDs of tetralogy of Fallot (TOF) and transposition of the great arteries (TGA) were selected as examples for constructing directed graphs and binary adjacency matrices. Patients with totally repaired TOF, surgically corrected d-TGA, and Fontan circulation undergoing four-dimensional (4D) flow magnetic resonance imaging (MRI) were included as examples for constructing the weighted adjacency matrices. The directed graphs and binary adjacency matrices of the normal heart, extreme TOF undergoing a right modified Blalock–Taussig shunt, and d-TGA with a ventricular septal defect were constructed. The weighted adjacency matrix of totally repaired TOF was constructed using the peak velocities obtained from 4D flow MRI. The developed method is promising for representing CHDs and may be helpful in developing artificial intelligence and conducting future research on CHD.

Recognizing Series-Parallel Matrices in Linear Time

A series-parallel matrix is a binary matrix that can be obtained from an empty matrix by successively adjoining rows or columns that are copies of an existing row/column or have at most one one-entry. Equivalently, series-parallel matrices are representation matrices of graphic matroids of series-parallel graphs, which can be recognized in linear time. We propose an algorithm that, for an m-by-n matrix A with k nonzeros, determines in expected time whether A is series-parallel or returns a minimal non–series-parallel submatrix of A. We complement the developed algorithm by an efficient [Formula: see text]implementation and report about computational results. History: Accepted by Andrea Lodi, Area Editor for Design &amp; Analysis of Algorithms–Discrete. Funding: This work was supported by Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant OCENW.M20.151]. Supplemental Material: The software that supports the findings of this study is available at the GitHub software repository ( https://github.com/discopt/cmr-series-parallel ).