Projective Graphs Research Articles

Discriminative fuzzy [formula omitted]-means clustering with local structure preservation for high-dimensional data

K-means clustering, which aims to distribute data points into K different clusters, is an effective technique for data mining and machine learning. However, several factors degrade clustering performance in real-world applications. High-dimensional data containing redundant features is one of the key issues in the clustering process. Many traditional hard or fuzzy versions of K-means clustering fail to handle high-dimensional data effectively. In this paper, we present a novel model referred to as discriminative fuzzy K-means clustering, which incorporates discriminative projection and p-Laplacian graph regularization into a joint framework. Specifically, the proposed model can reduce the negative impact of redundant features and enhance the discriminative power when projecting the original data into a lower-dimensional space. It simultaneously preserves the structural locality properties of the data by performing p-Laplacian graph regularization on the membership matrix. Consequently, clustering performance is significantly enhanced for high-dimensional data. Finally, an effective algorithm is presented to solve the formulated optimization problem. Experimental results obtained on benchmark datasets are promising and demonstrate the superiority of the proposed method.

Characterization of rings with planar, toroidal or projective planar prime ideal sum graphs

Let R be a commutative ring with unity. The prime ideal sum graph PIS ( R ) of the ring R is the simple undirected graph whose vertex set is the set of all nonzero proper ideals of R and two distinct vertices I and J are adjacent if and only if I + J is a prime ideal of R. In this paper, we study some interplay between algebraic properties of rings and graph-theoretic properties of their prime ideal sum graphs. In this connection, we classify non-local commutative Artinian rings R such that PIS ( R ) is of crosscap at most two. We prove that there does not exist a non-local commutative Artinian ring whose prime ideal sum graph is projective planar. Further, we classify non-local commutative Artinian rings of genus one prime ideal sum graphs.

Projective non-commuting graph of a group

Let $G$ be a finite non-abelian group and let $T$ be a transversal of the center of $G$ in $G$. The non-commuting graph of $G$ on a transversal of the center is the graph whose vertices are the non-central elements of $T$ and two vertices $x$ and $y$ are joined by an edge whenever $xy \neq yx$. In this paper, we classify the groups whose non-commuting graph on a transversal of the center is projective.

Semi-Supervised Multiview Feature Selection With Adaptive Graph Learning.

As data sources become ever more numerous with increased feature dimensionality, feature selection for multiview data has become an important technique in machine learning. Semi-supervised multiview feature selection (SMFS) focuses on the problem of how to obtain a discriminative feature subset from heterogeneous feature spaces in the case of abundant unlabeled data with little labeled data. Most existing methods suffer from unreliable similarity graph structure across different views since they separate the graph construction from feature selection and use the fixed graphs that are susceptible to noisy features. Furthermore, they directly concatenate multiple feature projections for feature selection, neglecting the contribution diversity among projections. To alleviate these problems, we present an SMFS to simultaneously select informative features and learn a unified graph through the data fusion from aspects of feature projection and similarity graph. Specifically, SMFS adaptively weights different feature projections and flexibly fuses them to form a joint weighted projection, preserving the complementarity and consensus of the original views. Moreover, an implicit graph fusion is devised to dynamically learn a compatible graph across views according to the similarity structure in the learned projection subspace, where the undesirable effects of noisy features are largely alleviated. A convergent method is derived to iteratively optimize SMFS. Experiments on various datasets validate the effectiveness and superiority of SMFS over state-of-the-art methods.

Adaptive Pair-Weight Vector Projection Classifier for Semi-Supervised Classification

Manifold regularization is a popular technology based on graph theory and has been widely applied to nonparallel hyperplane classifiers for semi-supervised learning. However, these classifiers adopt the fixed similarity matrix that may be sensitive to noises and outliers. Thus, we propose a novel nonparallel hyperplane classifier, named the adaptive pair-weight vector projection (APVP) classifier, for semi-supervised classification tasks. The proposed APVP unifies projection learning and graph construction into a general framework. For projection learning, APVP achieves two projection vectors by solving the pair-wise optimization problems in which we need to simultaneously maximize the between-class scatter of data and minimize both the within-class scatter of data and the adaptive manifold regularization. For graph construction, the adaptive similarity matrix is constructed during the procedure of optimization. Thus, APVP can weaken the effect of noises and outliers by the adaptive similarity matrix and strengthen the discriminant capability by the Fisher criterion. To classify unseen data, we also design a new classification rule. Experimental results show that APVP has good performance in semi-supervised scene.

