Journal articles: 'Graph projection'

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Bae, Yeolhui, Yugyeom Yi, Jeongmoo Lee, and Sungmo Kang. "Research on Definition of BLL Graphs of Knot Diagrams and its Applications." Korean Science Education Society for the Gifted 14, no. 3 (December 30, 2022): 229–36. http://dx.doi.org/10.29306/jseg.2022.14.3.229.

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This paper is the research on the Knot theory in Topology. A knot is a simple closed curve in ℝ and its projection onto a plane in ℝ is called a knot projection. As the results of this paper we define a BLL(Bidirectional Linear Link) graph for a knot projection which is a bidirectional linear link representing the relations between arcs of a knot projection and obtain some properties of the BLL graphs. We also define an Eulerian cycle of the BLL graph and an Eulerian cycle of a knot projection. As the main results of this paper, we obtain the equivalent conditions of being an alternation knot projection as follows: (1) an out-degree of every vertex of the corresponding BLL graph is 2; (2) the corresponding BLL graph has an Eulerian cycle; (3) the knot projection has an Eulerian cycle. As the subsequent study, using these results of the BLL graphs, we propose the analysis on the BLL graphs for deformation operation obtaining a new alternating knot projection, decision on the tricolorability of a knot projection, and a polynomial of a knot projection.

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Ledermann, Florian. "Classifying Cartographic Projections Based on Dynamic Analysis of Program Code." Abstracts of the ICA 2 (October 9, 2020): 1. http://dx.doi.org/10.5194/ica-abs-2-38-2020.

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Abstract. Analyzing a given map to identify its projection and other geometrical properties has long been an important aspect of cartographic analysis. If explicit information about the projection used in a particular map is not available, the properties of the cartographic transformation can sometimes be reconstructed from the map image. However, such a process of projection analysis requires significant manual labor and oversight.For digital maps, we usually expect the projection from geographic space to map space to have been calculated by a computer program. Such a program can be expected to contain the implementation of the mathematical rules of the projection and subsequent coordinate transformations such as translation and scaling. The program code, therefore, contains information that would allow an analyst to reliably identify map projections and other geometrical transformations applied to the input data.In the case of interactive online maps, the code generating the map is in fact delivered to the map user and could be used for cartographic analysis. The core idea of our novel method proposed for map analysis is to apply reverse engineering techniques on the code implementing the cartographic transformations in order to retrieve the properties of the applied map projection. However, automatic reasoning about computer code by way of static analysis (analyzing the source code without running it) is provably limited – for example, the code delivered to the map user may contain a whole library of different map projections, of which only a specific one may be actually used at runtime. Instead, we propose a dynamic analysis approach to observe and monitor the operations performed by the code as the program runs, and to retrieve the mathematical operations that have been used to calculate the coordinates of every graphical element on the map.The presented method produces, for every graphical element of the map, a transformation graph consisting of low-level mathematical operations. Cartographic projections can be identified as distinctive patterns in the transformation graph, and can be distinguished in a fully automatic way by matching a set of predefined patterns against a particular graph.Projections vary widely in their arithmetic structure, and therefore by the structure of the corresponding transformation graphs extracted from program code. Some projections can be computed directly using continuous equations involving trigonometric functions. Other projections involve solving nonlinear equations, which need to be solved by approximation. Composite projections use different projections depending on some threshold value. Yet other projections, such as the Robinson projection, define a table of predefined values, between which interpolation is used etc.. In each of these cases, we expect to find the operations corresponding to the mathematical structure of the projection in the transformation graph extracted by the presented method.For verifying the method, we have implemented the patterns of several well-known cartographic projections based on the literature and have used it on the transformation graphs extracted from a variety of sample programs. To ensure a diversity of implementations, we have evaluated programs using different and independent JavaScript implementations of projections, including the open source libraries D3.js, proj4js, Leaflet, OpenLayers, and informal implementations of example programs found online. For these case studies, we could successfully identify many projections based on identifying patterns in the transformation graph in a fully automated, unsupervised manner.In the future, the proposed method may be further developed for many innovative application scenarios, such as building a “cartographic search engine” or constructing novel tools for semi-automatic cartographic analysis and review.

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CAELLI, TERRY, and SERHIY KOSINOV. "INEXACT GRAPH MATCHING USING EIGEN-SUBSPACE PROJECTION CLUSTERING." International Journal of Pattern Recognition and Artificial Intelligence 18, no. 03 (May 2004): 329–54. http://dx.doi.org/10.1142/s0218001404003186.

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Graph eigenspaces have been used to encode many different properties of graphs. In this paper we explore how such methods can be used for solving inexact graph matching (the matching of sets of vertices in one graph to those in another) having the same or different numbers of vertices. In this case we explore eigen-subspace projections and vertex clustering (EPS) methods. The correspondence algorithm enables the EPC method to discover a range of correspondence relationships from one-to-one vertex matching to that of inexact (many-to-many) matching of structurally similar subgraphs based on the similarities of their vertex connectivities defined by their positions in the common subspace. Examples in shape recognition and random graphs are used to illustrate this method.

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Dal Col, Alcebiades, and Fabiano Petronetto. "Graph regularization multidimensional projection." Pattern Recognition 129 (September 2022): 108690. http://dx.doi.org/10.1016/j.patcog.2022.108690.

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NIKKUNI, RYO, MAKOTO OZAWA, KOUKI TANIYAMA, and YUKIHIRO TSUTSUMI. "NEWLY FOUND FORBIDDEN GRAPHS FOR TRIVIALIZABILITY." Journal of Knot Theory and Its Ramifications 14, no. 04 (June 2005): 523–38. http://dx.doi.org/10.1142/s0218216505003932.

