scholarly journals An Unsupervised Learning Method for Attributed Network Based on Non-Euclidean Geometry

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 905
Author(s):  
Wei Wu ◽  
Guangmin Hu ◽  
Fucai Yu
Keyword(s):  
Ricci Curvature ◽  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Structural Information ◽  
Information Aggregation ◽  
Network Embedding ◽  
Heterogeneous Information ◽  
Non Euclidean Geometry ◽  
Attributed Network ◽  
Attribute Information

Many real-world networks can be modeled as attributed networks, where nodes are affiliated with attributes. When we implement attributed network embedding, we need to face two types of heterogeneous information, namely, structural information and attribute information. The structural information of undirected networks is usually expressed as a symmetric adjacency matrix. Network embedding learning is to utilize the above information to learn the vector representations of nodes in the network. How to integrate these two types of heterogeneous information to improve the performance of network embedding is a challenge. Most of the current approaches embed the networks in Euclidean spaces, but the networks themselves are non-Euclidean. As a consequence, the geometric differences between the embedded space and the underlying space of the network will affect the performance of the network embedding. According to the non-Euclidean geometry of networks, this paper proposes an attributed network embedding framework based on hyperbolic geometry and the Ricci curvature, namely, RHAE. Our method consists of two modules: (1) the first module is an autoencoder module in which each layer is provided with a network information aggregation layer based on the Ricci curvature and an embedding layer based on hyperbolic geometry; (2) the second module is a skip-gram module in which the random walk is based on the Ricci curvature. These two modules are based on non-Euclidean geometry, but they fuse the topology information and attribute information in the network from different angles. Experimental results on some benchmark datasets show that our approach outperforms the baselines.

scholarly journals KONSISTENSI AKSIOMA-AKSIOMA TERHADAP ISTILAH-ISTILAH TAKTERDEFINISI GEOMETRI HIPERBOLIK PADA MODEL PIRINGAN POINCARE

EDUPEDIA ◽  
2018 ◽  
Vol 2 (2) ◽  
pp. 161
Author(s):  
Febriyana Putra Pratama ◽  
Julan Hernadi
Keyword(s):  
Half Plane ◽  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Cross Ratio ◽  
Literature Study ◽  
Disk Model ◽  
Non Euclidean Geometry ◽  
The Cross ◽  
Definition Of ◽  
Poincaré Disk

This research aims to know the interpretation the undefined terms on Hyperbolic geometry and it’s consistence with respect to own axioms of Poincare disk model. This research is a literature study that discusses about Hyperbolic geometry. This study refers to books of Foundation of Geometry second edition by Gerard A. Venema (2012), Euclidean and Non Euclidean Geometry (Development and History)  by Greenberg (1994), Geometry : Euclid and Beyond by Hartshorne (2000) and Euclidean Geometry: A First Course by M. Solomonovich (2010). The steps taken in the study are: (1) reviewing the various references on the topic of Hyperbolic geometry. (2) representing the definitions and theorems on which the Hyperbolic geometry is based. (3) prepare all materials that have been collected in coherence to facilitate the reader in understanding it. This research succeeded in interpret the undefined terms of Hyperbolic geometry on Poincare disk model. The point is coincide point in the Euclid on circle . Then the point onl γ is not an Euclid point. That point interprets the point on infinity. Lines are categoried in two types. The first type is any open diameters of   . The second type is any open arcs of circle. Half-plane in Poincare disk model is formed by Poincare line which divides Poincare field into two parts. The angle in this model is interpreted the same as the angle in Euclid geometry. The distance is interpreted in Poincare disk model defined by the cross-ratio as follows. The definition of distance from  to  is , where  is cross-ratio defined by  . Finally the study also is able to show that axioms of Hyperbolic geometry on the Poincare disk model consistent with respect to associated undefined terms.

On the Medians of a Triangle in Hyperbolic Geometry

1958 ◽  
Vol 10 ◽  
pp. 502-506 ◽  
Author(s):  
O. Bottema
Keyword(s):  
Hyperbolic Geometry ◽  
Euclidean Geometry ◽  
Common Point ◽  
Non Euclidean Geometry ◽  
Image Position

In non-Euclidean geometry the three medians of a triangle A 1A2A3 (each joining a vertex A i with the internal midpoint G i of the opposite side) are concurrent; their common point is the centroid G. But the Euclidean theorem ' which depends on similarity, does not hold.

scholarly journals NEMPD: A network embedding-based method for predicting miRNA-disease associations by preserving behavior and attribute information