Geometric Algebras of Light Cone Projective Graph Geometries

Geometric Algebras of Light Cone Projective Graph Geometries

The non-existence of a super-Janko group

Locally projective graphs in Mathieu–Conway–Monster series appear in thin–thick pairs. A possible thick extension of a thin locally projective graph associated with the fourth Janko group has been questioned for a while. Such an extension could lead, if not to a new sporadic simple group, to something equally exciting. This paper resolves this issue ultimately in the non-existence form confirming that the list of 26 sporadic simple groups, although mysterious, is now stable. The result in fact concludes the classification project of locally projective graphs, which has been running for some twenty years.

Connectedness in Projection Graphs of Commutative Rings

Connectedness in Projection Graphs of Commutative Rings

How Graphs can Improve Targeting of Employee Trainings?

Abstract: Skills matrices, also known as competency matrices, can help shift managers in a manufacturing environment in proper allocation of operators to workplaces. However, improving the skills portfolio of shift workers is often based on perceived problems with skills of absent workers. This study examines a company’s skills matrices of the 3 shifts, questioning if graph metrics can help estimating substitutability, i.e., robustness of skills portfolio of workers to absenteeism; and how can graph mapping help better targeting trainings. The author has constructed bipartite graphs where one set of nodes are from the set of competencies and the other set of nodes are from the set of workers; and evaluated metrics comparing the skills portfolio of each shift. One projection of the bipartite graph shows the interlinks between people: when two workers are connected, they share the same skill and can substitute each other. The overall level of substitutability of people is then measured with the average degree of nodes of the projection graph. Weak connectedness, that is, low k values can highlight risks and exposedness to fallout of the respective workers. Disjoint graphs indicate if there is an option for a sub-team setup based on competencies. The other projection has an edge between to skills if and only if there is minimum one worker who is capable for both. Disjoint subgraphs of skills are helping team formation based on competencies.

Determination of seafood spoilage by digital colorimetry of indicator test systems

A simple and affordable colorimetric procedure for determination of the seafood spoilage (e.g., shrimp, squid, catfish and herring) using a smartphone and chemometric analysis is considered. The proposed colorimetric sensor consists of 12 zones, i.e., disks of cellulose paper 4 mm in diameter impregnated with acid-base indicators with a color change in the pH range of 3 – 8.8. Spoiling of the seafood is accompanied with a release of volatile biogenic amines that change the color of the indicator zones. A device and a method for measuring the colorimetric parameters of a test system using a smartphone as a recording device equipped with a specialized RGBer product are described. Processing of the data array (the sum of the R, G, and B channel values for each indicator, or the R, G, and B values for individual indicators) was performed using the XLSTAT software. Patterns of the degradation of food products identified in the study made it possible to propose a method for assessing the quality of seafood in real time. The optimal time regime of heat treatment of the sample was determined, which is necessary for the isolation of biogenic amines and the formation of an analytical signal. The parameters for identification of the seafood spoilage are the values of the main component F1 (or the position of the images on the canonical function projection graph) after evaluating the colorimetric data using the principal component method. The results obtained with a colorimetric sensor match the data for determination of the total microbial number of the analyzed products. The considered method for assessing spoilage of the seafood is distinguished by the simplicity of hardware design, the availability of the materials and software resources used, the rapidity of the procedure, and the mobility of the means for recording the analytical signal.

Locally projective graphs of symplectic type

Locally projective graphs of symplectic type

Semi-supervised classifier with projection graph embedding for motor imagery electroencephalogram recognition

Semi-supervised classifier with projection graph embedding for motor imagery electroencephalogram recognition