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A planar graph is said to be trivializable if every regular projection of the graph produces a trivial spatial embedding by giving some over/under informations to the double points. Every minor of a trivializable graph is also trivializable, thus the set of forbidden graphs is finite. Seven forbidden graphs for the trivializability were previously known. In this paper, we exhibit nine more forbidden graphs.

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HUH, YOUNGSIK. "AN ELEMENTARY SET FOR EMBEDDED BOUQUET GRAPHS WITH TWO CYCLES." Journal of Knot Theory and Its Ramifications 20, no. 02 (February 2011): 305–25. http://dx.doi.org/10.1142/s0218216511008796.

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A projection of the bouquet graph B with two cycles is said to be trivial if only trivial embeddings are obtained from the projection. In this paper a finite set of nontrivial embeddings of B is shown to be minimal among those which produce all nontrivial projections of B.

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HUH, YOUNGSIK, and KOUKI TANIYAMA. "IDENTIFIABLE PROJECTIONS OF SPATIAL GRAPHS." Journal of Knot Theory and Its Ramifications 13, no. 08 (December 2004): 991–98. http://dx.doi.org/10.1142/s0218216504003640.

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A generic map from a finite graph to the 2-space is called identifiable if any two embeddings of the graph into the 3-space obtained by lifting the map with respect to the natural projection from the 3-space to the 2-space are ambient isotopic in the 3-space. We show that only planar graphs have identifiable maps. We characterize the identifiable maps for some planar graphs.

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Douar, Brahim, Chiraz Latiri, Michel Liquiere, and Yahya Slimani. "A Projection Bias in Frequent Subgraph Mining Can Make a Difference." International Journal on Artificial Intelligence Tools 23, no. 05 (October 2014): 1450005. http://dx.doi.org/10.1142/s0218213014500055.

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The aim of the frequent subgraph mining task is to find frequently occurring subgraphs in a large graph database. However, this task is a thriving challenge, as graph and subgraph isomorphisms play a key role throughout the computations. Since subgraph isomorphism testing is a hard problem, subgraph miners are exponential in runtime. To alleviate the complexity issue, we propose to introduce a bias in the projection operator and instead of using the costly subgraph isomorphism projection, one can use a polynomial projection having a semantically-valid structural interpretation. This paper presents a new projection operator for graphs named AC-projection, which exhibits nice theoretical complexity properties. We study the size of the search space as well as some practical properties of the projection operator. We also introduce a novel breadth-first algorithm for frequent AC-reduced subgraphs mining. Then, we prove experimentally that we can achieve an important performance gain (polynomial complexity projection) without or with non-significant loss of discovered patterns in terms of quality.

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Bach, Nguyen Gia, Chanh Minh Tran, Tho Nguyen Duc, Phan Xuan Tan, and Eiji Kamioka. "Novel Projection Schemes for Graph-Based Light Field Coding." Sensors 22, no. 13 (June 30, 2022): 4948. http://dx.doi.org/10.3390/s22134948.

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In light field compression, graph-based coding is powerful to exploit signal redundancy along irregular shapes and obtains good energy compaction. However, apart from high time complexity to process high dimensional graphs, their graph construction method is highly sensitive to the accuracy of disparity information between viewpoints. In real-world light field or synthetic light field generated by computer software, the use of disparity information for super-rays projection might suffer from inaccuracy due to vignetting effect and large disparity between views in the two types of light fields, respectively. This paper introduces two novel projection schemes resulting in less error in disparity information, in which one projection scheme can also significantly reduce computation time for both encoder and decoder. Experimental results show projection quality of super-pixels across views can be considerably enhanced using the proposals, along with rate-distortion performance when compared against original projection scheme and HEVC-based or JPEG Pleno-based coding approaches.

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Hjouj, Fawaz. "On Tomography with Unknown Orientation." Journal of Mathematical Sciences & Computer Applications 2, no. 2 (June 10, 2017): 125–35. http://dx.doi.org/10.5147/jmsca.v2i1.99.

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We consider the two-dimensional parallel beam Tomography problem in which both the object being imaged and the projection directions are unknown. The angles of projections need not to be uniformly distributed. Our solution combines two known approaches: the Geometric Moment and the Graph Laplacian. After sorting the projections using the Graph Laplacian method we create a one to one moment function of the angles. We then solve for each angle uniquely.

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Li, Haohao, Mingliang Gao, Huibing Wang, and Gwanggil Jeon. "Multi-View Projection Learning via Adaptive Graph Embedding for Dimensionality Reduction." Electronics 12, no. 13 (July 3, 2023): 2934. http://dx.doi.org/10.3390/electronics12132934.

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In order to explore complex structures and relationships hidden in data, plenty of graph-based dimensionality reduction methods have been widely investigated and extended to the multi-view learning field. For multi-view dimensionality reduction, the key point is extracting the complementary and compatible multi-view information to analyze the complex underlying structure of the samples, which is still a challenging task. We propose a novel multi-view dimensionality reduction algorithm that integrates underlying structure learning and dimensionality reduction for each view into one framework. Because the prespecified graph derived from original noisy high-dimensional data is usually low-quality, the subspace constructed based on such a graph is also low-quality. To obtain the optimal graph for dimensionality reduction, we propose a framework that learns the affinity based on the low-dimensional representation of all views and performs the dimensionality reduction based on it jointly. Although original data is noisy, the local structure information of them is also valuable. Therefore, in the graph learning process, we also introduce the information of predefined graphs based on each view feature into the optimal graph. Moreover, assigning the weight to each view based on its importance is essential in multi-view learning, the proposed GoMPL automatically allocates an appropriate weight to each view in the graph learning process. The obtained optimal graph is then adopted to learn the projection matrix for each individual view by graph embedding. We provide an effective alternate update method for learning the optimal graph and optimal subspace jointly for each view. We conduct many experiments on various benchmark datasets to evaluate the effectiveness of the proposed method.