2020 ◽  
Author(s):  
Bo-Ya Ji ◽  
Zhu-Hong You ◽  
Zhan-Heng Chen ◽  
Leon Wong ◽  
Hai-Cheng Yi
Keyword(s):  
Structural Information ◽  
Disease Association ◽  
Single Type ◽  
Network Embedding ◽  
Graph Representations ◽  
Non Coding Rna ◽  
Attribute Information ◽  
Disease Associations ◽  
Representation Method ◽  
Great Potency

Abstract Background: As an important non-coding RNA, microRNA (miRNA) plays a significant role in a series of life processes and is closely associated with a variety of Human diseases. Hence, identification of potential miRNA-disease associations can make great contributions to the research and treatment of Human diseases. However, to our knowledge, many existing computational methods only utilize the single type of known association information between miRNAs and diseases to predict their potential associations, without focusing on their interactions or associations with other types of molecules. Results: In this paper, we propose a network embedding-based method for predicting miRNA-disease associations by preserving behavior and attribute information. Firstly, a heterogeneous network is constructed by integrating known associations among miRNA, protein and disease, and the network representation method Learning Graph Representations with Global Structural Information (GraRep) is implemented to learn the behavior information of miRNAs and diseases in the network. Then, the behavior information of miRNAs and diseases is combined with the attribute information of them to represent miRNA-disease association pairs. Finally, the prediction model is established based on the Random Forest algorithm. Under the five-fold cross validation, the proposed NEMPD model obtained average 85.41% prediction accuracy with 80.96% sensitivity at the AUC of 91.58%. Furthermore, the performance of NEMPD is also validated by the case studies. Among the top 50 predicted disease-related miRNAs, 48 (breast neoplasms), 47 (colon neoplasms), 47 (lung neoplasms) were confirmed by two other databases.Conclusions: The proposed NEMPD model has a good performance in predicting the potential associations between miRNAs and diseases, and has great potency in the field of miRNA-disease association prediction in the future.

scholarly journals Hyperbolic Heterogeneous Information Network Embedding

2019 ◽  
Vol 33 ◽  
pp. 5337-5344 ◽  
Author(s):  
Xiao Wang ◽  
Yiding Zhang ◽  
Chuan Shi
Keyword(s):  
Complex Network ◽  
Power Law ◽  
Hyperbolic Geometry ◽  
Hyperbolic Spaces ◽  
Superior Performance ◽  
Information Network ◽  
Network Embedding ◽  
Euclidean Spaces ◽  
Heterogeneous Information Network ◽  
Heterogeneous Information

Heterogeneous information network (HIN) embedding, aiming to project HIN into a low-dimensional space, has attracted considerable research attention. Most of the exiting HIN embedding methods focus on preserving the inherent network structure and semantic correlations in Euclidean spaces. However, one fundamental problem is that whether the Euclidean spaces are the appropriate or intrinsic isometric spaces of HIN? Recent researches argue that the complex network may have the hyperbolic geometry underneath, because the underlying hyperbolic geometry can naturally reflect some properties of complex network, e.g., hierarchical and power-law structure. In this paper, we make the first effort toward HIN embedding in hyperbolic spaces. We analyze the structures of two real-world HINs and discover some properties, e.g., the power-law distribution, also exist in HIN. Therefore, we propose a novel hyperbolic heterogeneous information network embedding model. Specifically, to capture the structure and semantic relations between nodes, we employ the meta-path guided random walk to sample the sequences for each node. Then we exploit the distance in hyperbolic spaces as the proximity measurement. The hyperbolic distance is able to meet the triangle inequality and well preserve the transitivity in HIN. Our model enables the nodes and their neighborhoods have small hyperbolic distances. We further derive the effective optimization strategy to update the hyperbolic embeddings iteratively. The experimental results, in comparison with the state-of-the-art, demonstrate that our proposed model not only has superior performance on network reconstruction and link prediction tasks but also shows its ability of capture hierarchy structure in HIN via visualization.

scholarly journals NEMPD: a network embedding-based method for predicting miRNA-disease associations by preserving behavior and attribute information

2020 ◽  
Vol 21 (1) ◽  
Author(s):  
Bo-Ya Ji ◽  
Zhu-Hong You ◽  
Zhan-Heng Chen ◽  
Leon Wong ◽  
Hai-Cheng Yi
Keyword(s):  
Structural Information ◽  
Disease Association ◽  
Single Type ◽  
Network Embedding ◽  
Graph Representations ◽  
Non Coding Rna ◽  
Attribute Information ◽  
Disease Associations ◽  
Representation Method ◽  
Great Potency

