scholarly journals Optimal Linear Arrangement of Turán Graphs

2020 ◽  
Vol 8 (6) ◽  
pp. 3618-3621
Keyword(s):  
Parallel Processing ◽  
Dimensional Space ◽  
Graph Embedding ◽  
Optimal Layout ◽  
Linear Arrangement ◽  
Efficient Approach ◽  
Optimal Linear ◽  
Low Dimensional ◽  
Processing Techniques ◽  
Turán Graph

Graph embedding in parallel processing techniques has acquired considerable attention and hence raised as an efficient approach for reducing overhead data into low-dimensional space. Optimal layout and congestion are powerful parameters to examine the capability of embedding. In this study, Modified Congestion and  -Partition lemmas are utilized to obtain the optimal layout of Turán graph into path and windmill graphs.

scholarly journals Adversarially Regularized Graph Autoencoder for Graph Embedding

2018 ◽  
Author(s):  
Shirui Pan ◽  
Ruiqi Hu ◽  
Guodong Long ◽  
Jing Jiang ◽  
Lina Yao ◽  
...  
Keyword(s):  
Real World ◽  
Topological Structure ◽  
Dimensional Space ◽  
Experimental Studies ◽  
Graph Embedding ◽  
Compact Representation ◽  
Graph Visualization ◽  
Graph Data ◽  
Training Scheme ◽  
Low Dimensional

Graph embedding is an effective method to represent graph data in a low dimensional space for graph analytics.  Most existing embedding algorithms typically focus on preserving the topological structure or minimizing the reconstruction errors of graph data,  but they have mostly ignored the data distribution of the latent codes from the graphs, which often results in inferior embedding in  real-world  graph data. In this paper, we propose a novel adversarial graph embedding framework for graph data. The framework encodes the topological structure and node content in a graph to a compact representation, on which a decoder is trained to reconstruct the graph structure. Furthermore, the latent representation is enforced to match a prior distribution via an adversarial training scheme. To learn a robust embedding,  two variants of adversarial approaches,  adversarially regularized graph autoencoder (ARGA) and adversarially regularized variational graph autoencoder (ARVGA), are developed. Experimental studies on real-world graphs validate our design and demonstrate that our algorithms outperform baselines by a wide margin in link prediction,  graph clustering, and graph visualization tasks.

scholarly journals The spring bounces back: introducing the strain elevation tension spring embedding algorithm for network representation

2020 ◽  
Vol 5 (1) ◽  
Author(s):  
Jonathan Bourne
Keyword(s):  
Dimensional Space ◽  
Directed Graphs ◽  
Graph Embedding ◽  
Graph Classification ◽  
Embedding Method ◽  
Tension Spring ◽  
The Social ◽  
Node Attributes ◽  
Low Dimensional ◽  
Memory Complexity

AbstractThis paper introduces the strain elevation tension spring embedding (SETSe) algorithm. SETSe is a novel graph embedding method that uses a physical model to project feature-rich networks onto a manifold with semi-Euclidean properties. Due to its method, SETSe avoids the tractability issues faced by traditional force-directed graphs, having an iteration time and memory complexity that is linear to the number of edges in the network. SETSe is unusual as an embedding method as it does not reduce dimensionality or explicitly attempt to place similar nodes close together in the embedded space. Despite this, the algorithm outperforms five common graph embedding algorithms, on graph classification and node classification tasks, in low-dimensional space. The algorithm is also used to embed 100 social networks ranging in size from 700 to over 40,000 nodes and up to 1.5 million edges. The social network embeddings show that SETSe provides a more expressive alternative to the popular assortativity metric and that even on large complex networks, SETSe’s classification ability outperforms the naive baseline and the other embedding methods in low-dimensional representation. SETSe is a fast and flexible unsupervised embedding algorithm that integrates node attributes and graph topology to produce interpretable results.

TemporalNode2vec: Task-agnostic and Task-specific Temporal Node Embedding

2020 ◽  
Author(s):  
Mounir HADDAD ◽  
Cécile BOTHOREL ◽  
Philippe LENCA ◽  
Dominique BEDART
Keyword(s):  
Structural Information ◽  
Dimensional Space ◽  
Graph Embedding ◽  
Dynamic Graph ◽  
Time Step ◽  
Classification Tasks ◽  
Node Classification ◽  
Low Dimensional ◽  
Data Efficiency ◽  
Over Time

Abstract The goal of graph embedding is to learn a representation of graphs vertices in a latent low-dimensional space in order to encode the structural information that lies in graphs. While real-world networks evolve over time, the majority of research focuses on static networks, ignoring local and global evolution patterns. A simplistic approach consists of learning nodes embeddings independently for each time step. This can cause unstable and inefficient representations over time. In this paper, we present TemporalNode2vec, a novel dynamic graph embedding approach that learns continuous time-aware node representations. Overall, we demonstrate that our method improves node classification tasks comparing to previous static and dynamic approaches as it achieves up to 14% gain regarding the F1 score metric. We also prove that our model is more data-efficient than several baseline methods, as it affords to achieve good performances with a limited number of node representation features. Moreover, we develop and evaluate a task-specific variant of our method called TsTemporalNode2vec, aiming to improve the performances and the data-efficiency of node classification tasks.