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Fukś, Henryk, Babak Farzad, and Yi Cao. "A model of language inflection graphs." International Journal of Modern Physics C 25, no. 06 (April 23, 2014): 1450013. http://dx.doi.org/10.1142/s0129183114500132.

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Inflection graphs are highly complex networks representing relationships between inflectional forms of words in human languages. For so-called synthetic languages, such as Latin or Polish, they have particularly interesting structure due to the abundance of inflectional forms. We construct the simplest form of inflection graphs, namely a bipartite graph in which one group of vertices corresponds to dictionary headwords and the other group to inflected forms encountered in a given text. We, then, study projection of this graph on the set of headwords. The projection decomposes into a large number of connected components, to be called word groups. Distribution of sizes of word group exhibits some remarkable properties, resembling cluster distribution in a lattice percolation near the critical point. We propose a simple model which produces graphs of this type, reproducing the desired component distribution and other topological features.

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VARADI, Zoltan. "How Graphs can Improve Targeting of Employee Trainings?" Eurasia Proceedings of Educational and Social Sciences 31 (October 30, 2023): 135–42. http://dx.doi.org/10.55549/epess.1381972.

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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.

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TANIYAMA, KOUKI, and TATSUYA TSUKAMOTO. "KNOT-INEVITABLE PROJECTIONS OF PLANAR GRAPHS." Journal of Knot Theory and Its Ramifications 05, no. 06 (December 1996): 877–83. http://dx.doi.org/10.1142/s0218216596000485.

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For each odd number n, we describe a regular projection of a planar graph such that every spatial graph obtained by giving it over/under information of crossing points contains a (2, n)-torus knot. We also show that for any spatial graph H, there is a regular projection of a (possibly nonplanar) graph such that every spatial graph obtained from it contains a subgraph that is ambient isotopic to H.

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Pan, Heng, Jinrong He, Yu Ling, Lie Ju, and Guoliang He. "Graph regularized multiview marginal discriminant projection." Journal of Visual Communication and Image Representation 57 (November 2018): 12–22. http://dx.doi.org/10.1016/j.jvcir.2018.10.009.

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Dilworth, Stephen J., Denka Kutzarova, and Mikhail I. Ostrovskii. "Lipschitz-free Spaces on Finite Metric Spaces." Canadian Journal of Mathematics 72, no. 3 (February 13, 2019): 774–804. http://dx.doi.org/10.4153/s0008414x19000087.

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AbstractMain results of the paper are as follows:(1) For any finite metric space $M$ the Lipschitz-free space on $M$ contains a large well-complemented subspace that is close to $\ell _{1}^{n}$.(2) Lipschitz-free spaces on large classes of recursively defined sequences of graphs are not uniformly isomorphic to $\ell _{1}^{n}$ of the corresponding dimensions. These classes contain well-known families of diamond graphs and Laakso graphs.Interesting features of our approach are: (a) We consider averages over groups of cycle-preserving bijections of edge sets of graphs that are not necessarily graph automorphisms. (b) In the case of such recursive families of graphs as Laakso graphs, we use the well-known approach of Grünbaum (1960) and Rudin (1962) for estimating projection constants in the case where invariant projections are not unique.

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Lin, Lin, Jie Liu, Feng Guo, Changsheng Tong, Lizheng Zu, and Hao Guo. "ERDERP: Entity and Relation Double Embedding on Relation Hyperplanes and Relation Projection Hyperplanes." Mathematics 10, no. 22 (November 9, 2022): 4182. http://dx.doi.org/10.3390/math10224182.

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Since data are gradually enriched over time, knowledge graphs are inherently imperfect. Thus, knowledge graph completion is proposed to perfect knowledge graph by completing triples. Currently, a family of translation models has become the most effective method for knowledge graph completion. These translation models are modeled to solve the complexity and diversity of entities, such as one-to-many, many-to-one, and many-to-many, which ignores the diversity of relations themselves, such as multiple relations between a pair of entities. As a result, with current translation models, it is difficult to effectively extract the semantic information of entities and relations. To effectively extract the semantic information of the knowledge graph, this paper fundamentally analyzes the complex relationships of the knowledge graph. Then, considering the diversity of relations themselves, the complex relationships are refined as one-to-one-to-many, many-to-one-to-one, one-to-many-to-one, many-to-one-to-many, many-to-many-to-one, one-to-many-to-many, and many-to-many-to-many. By analyzing the complex relationships, a novel knowledge graph completion model, entity and relation double embedding on relation hyperplanes and relation projection hyperplanes (ERDERP), is proposed to extract the semantic information of entities and relations. First, ERDERP establishes a relation hyperplane for each relation and projects the relation embedding into the relation hyperplane. Thus, the semantic information of the relations is extracted effectively. Second, ERDERP establishes a relation projection hyperplane for each relation projection and projects entities into relation projection hyperplane. Thus, the semantic information of the entities is extracted effectively. Moreover, it is theoretically proved that ERDERP can solve antisymmetric problems. Finally, the proposed ERDERP are compared with several typical knowledge graph completion models. The experimental results show that ERDERP is significantly effective in link prediction, especially in relation prediction. For instance, on FB15k and FB15k-237, Hits@1 of ERDERP outperforms TransH at least 30%.