Strong 3‐Flow Conjecture for projective planar graphs

AbstractIn 1972, Tutte posed the 3‐Flow Conjecture: that all 4‐edge‐connected graphs have a nowhere‐zero 3‐flow. This was extended by Jaeger et al. to allow vertices to have a prescribed, possibly nonzero difference (modulo 3) between the inflow and outflow. They conjectured that all 5‐edge‐connected graphs with a prescription function have a nowhere‐zero 3‐flow meeting that prescription. Kochol showed that replacing 4‐edge‐connected with 5‐edge‐connected would suffice to prove the 3‐Flow Conjecture and Lovász et al. showed that both conjectures hold if the edge connectivity condition is relaxed to 6‐edge‐connected. Both problems are still open for 5‐edge‐connected graphs. The 3‐Flow Conjecture was known to hold for planar graphs, as it is the dual of Grötzsch's Colouring Theorem. Steinberg and Younger provided the first direct proof using flows for planar graphs, as well as a proof for projective planar graphs. Richter et al. provided the first direct proof using flows of the Strong 3‐Flow Conjecture for planar graphs. We prove the Strong 3‐Flow Conjecture for projective planar graphs.

Single-cell RNA sequencing reveals the suppressive effect of PPP1R15A inhibitor Sephin1 in antitumor immunity

Protein phosphatase 1 regulatory subunit 15A (PPP1R15A) is an important factor in the integrated stress response (ISR) in mammals and may play a crucial role in tumorigenesis. In our studies, we found an inhibitor of PPP1R15A, Sephin1, plays a protumorigenic role in mouse tumor models. By analyzing the single-cell transcriptome data of the mouse tumor models, we found that in C57BL/6 mice, Sephin1 treatment could lead to higher levels of ISR activity and lower levels of antitumor immune activities. Specifically, Sephin1 treatment caused reductions in antitumor immune cell types and lower expression levels of cytotoxicity-related genes. In addition, Tcell receptor (TCR) repertoire analysis demonstrated that the clonal expansion of tumor-specific Tcells was inhibited by Sephin1. A special TCR+ macrophage subtype in tumor was identified to be significantly depleted upon Sephin1 treatment, implying its key antitumor role. These results suggest that PPP1R15A has the potential to be an effective target for tumor therapy.

The automorphism group of projective norm graphs

The projective norm graphs are central objects to extremal combinatorics. They appear in a variety of contexts, most importantly they provide tight constructions for the Turán number of complete bipartite graphs Kt,s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_{t,s}$$\\end{document} with s>(t-1)!\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$s>(t-1)!$$\\end{document}. In this note we deepen their understanding further by determining their automorphism group.

Modified celluloses improve the proofing performance and quality of bread made with a high content of resistant starch.

Adding resistant starch (RS) to bread formulations is a promising way of increasing fiber content of white bread. However, the partial replacement of wheat flour (WF) by RS can lead to a decrease in technological quality. The objective of this study was to analyze the performance of hydroxypropylmethylcellulose and carboxymethylcellulose as improvers of wheat bread with a high level of replacement (30%) with maize RS. The levels of the modified celluloses were 1% and 1.5% (WF + RS basis), and a formulation without modified celluloses was used as control. Proofing time, loaf volume, crumb characteristics (porosity, texture), and bread staling parameters (hardness increase, moisture loss), among other attributes, were analyzed, and principal component analysis was applied to compare samples. The use of both modified celluloses was effective in improving the quality of breads. Specific volume and crumb porosity were enhanced, particularly at the 1.5% level. Breads with modified celluloses also allowed a higher retention of water and a better preservation of mechanical properties during storage. The principal component analysis projection graph for the first two principal components showed that samples with modified celluloses were clustered by the level of hydrocolloid addition rather than by the type of hydrocolloid used, although all the samples with modified celluloses were close to each other and distant from the control sample without hydrocolloids. The quality decrease resulting from the replacement of WF by a high level of RS can be greatly compensated by the use of structuring agents such as hydroxypropylmethylcellulose and carboxymethylcellulose. © 2022 Society of Chemical Industry.

Distributed Subspace Projection Graph Signal Estimation with Anomaly Interference

The estimation of graph signal is a vital problem in many distributed networks, such as vehicular networks, smart grids, unmanned aerial vehicles (UAVs), and the Internet of Things. In those networks, anomaly interference widely exists, such as network attack, noise, device fault, which will hazard the healthy of the entire system. In the paper, the estimation of graph signals with anomaly interference is investigated. We show that the graph signal estimation problem can be treated as a bandlimited subspace optimization problem, and propose a distributed subspace projection graph signal estimation algorithm based on the graph filter (DispGF), which can achieve better performance with less communication burden. In addition, a graph filter matrix that produces subspace projection is proposed to replace the nonsparse projection matrix, which guarantees distributed implementation and projection accuracy. Different from previous work, here, graph signal estimation is studied with no prior anomaly information. To this end, for FDI attack, random attack, noise interference, we propose anomaly detection and node localization scheme based on smoothness, that can achieve similar performance compared with the case of prior anomaly information known. Numerical experiments verify the effectiveness of the proposed DispGF algorithm. The convergence of the algorithm is theoretically analyzed.

