scholarly journals Hyperplane-based time-aware knowledge graph embedding for temporal knowledge graph completion

2021 ◽  
pp. 1-13
Author(s):  
Peng He ◽  
Gang Zhou ◽  
Hongbo Liu ◽  
Yi Xia ◽  
Ling Wang
Keyword(s):  
Temporal Dynamics ◽  
Sampling Strategy ◽  
Knowledge Graph ◽  
Polar Coordinate System ◽  
Training Procedure ◽  
Completion Task ◽  
Polar Coordinate ◽  
Time Specific ◽  
Time Information ◽  
Time Aware

Knowledge Graph (KG) embedding approaches have been proved effective to infer new facts for a KG based on the existing ones–a problem known as KG completion. However, most of them have focused on static KGs, in fact, relational facts in KGs often show temporal dynamics, e.g., the fact (US, has president, Barack Obama, [2009–2017]) is only valid from 2009 to 2017. Therefore, utilizing available time information to develop temporal KG embedding models is an increasingly important problem. In this paper, we propose a new hyperplane-based time-aware KG embedding model for temporal KG completion. By employing the method of time-specific hyperplanes, our model could explicitly incorporate time information in the entity-relation space to predict missing elements in the KG more effectively, especially temporal scopes for facts with missing time information. Moreover, in order to model and infer four important relation patterns including symmetry, antisymmetry, inversion and composition, we map facts happened at the same time into a polar coordinate system. During training procedure, a time-enhanced negative sampling strategy is proposed to get more effective negative samples. Experimental results on datasets extracted from real-world temporal KGs show that our model significantly outperforms existing state-of-the-art approaches for the KG completion task.

scholarly journals Learning Hierarchy-Aware Knowledge Graph Embeddings for Link Prediction

2020 ◽  
Vol 34 (03) ◽  
pp. 3065-3072 ◽  
Author(s):  
Zhanqiu Zhang ◽  
Jianyu Cai ◽  
Yongdong Zhang ◽  
Jie Wang
Keyword(s):  
Coordinate System ◽  
Link Prediction ◽  
Graph Embedding ◽  
Knowledge Graph ◽  
Polar Coordinate System ◽  
Radial Coordinate ◽  
Polar Coordinate ◽  
Benchmark Datasets ◽  
Knowledge Graphs ◽  
Semantic Hierarchies

Knowledge graph embedding, which aims to represent entities and relations as low dimensional vectors (or matrices, tensors, etc.), has been shown to be a powerful technique for predicting missing links in knowledge graphs. Existing knowledge graph embedding models mainly focus on modeling relation patterns such as symmetry/antisymmetry, inversion, and composition. However, many existing approaches fail to model semantic hierarchies, which are common in real-world applications. To address this challenge, we propose a novel knowledge graph embedding model—namely, Hierarchy-Aware Knowledge Graph Embedding (HAKE)—which maps entities into the polar coordinate system. HAKE is inspired by the fact that concentric circles in the polar coordinate system can naturally reflect the hierarchy. Specifically, the radial coordinate aims to model entities at different levels of the hierarchy, and entities with smaller radii are expected to be at higher levels; the angular coordinate aims to distinguish entities at the same level of the hierarchy, and these entities are expected to have roughly the same radii but different angles. Experiments demonstrate that HAKE can effectively model the semantic hierarchies in knowledge graphs, and significantly outperforms existing state-of-the-art methods on benchmark datasets for the link prediction task.

Reasoning over temporal knowledge graph with temporal consistency constraints

2021 ◽  
pp. 1-10
Author(s):  
Xiaojun Chen ◽  
Shengbin Jia ◽  
Ling Ding ◽  
Yang Xiang
Keyword(s):  
Short Term Memory ◽  
Knowledge Graph ◽  
Temporal Consistency ◽  
Short Term ◽  
Basic Model ◽  
Consistency Constraints ◽  
Memory Network ◽  
Long Short Term Memory ◽  
Relation Prediction ◽  
Time Information

Knowledge graph reasoning or completion aims at inferring missing facts by reasoning about the information already present in the knowledge graph. In this work, we explore the problem of temporal knowledge graph reasoning that performs inference on the graph over time. Most existing reasoning models ignore the time information when learning entities and relations representations. For example, the fact (Scarlett Johansson, spouse Of, Ryan Reynolds) was true only during 2008 - 2011. To facilitate temporal reasoning, we present TA-TransRILP, which involves temporal information by utilizing RNNs and takes advantage of Integer Linear Programming. Specifically, we utilize a character-level long short-term memory network to encode relations with sequences of temporal tokens, and combine it with common reasoning model. To achieve more accurate reasoning, we further deploy temporal consistency constraints to basic model, which can help in assessing the validity of a fact better. We conduct entity prediction and relation prediction on YAGO11k and Wikidata12k datasets. Experimental results demonstrate that TA-TransRILP can make more accurate predictions by taking time information and temporal consistency constraints into account, and outperforms existing methods with a significant improvement about 6-8% on Hits@10.