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SHTYLLA, BLERTA, and LOUIS ZULLI. "AN EXTENSION OF THE JONES POLYNOMIAL OF CLASSICAL KNOTS." Journal of Knot Theory and Its Ramifications 15, no. 01 (January 2006): 81–100. http://dx.doi.org/10.1142/s0218216506004294.

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We define a linear algebraic extension of the Jones polynomial of classical knots, and prove that certain key properties of the classical Jones polynomial are properties of the extension. This shows that these properties are linear algebraic in nature, not topological. We identify a topological property of the classical Jones polynomial, that is, a property of the classical Jones polynomial that the extension does not possess. We discuss ortho-projection matrices, ortho-projection graphs, and their Jones polynomials. We classify, up to isomorphism, the connected ortho-projection graphs with at most eight vertices, and show that each such isomorphism class corresponds to a prime alternating classical knot diagram. We give an example of a connected ortho-projection graph with nine vertices that does not correspond to such a diagram.

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Prakash, Sudhir, Rakesh Kumar, Piyush Rai, Shiksha Jain, Manish Singh, Rajnish Pandey, Saanidhya Dubey, Shobhit Srivatava, and Anoop K. Srivastava. "A Study of Chemical Compound of Graph with help of Computer Coding." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 10, no. 3 (December 13, 2019): 1553–64. http://dx.doi.org/10.61841/turcomat.v10i3.14357.

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In this research work we study about the outline of graph structures algorithms required for the recognition of chemical graphs by a computer automatic encoding of organic chemical structures into the line formula notation. During the study we will first classify chemical graph then find a planar projection and fundamental cycles of a chemical graph with its characterization. Then we draw that for automatic construction code from the connection table for this we need some algorithms. Thus a graph structure language like GRAAL should prove useful for chemical coding systems. Further development along these lines should be helpful in coding knotted chemical structures.

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Pan, Lei, Hengchao Li, Xiang Dai, Ying Cui, Xifeng Huang, and Lican Dai. "Latent Low-Rank Projection Learning with Graph Regularization for Feature Extraction of Hyperspectral Images." Remote Sensing 14, no. 13 (June 27, 2022): 3078. http://dx.doi.org/10.3390/rs14133078.

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Due to the great benefit of rich spectral information, hyperspectral images (HSIs) have been successfully applied in many fields. However, some problems of concern also limit their further applications, such as high dimension and expensive labeling. To address these issues, an unsupervised latent low-rank projection learning with graph regularization (LatLRPL) method is presented for feature extraction and classification of HSIs in this paper, in which discriminative features can be extracted from the view of latent space by decomposing the latent low-rank matrix into two different matrices, also benefiting from the preservation of intrinsic subspace structures by the graph regularization. Different from the graph embedding-based methods that need two phases to obtain the low-dimensional projections, one step is enough for LatLRPL by constructing the integrated projection learning model, reducing the complexity and simultaneously improving the robustness. To improve the performance, a simple but effective strategy is exploited by conducting the local weighted average on the pixels in a sliding window for HSIs. Experiments on the Indian Pines and Pavia University datasets demonstrate the superiority of the proposed LatLRPL method.

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Zhang, Zhao Yang, Zheng Tian, and Wei Dong Yan. "Spectral Feature Matching Based on Isometric Projection of Matrix." Applied Mechanics and Materials 121-126 (October 2011): 4161–65. http://dx.doi.org/10.4028/www.scientific.net/amm.121-126.4161.

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This paper presents a spectral method to matching a pair of feature sets based on isometric projection of matrix. In the proposed method, a graph is constructed to model the structure relationships between features. Then the correspondence is found by minimizing the inner product between two isometric projections of the weighted adjacency matrix of graph. Finally, transformation between the two feature sets is estimated according to correct correspondences. The performance of the proposed approach is better than the state-of-the-art method in terms of correct ratio under position perturbation and computation time. Experiments on a number of simulated data, synthetic and real-world images show the validity of the proposed algorithm.

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Jin, Wei, Fangyue Chen, and Qinbin He. "Directed Projection Graph of N-Dimensional Hypercube and Subhypercube Decomposition of Balanced Linearly Separable Boolean Functions." International Journal of Bifurcation and Chaos 31, no. 09 (July 2021): 2150138. http://dx.doi.org/10.1142/s0218127421501388.

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A directed projection graph of the [Formula: see text]-dimensional hypercube on the two-dimensional plane is successfully created. Any [Formula: see text]-variable Boolean function can be easily transformed to an induced subgraph of the projection. Therefore, the discussions on [Formula: see text]-variable Boolean functions only need to focus on a two-dimensional planar graph. Some mathematical theories on the projection graph and the induced subgraph are established, and some properties and characteristics of a balanced linearly separable Boolean function (BLSBF) are uncovered. In particular, the sub-hypercube decompositions of BLSBF is easily represented on the projection, and meanwhile, the enumeration scheme for counting the number of [Formula: see text]-variable BLSBFs is developed by using equivalence classification and conformal transformation. With the aid of the directed projection grap constructed in this paper, one can further study many difficult problems in some fields such as Boolean functions and artificial neural networks.

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Zhang, Xianhang, Hanchen Wang, Jianke Yu, Chen Chen, Xiaoyang Wang, and Wenjie Zhang. "Polarity-based graph neural network for sign prediction in signed bipartite graphs." World Wide Web 25, no. 2 (February 16, 2022): 471–87. http://dx.doi.org/10.1007/s11280-022-01015-4.