scholarly journals A Generative-Discriminative Framework that Integrates Imaging, Genetic, and Diagnosis into Coupled Low Dimensional Space

NeuroImage ◽  
2021 ◽  
pp. 118200
Author(s):  
Sayan Ghosal ◽  
Qiang Chen ◽  
Giulio Pergola ◽  
Aaron L. Goldman ◽  
William Ulrich ◽  
...  
Keyword(s):  
Dimensional Space ◽  
Low Dimensional

scholarly journals TransET: Knowledge Graph Embedding with Entity Types

Electronics ◽  
2021 ◽  
Vol 10 (12) ◽  
pp. 1407
Author(s):  
Peng Wang ◽  
Jing Zhou ◽  
Yuzhang Liu ◽  
Xingchen Zhou
Keyword(s):  
Link Prediction ◽  
State Of The Art ◽  
Score Function ◽  
Graph Embedding ◽  
Vector Spaces ◽  
Knowledge Graph ◽  
Semantic Features ◽  
Knowledge Graphs ◽  
Real World Datasets ◽  
Low Dimensional

Knowledge graph embedding aims to embed entities and relations into low-dimensional vector spaces. Most existing methods only focus on triple facts in knowledge graphs. In addition, models based on translation or distance measurement cannot fully represent complex relations. As well-constructed prior knowledge, entity types can be employed to learn the representations of entities and relations. In this paper, we propose a novel knowledge graph embedding model named TransET, which takes advantage of entity types to learn more semantic features. More specifically, circle convolution based on the embeddings of entity and entity types is utilized to map head entity and tail entity to type-specific representations, then translation-based score function is used to learn the presentation triples. We evaluated our model on real-world datasets with two benchmark tasks of link prediction and triple classification. Experimental results demonstrate that it outperforms state-of-the-art models in most cases.

scholarly journals Artifacts in Simultaneous hdEEG/fMRI Imaging: A Nonlinear Dimensionality Reduction Approach

Sensors ◽  
2019 ◽  
Vol 19 (20) ◽  
pp. 4454 ◽  
Author(s):  
Marek Piorecky ◽  
Vlastimil Koudelka ◽  
Jan Strobl ◽  
Martin Brunovsky ◽  
Vladimir Krajca
Keyword(s):  
Data Structure ◽  
Spatial Clustering ◽  
Dimensional Space ◽  
Head Movements ◽  
Nonlinear Dimensionality Reduction ◽  
Space Resolution ◽  
Additional Information ◽  
Nonlinear Dimension ◽  
The Time Domain ◽  
Low Dimensional

Simultaneous recordings of electroencephalogram (EEG) and functional magnetic resonance imaging (fMRI) are at the forefront of technologies of interest to physicians and scientists because they combine the benefits of both modalities—better time resolution (hdEEG) and space resolution (fMRI). However, EEG measurements in the scanner contain an electromagnetic field that is induced in leads as a result of gradient switching slight head movements and vibrations, and it is corrupted by changes in the measured potential because of the Hall phenomenon. The aim of this study is to design and test a methodology for inspecting hidden EEG structures with respect to artifacts. We propose a top-down strategy to obtain additional information that is not visible in a single recording. The time-domain independent component analysis algorithm was employed to obtain independent components and spatial weights. A nonlinear dimension reduction technique t-distributed stochastic neighbor embedding was used to create low-dimensional space, which was then partitioned using the density-based spatial clustering of applications with noise (DBSCAN). The relationships between the found data structure and the used criteria were investigated. As a result, we were able to extract information from the data structure regarding electrooculographic, electrocardiographic, electromyographic and gradient artifacts. This new methodology could facilitate the identification of artifacts and their residues from simultaneous EEG in fMRI.

scholarly journals Optimizing the structure and movement of a robotic bat with biological kinematic synergies

2018 ◽  
Vol 37 (10) ◽  
pp. 1233-1252 ◽  
Author(s):  
Jonathan Hoff ◽  
Alireza Ramezani ◽  
Soon-Jo Chung ◽  
Seth Hutchinson
Keyword(s):  
Principal Component Analysis ◽  
Topological Structure ◽  
Degrees Of Freedom ◽  
Dimensional Space ◽  
Principal Component ◽  
Biologically Inspired ◽  
Wing Kinematics ◽  
Wing Motion ◽  
Kinematic Synergies ◽  
Low Dimensional

In this article, we present methods to optimize the design and flight characteristics of a biologically inspired bat-like robot. In previous, work we have designed the topological structure for the wing kinematics of this robot; here we present methods to optimize the geometry of this structure, and to compute actuator trajectories such that its wingbeat pattern closely matches biological counterparts. Our approach is motivated by recent studies on biological bat flight that have shown that the salient aspects of wing motion can be accurately represented in a low-dimensional space. Although bats have over 40 degrees of freedom (DoFs), our robot possesses several biologically meaningful morphing specializations. We use principal component analysis (PCA) to characterize the two most dominant modes of biological bat flight kinematics, and we optimize our robot’s parametric kinematics to mimic these. The method yields a robot that is reduced from five degrees of actuation (DoAs) to just three, and that actively folds its wings within a wingbeat period. As a result of mimicking synergies, the robot produces an average net lift improvesment of 89% over the same robot when its wings cannot fold.

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