GCT: Graph Co-Training for Semi-Supervised Few-Shot Learning

Few-shot learning (FSL), purposing to resolve the problem of data-scarce, has attracted considerable attention in recent years. A popular FSL framework contains two phases: (i) the pre-train phase employs the base data to train a CNN-based feature extractor. (ii) the meta-test phase applies the frozen feature extractor to novel data (novel data has different categories from base data) and designs a classifier for recognition. To correct few-shot data distribution, researchers propose Semi-Supervised Few-Shot Learning (SSFSL) by introducing unlabeled data. Although SSFSL has been proved to achieve outstanding performances in the FSL community, there still exists a fundamental problem: the pre-trained feature extractor cannot adapt to the novel data flawlessly due to the cross-category setting. Usually, large amounts of noises are introduced to the novel feature. We dub it as Feature-Extractor-Maladaptive (FEM) problem. To tackle FEM, we make two efforts in this paper. First, we propose a novel label prediction method, Isolated Graph Learning (IGL). IGL introduces the Laplacian operator to encode the raw data to graph space, which helps reduce the dependence on features when classifying, and then project graph representation to label space for prediction. The key point is that: IGL can weaken the negative influence of noise from the feature representation perspective, and is also flexible to independently complete training and testing procedures, which is suitable for SSFSL. Second, we propose Graph Co-Training (GCT) to tackle this challenge from a multi-modal fusion perspective by extending the proposed IGL to the co-training framework. GCT is a semi-supervised method that exploits the unlabeled samples with two modal features to crossly strengthen the IGL classifier. We estimate our method on five benchmark few-shot learning datasets and achieve outstanding performances compared with other state-of-the-art methods. It demonstrates the effectiveness of our GCT.

Injective and projective graphs

Injective and projective graphs

MODELLING GAME TASK OF ASSIGNING STAFF TO PERFORM IT-PROJECTS BASED ON ONTOLOG IES

Context. This article describes how to solve the game problem of assigning staff to work on projects based on an ontological approach. The essence of the problem is this. There is a need to create teams to carry out several projects. Each project is defined by a set of necessary ontological knowledge. To implement projects, managers invite qualified specialists (agents), whose abilities are also defined by sets of ontologies. The composition of the teams should be such that the combined ontologies of their agents cover the set of ontologies of the respective projects. Each agent with a certain probability can take part in the implementation of several projects. Simultaneous work of the agent on different projects is not allowed. It is necessary to determine the order of project implementation and the corresponding order of personnel appointment.
 Objective of the study is to develop a mathematical model of stochastic game, recurrent Markov methods for its solution, algorithmic and software, computer experiment, analysis of results and development of recommendations for their practical application.
 Method. A stochastic game algorithm for coloring an undirected random graph was used to plan project execution. To do this, the number of vertices of the graph is taken equal to the number of projects. The edges of the project graph for which the same agent is invited are connected by edges. Due to the recovery failures of agents, the connections between the vertices of the graph change dynamically. It is necessary to achieve the correct coloring of the random graph. Then projects with the same colored vertices of the graph can be executed in parallel, and projects with different colors of vertices – in series.
 Results. The article builds a mathematical model of a stochastic game and a self-learning Markov method for its solution. Each vertex of the graph is controlled by the player. The player’s pure strategies are the elements of the color palette. After selecting the color of their own top, each player calculates the current loss as a relative number of identical colors in the local set of neighboring players. The goal of the players is to minimize the functions of average losses. The Markov recurrent method provides an adaptive choice of colors for the vertices of a random graph based on dynamic vectors of mixed strategies, the values of which depend on the current losses of players. The result of a stochastic game is an asymptotically correctly colored random graph, when each edge of the initial deterministic graph will correspond on average to different colors of vertices.
 Conclusions. A computer experiment was performed, which confirmed the convergence of the stochastic game for the problem of coloring a random graph. This made it possible to determine the procedure for appointing staff to implement projects.