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AbstractAs a fundamental data structure, graphs are ubiquitous in various applications. Among all types of graphs, signed bipartite graphs contain complex structures with positive and negative links as well as bipartite settings, on which conventional graph analysis algorithms are no longer applicable. Previous works mainly focus on unipartite signed graphs or unsigned bipartite graphs separately. Several models are proposed for applications on the signed bipartite graphs by utilizing the heuristic structural information. However, these methods have limited capability to fully capture the information hidden in such graphs. In this paper, we propose the first graph neural network on signed bipartite graphs, namely Polarity-based Graph Convolutional Network (PbGCN), for sign prediction task with the help of balance theory. We introduce the novel polarity attribute to signed bipartite graphs, based on which we construct one-mode projection graphs to allow the GNNs to aggregate information between the same type nodes. Extensive experiments on five datasets demonstrate the effectiveness of our proposed techniques.

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Shen, Xiang-Jun, Stanley Ebhohimhen Abhadiomhen, Yang Yang, Zhifeng Liu, and Sirui Tian. "Edge Structure Learning via Low Rank Residuals for Robust Image Classification." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 2 (June 26, 2023): 2236–44. http://dx.doi.org/10.1609/aaai.v37i2.25318.

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Traditional low-rank methods overlook residuals as corruptions, but we discovered that low-rank residuals actually keep image edges together with corrupt components. Therefore, filtering out such structural information could hamper the discriminative details in images, especially in heavy corruptions. In order to address this limitation, this paper proposes a novel method named ESL-LRR, which preserves image edges by finding image projections from low-rank residuals. Specifically, our approach is built in a manifold learning framework where residuals are regarded as another view of image data. Edge preserved image projections are then pursued using a dynamic affinity graph regularization to capture the more accurate similarity between residuals while suppressing the influence of corrupt ones. With this adaptive approach, the proposed method can also find image intrinsic low-rank representation, and much discriminative edge preserved projections. As a result, a new classification strategy is introduced, aligning both modalities to enhance accuracy. Experiments are conducted on several benchmark image datasets, including MNIST, LFW, and COIL100. The results show that the proposed method has clear advantages over compared state-of-the-art (SOTA) methods, such as Low-Rank Embedding (LRE), Low-Rank Preserving Projection via Graph Regularized Reconstruction (LRPP_GRR), and Feature Selective Projection (FSP) with more than 2% improvement, particularly in corrupted cases.

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Liang, Yingyi, Lei You, Xiaohuan Lu, Zhenyu He, and Hongpeng Wang. "Low-Rank Projection Learning via Graph Embedding." Neurocomputing 348 (July 2019): 97–106. http://dx.doi.org/10.1016/j.neucom.2018.05.122.

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Li, Ji, and Hongkai Zhao. "Solving phase retrieval via graph projection splitting." Inverse Problems 36, no. 5 (May 1, 2020): 055003. http://dx.doi.org/10.1088/1361-6420/ab79fa.

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JEONG, JA A., EUN JI KANG, and GI HYUN PARK. "Purely infinite labeled graph -algebras." Ergodic Theory and Dynamical Systems 39, no. 8 (December 4, 2017): 2128–58. http://dx.doi.org/10.1017/etds.2017.123.

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In this paper, we consider pure infiniteness of generalized Cuntz–Krieger algebras associated to labeled spaces $(E,{\mathcal{L}},{\mathcal{E}})$. It is shown that a $C^{\ast }$-algebra $C^{\ast }(E,{\mathcal{L}},{\mathcal{E}})$ is purely infinite in the sense that every non-zero hereditary subalgebra contains an infinite projection (we call this property (IH)) if $(E,{\mathcal{L}},{\mathcal{E}})$ is disagreeable and every vertex connects to a loop. We also prove that under the condition analogous to (K) for usual graphs, $C^{\ast }(E,{\mathcal{L}},{\mathcal{E}})=C^{\ast }(p_{A},s_{a})$ is purely infinite in the sense of Kirchberg and Rørdam if and only if every generating projection $p_{A}$, $A\in {\mathcal{E}}$, is properly infinite, and also if and only if every quotient of $C^{\ast }(E,{\mathcal{L}},{\mathcal{E}})$ has property (IH).

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Wagenpfeil, Stefan, Binh Vu, Paul Mc Kevitt, and Matthias Hemmje. "Fast and Effective Retrieval for Large Multimedia Collections." Big Data and Cognitive Computing 5, no. 3 (July 22, 2021): 33. http://dx.doi.org/10.3390/bdcc5030033.

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The indexing and retrieval of multimedia content is generally implemented by employing feature graphs. These graphs typically contain a significant number of nodes and edges to reflect the level of detail in feature detection. A higher level of detail increases the effectiveness of the results, but also leads to more complex graph structures. However, graph traversal-based algorithms for similarity are quite inefficient and computationally expensive, especially for large data structures. To deliver fast and effective retrieval especially for large multimedia collections and multimedia big data, an efficient similarity algorithm for large graphs in particular is desirable. Hence, in this paper, we define a graph projection into a 2D space (Graph Code) and the corresponding algorithms for indexing and retrieval. We show that calculations in this space can be performed more efficiently than graph traversals due to the simpler processing model and the high level of parallelization. As a consequence, we demonstrate experimentally that the effectiveness of retrieval also increases substantially, as the Graph Code facilitates more levels of detail in feature fusion. These levels of detail also support an increased trust prediction, particularly for fused social media content. In our mathematical model, we define a metric triple for the Graph Code, which also enhances the ranked result representations. Thus, Graph Codes provide a significant increase in efficiency and effectiveness, especially for multimedia indexing and retrieval, and can be applied to images, videos, text and social media information.