Natural Frequencies and Mode Shapes of Elliptic Plates With Boundary Characteristic Orthogonal Polynomials As Assumed Shape Functions

1991 ◽  
Author(s):  
C. Rajalingham ◽  
R. B. Bhat ◽  
G. D. Xistris
Keyword(s):  
Coordinate System ◽  
Orthogonal Polynomials ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Mode Shapes ◽  
Polar Coordinate System ◽  
Free Boundaries ◽  
Natural Modes ◽  
Polar Coordinate ◽  
Boundary Characteristic

Abstract The natural frequencies and natural modes of vibration of uniform elliptic plates with clamped, simply supported and free boundaries are investigated using Rayleigh-Ritz method. A modified polar coordinate system is used to investigate the problem. Energy expressions in Cartesian coordinate system are transformed into the modified polar coordinate system. Boundary characteristic orthogonal polynomials in the radial direction, and trigonometric functions in the angular direction are used to express the deflection of the plate. These deflection shapes are classified into four basic categories, depending on its symmetrical or antisymmetrical property about the major and minor axes of the ellipse. The first six natural modes in each of the above categories are presented in the form of contour plots.

scholarly journals Aerosol Plume Detection Algorithm Based on Image Segmentation of Scanning Atmospheric Lidar Data

2016 ◽  
Vol 33 (4) ◽  
pp. 697-712 ◽  
Author(s):  
R. Andrew Weekley ◽  
R. Kent Goodrich ◽  
Larry B. Cornman
Keyword(s):  
Coordinate System ◽  
Original Data ◽  
Detection Algorithm ◽  
Polar Coordinate System ◽  
Lidar Data ◽  
Image Processing Algorithm ◽  
Polar Coordinate ◽  
Scanning Lidar ◽  
Performance Statistics ◽  
Background Fields

AbstractAn image-processing algorithm has been developed to identify aerosol plumes in scanning lidar backscatter data. The images in this case consist of lidar data in a polar coordinate system. Each full lidar scan is taken as a fixed image in time, and sequences of such scans are considered functions of time. The data are analyzed in both the original backscatter polar coordinate system and a lagged coordinate system. The lagged coordinate system is a scatterplot of two datasets, such as subregions taken from the same lidar scan (spatial delay), or two sequential scans in time (time delay). The lagged coordinate system processing allows for finding and classifying clusters of data. The classification step is important in determining which clusters are valid aerosol plumes and which are from artifacts such as noise, hard targets, or background fields. These cluster classification techniques have skill since both local and global properties are used. Furthermore, more information is available since both the original data and the lag data are used. Performance statistics are presented for a limited set of data processed by the algorithm, where results from the algorithm were compared to subjective truth data identified by a human.

scholarly journals The method for synthesis of the contact ratio of noncircular bevel gears

2021 ◽  
Vol 12 (1) ◽  
pp. 165-172
Author(s):  
Kan Shi ◽  
Shuai Lin ◽  
Yan'an Yao
Keyword(s):  
Transmission Ratio ◽  
Polar Coordinate System ◽  
Contact Ratio ◽  
Bevel Gears ◽  
Innovative Methods ◽  
Ratio Curve ◽  
Pure Rolling ◽  
Variable Transmission ◽  
Polar Coordinate ◽  
Pitch Curve

Abstract. As a type of spatial transmission mechanism, noncircular bevel gears can be used to transfer the power and motion with a variable transmission ratio between intersecting axes. In this paper, utilizing the spherical triangle theorem and meshing principle, the parametric equations of the contact ratio are established in the space polar coordinate system. Two innovative methods are proposed to analyze the contact ratio by using the rotation angle of the driving (driven) gears and the arc length of pitch curve as pure rolling. In the case of modified gear and X-zero gear, whether the noncircular bevel gear is continuously driven is deduced. The simulation transmission ratio curve and theoretical transmission ratio curve are compared to verify the rationality of the design.

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