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He, Qingdong, Zhengning Wang, Hao Zeng, Yi Zeng, and Yijun Liu. "SVGA-Net: Sparse Voxel-Graph Attention Network for 3D Object Detection from Point Clouds." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 1 (June 28, 2022): 870–78. http://dx.doi.org/10.1609/aaai.v36i1.19969.

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Accurate 3D object detection from point clouds has become a crucial component in autonomous driving. However, the volumetric representations and the projection methods in previous works fail to establish the relationships between the local point sets. In this paper, we propose Sparse Voxel-Graph Attention Network (SVGA-Net), a novel end-to-end trainable network which mainly contains voxel-graph module and sparse-to-dense regression module to achieve comparable 3D detection tasks from raw LIDAR data. Specifically, SVGA-Net constructs the local complete graph within each divided 3D spherical voxel and global KNN graph through all voxels. The local and global graphs serve as the attention mechanism to enhance the extracted features. In addition, the novel sparse-to-dense regression module enhances the 3D box estimation accuracy through feature maps aggregation at different levels. Experiments on KITTI detection benchmark and Waymo Open dataset demonstrate the efficiency of extending the graph representation to 3D object detection and the proposed SVGA-Net can achieve decent detection accuracy.

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Wang, Yong-mao, Zheng-guang Xu, and Shan Zhao. "Neighborhood Graph Embedding Based Local Adaptive Discriminant Projection." Journal of Electronics & Information Technology 35, no. 3 (January 20, 2014): 633–38. http://dx.doi.org/10.3724/sp.j.1146.2012.00793.

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Nie, Xiushan, Ju Liu, Qian Wang, and Wenjun Zeng. "Graph-based video fingerprinting using double optimal projection." Journal of Visual Communication and Image Representation 32 (October 2015): 120–29. http://dx.doi.org/10.1016/j.jvcir.2015.08.001.

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Wang, Zhuo, Tingting Hou, Dawei Song, Zhun Li, and Tianqi Kong. "Detecting Review Spammer Groups via Bipartite Graph Projection." Computer Journal 59, no. 6 (August 19, 2015): 861–74. http://dx.doi.org/10.1093/comjnl/bxv068.

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Wen, Jie, Na Han, Xiaozhao Fang, Lunke Fei, Ke Yan, and Shanhua Zhan. "Low-Rank Preserving Projection Via Graph Regularized Reconstruction." IEEE Transactions on Cybernetics 49, no. 4 (April 2019): 1279–91. http://dx.doi.org/10.1109/tcyb.2018.2799862.

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Alshammari, Mashaan, John Stavrakakis, Adel F. Ahmed, and Masahiro Takatsuka. "Random projection forest initialization for graph convolutional networks." MethodsX 11 (December 2023): 102315. http://dx.doi.org/10.1016/j.mex.2023.102315.

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TIAN, CONG, and ZHENHUA DUAN. "Complexity of propositional projection temporal logic with star." Mathematical Structures in Computer Science 19, no. 1 (February 2009): 73–100. http://dx.doi.org/10.1017/s096012950800738x.

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This paper investigates the complexity of Propositional Projection Temporal Logic with Star (PPTL*). To this end, Propositional Projection Temporal Logic (PPTL) is first extended to include projection star. Then, by reducing the emptiness problem of star-free expressions to the problem of the satisfiability of PPTL* formulas, the lower bound of the complexity for the satisfiability of PPTL* formulas is proved to be non-elementary. Then, to prove the decidability of PPTL*, the normal form, normal form graph (NFG) and labelled normal form graph (LNFG) for PPTL* are defined. Also, algorithms for transforming a formula to its normal form and LNFG are presented. Finally, a decision algorithm for checking the satisfiability of PPTL* formulas is formalised using LNFGs.

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Janson, Svante. "The Numbers of Spanning Trees, Hamilton Cycles and Perfect Matchings in a Random Graph." Combinatorics, Probability and Computing 3, no. 1 (March 1994): 97–126. http://dx.doi.org/10.1017/s0963548300001012.

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The numbers of spanning trees, Hamilton cycles and perfect matchings in a random graph Gnm are shown to be asymptotically normal if m is neither too large nor too small. At the lowest limit m ≍ n3/2, these numbers are asymptotically log-normal. For Gnp, the numbers are asymptotically log-normal for a wide range of p, including p constant. The same results are obtained for random directed graphs and bipartite graphs. The results are proved using decomposition and projection methods.

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Bowditch, Brian H., and Francesca Iezzi. "Projections of the sphere graph to the arc graph of a surface." Journal of Topology and Analysis 10, no. 02 (June 2018): 245–61. http://dx.doi.org/10.1142/s1793525318500115.

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Let [Formula: see text] be a compact surface, and [Formula: see text] be the double of a handlebody. Given a homotopy class of maps from [Formula: see text] to [Formula: see text] inducing an isomorphism of fundamental groups, we describe a canonical uniformly Lipschitz retraction of the sphere graph of [Formula: see text] to the arc graph of [Formula: see text]. We also show that this retraction is a uniformly bounded distance from the nearest point projection map.

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Ahmood, Wasan Ajeel, and Marwa Mohamed Ismaeel. "An Approximation Solution of Linear Differential Equation using Kantorovich Methods." WSEAS TRANSACTIONS ON APPLIED AND THEORETICAL MECHANICS 18 (March 16, 2023): 9–15. http://dx.doi.org/10.37394/232011.2023.18.2.

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In our work, we constructed a numerical approximations method to deal with approximations of a linear differential equation. We explained the general framework of the projection method which helps to clarify the basic ideas of the Kantorovich methods. We applied the iterative projection methods and presented a theorem to show the convergence of the constructed solutions to the exact solution. Also, most of the expressions encountered earlier can be used to define functions. Here are some illustrations. A great deal of information can be learned about a functioning relationship by studying its graph. A fundamental objective of section 4, is to acquaint with the graphs of some important functions and develop basic graphing procedures.

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Jinnai, Yuu, and Alex Fukunaga. "On Hash-Based Work Distribution Methods for Parallel Best-First Search." Journal of Artificial Intelligence Research 60 (October 30, 2017): 491–548. http://dx.doi.org/10.1613/jair.5225.

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Parallel best-first search algorithms such as Hash Distributed A* (HDA*) distribute work among the processes using a global hash function. We analyze the search and communication overheads of state-of-the-art hash-based parallel best-first search algorithms, and show that although Zobrist hashing, the standard hash function used by HDA*, achieves good load balance for many domains, it incurs significant communication overhead since almost all generated nodes are transferred to a different processor than their parents. We propose Abstract Zobrist hashing, a new work distribution method for parallel search which, instead of computing a hash value based on the raw features of a state, uses a feature projection function to generate a set of abstract features which results in a higher locality, resulting in reduced communications overhead. We show that Abstract Zobrist hashing outperforms previous methods on search domains using hand-coded, domain specific feature projection functions. We then propose GRAZHDA*, a graph-partitioning based approach to automatically generating feature projection functions. GRAZHDA* seeks to approximate the partitioning of the actual search space graph by partitioning the domain transition graph, an abstraction of the state space graph. We show that GRAZHDA* outperforms previous methods on domain-independent planning.

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Cao, Keyan, and Chuang Zheng. "TBRm: A Time Representation Method for Industrial Knowledge Graph." Applied Sciences 12, no. 22 (November 8, 2022): 11316. http://dx.doi.org/10.3390/app122211316.

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With the development of the artificial intelligence industry, Knowledge Graph (KG), as a concise and intuitive data presentation form, has received extensive attention and research from both academia and industry in recent years. At the same time, developments in the Internet of Things (IoT) have empowered modern industries to implement large-scale IoT ecosystems, such as the Industrial Internet of Things (IIoT). Using knowledge graphs (KG) to process data from the Industrial Internet of Things (IIoT) is a research field worthy of attention, but most of the researched knowledge graph technologies are mainly concentrated in the field of static knowledge graphs, which are composed of triples. In fact, many graphs also contain some dynamic information, such as time changes at points and time changes at edges; such knowledge graphs are called Temporal Knowledge Graphs (TKGs). We consider the temporal knowledge graph based on the projection and change of space. In order to combine the temporal information, we propose a new representation of the temporal knowledge graph, namely TBRm, which increases the temporal dimension of the translational distance model and utilizes relational predicates in time add representation in time dimension. We evaluate the proposed method on knowledge graph completion tasks using four benchmark datasets. Experiments demonstrate the effectiveness of TBRm representation in the temporal dimension. At the same time, it is also practiced on a network security data set of the Industrial Internet of Things. The practical results prove that the TBRm method can achieve good performance in terms of the degree of harm to IIoT network security.

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DAMIAN, MIRELA, and KRISTIN RAUDONIS. "YAO GRAPHS SPAN THETA GRAPHS." Discrete Mathematics, Algorithms and Applications 04, no. 02 (June 2012): 1250024. http://dx.doi.org/10.1142/s1793830912500243.

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Yao and Theta graphs are defined for a given point set and a fixed integer k > 0. The space around each point is divided into k cones of equal angle, and each point is connected to a nearest neighbor in each cone. The difference between Yao and Theta graphs is in the way the nearest neighbor is defined: Yao graphs minimize the Euclidean distance between a point and its neighbor, and Theta graphs minimize the Euclidean distance between a point and the orthogonal projection of its neighbor on the bisector of the hosting cone. We prove that, corresponding to each edge of the Theta graph Θ6, there is a path in the Yao graph Y6 whose length is at most 8.82 times the edge length. Combined with the result of Bonichon et al., who prove an upper bound of 2 on the stretch factor of Θ6, we obtain an upper bound of 17.64 on the stretch factor of Y6.

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Gumpula, K., N. Koloskov, D. Grzenda, V. Hewes, A. Aurisano, G. Cerati, A. Day, et al. "Graph Neural Network for Object Reconstruction in Liquid Argon Time Projection Chambers." Journal of Physics: Conference Series 2438, no. 1 (February 1, 2023): 012091. http://dx.doi.org/10.1088/1742-6596/2438/1/012091.

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Abstract The Exa.TrkX project presents a graph neural network (GNN) technique for low-level reconstruction of neutrino interactions in a Liquid Argon Time Projection Chamber (LArTPC). GNNs are still a relatively novel technique, and have shown great promise for similar reconstruction tasks in the Large Hadron Collider (LHC). Graphs describing particle interactions are formed by treating each detector hit as a node, with edges describing the relationships between hits. We utilise a multi-head attention message passing network which performs graph convolutions in order to label each node with a particle type. We present an updated variant of our GNN architecture, with several improvements. After testing the model on more realistic simulation with regions of unresponsive wires, the target was modified from edge classification to node classification in order to increase robustness. Removing edges as a classification target opens up a broader possibility space for edge-forming techniques; we explore the model’s performance across a variety of approaches, such as Delaunay triangulation, kNN, and radius-based methods. We also extend this model to the 3D context, sharing information between detector views. By using reconstructed 3D spacepoints to map detector hits from each wire plane, the model naively constructs 2D representations that are independent yet fully consistent.

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Wang, Peng, Jingju Liu, Dongdong Hou, and Shicheng Zhou. "A Cybersecurity Knowledge Graph Completion Method Based on Ensemble Learning and Adversarial Training." Applied Sciences 12, no. 24 (December 16, 2022): 12947. http://dx.doi.org/10.3390/app122412947.

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The application of cybersecurity knowledge graphs is attracting increasing attention. However, many cybersecurity knowledge graphs are incomplete due to the sparsity of cybersecurity knowledge. Existing knowledge graph completion methods do not perform well in domain knowledge, and they are not robust enough relative to noise data. To address these challenges, in this paper we develop a new knowledge graph completion method called CSEA based on ensemble learning and adversarial training. Specifically, we integrate a variety of projection and rotation operations to model the relationships between entities, and use angular information to distinguish entities. A cooperative adversarial training method is designed to enhance the generalization and robustness of the model. We combine the method of generating perturbations for the embedding layers with the self-adversarial training method. The UCB (upper confidence bound) multi-armed bandit method is used to select the perturbations of the embedding layer. This achieves a balance between perturbation diversity and maximum loss. To this end, we build a cybersecurity knowledge graph based on the CVE, CWE, and CAPEC cybersecurity databases. Our experimental results demonstrate the superiority of our proposed model for completing cybersecurity knowledge graphs.

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Jia, Xiuyi, Tao Wen, Weiping Ding, Huaxiong Li, and Weiwei Li. "Semi-supervised label distribution learning via projection graph embedding." Information Sciences 581 (December 2021): 840–55. http://dx.doi.org/10.1016/j.ins.2021.10.009.

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Li, Bin. "Corresponding Block Based Graph Construction for Locality Preserving Projection." Journal of Information and Computational Science 11, no. 11 (July 20, 2014): 3967–74. http://dx.doi.org/10.12733/jics20104220.

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Caelli, T., and S. Kosinov. "An eigenspace projection clustering method for inexact graph matching." IEEE Transactions on Pattern Analysis and Machine Intelligence 26, no. 4 (April 2004): 515–19. http://dx.doi.org/10.1109/tpami.2004.1265866.

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Yi, Yugen, Jianzhong Wang, Wei Zhou, Yuming Fang, Jun Kong, and Yinghua Lu. "Joint graph optimization and projection learning for dimensionality reduction." Pattern Recognition 92 (August 2019): 258–73. http://dx.doi.org/10.1016/j.patcog.2019.03.024.

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Dwyer, Tim, Yehuda Koren, and Kim Marriott. "Constrained graph layout by stress majorization and gradient projection." Discrete Mathematics 309, no. 7 (April 2009): 1895–908. http://dx.doi.org/10.1016/j.disc.2007.12.103.

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Zhang, Sensen, Xun Liang, Simin Niu, Xuan Zhang, Chen Feng, and Yuefeng Ma. "Biomedical Knowledge Graph Embedding with Householder Projection (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 38, no. 21 (March 24, 2024): 23707–8. http://dx.doi.org/10.1609/aaai.v38i21.30535.

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Researchers have applied knowledge graph embedding (KGE) techniques with advanced neural network techniques, such as capsule networks, for predicting drug-drug interactions (DDIs) and achieved remarkable results. However, most ignore molecular structure and position features between drug pairs. They cannot model the biomedical field's significant relational mapping properties (RMPs,1-N, N-1, N-N) relation. To solve these problems, we innovatively propose CDHse that consists of two crucial modules: 1) Entity embedding module, we obtain position feature obtained by PubMedBERT and Convolutional Neural Network (CNN), obtain molecular structure feature with Graphic Nuaral Network (GNN), obtain entity embedding feature of drug pairs, and then incorporate these features into one synthetic feature. 2) Knowledge graph embedding module, the synthetic feature is Householder projections and then embedded in the complex vector space for training. In this paper, we have selected several advanced models for the DDIs task and performed experiments on three standard BioKG to validate the effectiveness of CDHse.

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Wang, Beilei, Yun Xiao, Zhihui Li, Xuanhong Wang, Xiaojiang Chen, and Dingyi Fang. "Robust Self-Weighted Multi-View Projection Clustering." Proceedings of the AAAI Conference on Artificial Intelligence 34, no. 04 (April 3, 2020): 6110–17. http://dx.doi.org/10.1609/aaai.v34i04.6075.

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Many real-world applications involve data collected from different views and with high data dimensionality. Furthermore, multi-view data always has unavoidable noise. Clustering on this kind of high-dimensional and noisy multi-view data remains a challenge due to the curse of dimensionality and ineffective de-noising and integration of multiple views. Aiming at this problem, in this paper, we propose a Robust Self-weighted Multi-view Projection Clustering (RSwMPC) based on ℓ2,1-norm, which can simultaneously reduce dimensionality, suppress noise and learn local structure graph. Then the obtained optimal graph can be directly used for clustering while no further processing is required. In addition, a new method is introduced to automatically learn the optimal weight of each view with no need to generate additional parameters to adjust the weight. Extensive experimental results on different synthetic datasets and real-world datasets demonstrate that the proposed algorithm outperforms other state-of-the-art methods on clustering performance and robustness.

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Journal articles on the topic 'Graph projection'

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