Abstract Background As an important non-coding RNA, microRNA (miRNA) plays a significant role in a series of life processes and is closely associated with a variety of Human diseases. Hence, identification of potential miRNA-disease associations can make great contributions to the research and treatment of Human diseases. However, to our knowledge, many existing computational methods only utilize the single type of known association information between miRNAs and diseases to predict their potential associations, without focusing on their interactions or associations with other types of molecules. Results In this paper, we propose a network embedding-based method for predicting miRNA-disease associations by preserving behavior and attribute information. Firstly, a heterogeneous network is constructed by integrating known associations among miRNA, protein and disease, and the network representation method Learning Graph Representations with Global Structural Information (GraRep) is implemented to learn the behavior information of miRNAs and diseases in the network. Then, the behavior information of miRNAs and diseases is combined with the attribute information of them to represent miRNA-disease association pairs. Finally, the prediction model is established based on the Random Forest algorithm. Under the five-fold cross validation, the proposed NEMPD model obtained average 85.41% prediction accuracy with 80.96% sensitivity at the AUC of 91.58%. Furthermore, the performance of NEMPD is also validated by the case studies. Among the top 50 predicted disease-related miRNAs, 48 (breast neoplasms), 47 (colon neoplasms), 47 (lung neoplasms) were confirmed by two other databases. Conclusions The proposed NEMPD model has a good performance in predicting the potential associations between miRNAs and diseases, and has great potency in the field of miRNA-disease association prediction in the future.

Attributed Network Embedding with Micro-Meso Structure

2021 ◽  
Vol 15 (4) ◽  
pp. 1-26
Author(s):  
Juan-Hui Li ◽  
Ling Huang ◽  
Chang-Dong Wang ◽  
Dong Huang ◽  
Jian-Huang Lai ◽  
...  
Keyword(s):  
Community Structure ◽  
Optimization Problems ◽  
Nonnegative Matrix ◽  
Superior Performance ◽  
Network Embedding ◽  
Attributed Network ◽  
Attribute Information ◽  
Low Dimensional ◽  
Embedding Methods ◽  
Proximity Structure

Recently, network embedding has received a large amount of attention in network analysis. Although some network embedding methods have been developed from different perspectives, on one hand, most of the existing methods only focus on leveraging the plain network structure, ignoring the abundant attribute information of nodes. On the other hand, for some methods integrating the attribute information, only the lower-order proximities (e.g., microscopic proximity structure) are taken into account, which may suffer if there exists the sparsity issue and the attribute information is noisy. To overcome this problem, the attribute information and mesoscopic community structure are utilized. In this article, we propose a novel network embedding method termed Attributed Network Embedding with Micro-Meso structure, which is capable of preserving both the attribute information and the structural information including the microscopic proximity structure and mesoscopic community structure. In particular, both the microscopic proximity structure and node attributes are factorized by Nonnegative Matrix Factorization (NMF), from which the low-dimensional node representations can be obtained. For the mesoscopic community structure, a community membership strength matrix is inferred by a generative model (i.e., BigCLAM) or modularity from the linkage structure, which is then factorized by NMF to obtain the low-dimensional node representations. The three components are jointly correlated by the low-dimensional node representations, from which two objective functions (i.e., ANEM_B and ANEM_M) can be defined. Two efficient alternating optimization schemes are proposed to solve the optimization problems. Extensive experiments have been conducted to confirm the superior performance of the proposed models over the state-of-the-art network embedding methods.

W-MMP2Vec: Topic-driven network embedding model for link prediction in content-based heterogeneous information network

2021 ◽  
Vol 25 (3) ◽  
pp. 711-738
Author(s):  
Phu Pham ◽  
Phuc Do
Keyword(s):  
Link Prediction ◽  
Representation Learning ◽  
Information Network ◽  
Network Embedding ◽  
Heterogeneous Information Network ◽  
Heterogeneous Information ◽  
Learning Framework ◽  
Novel Approach ◽  
Proposed Model ◽  
Meta Path

Link prediction on heterogeneous information network (HIN) is considered as a challenge problem due to the complexity and diversity in types of nodes and links. Currently, there are remained challenges of meta-path-based link prediction in HIN. Previous works of link prediction in HIN via network embedding approach are mainly focused on exploiting features of node rather than existing relations in forms of meta-paths between nodes. In fact, predicting the existence of new links between non-linked nodes is absolutely inconvincible. Moreover, recent HIN-based embedding models also lack of thorough evaluations on the topic similarity between text-based nodes along given meta-paths. To tackle these challenges, in this paper, we proposed a novel approach of topic-driven multiple meta-path-based HIN representation learning framework, namely W-MMP2Vec. Our model leverages the quality of node representations by combining multiple meta-paths as well as calculating the topic similarity weight for each meta-path during the processes of network embedding learning in content-based HINs. To validate our approach, we apply W-TMP2Vec model in solving several link prediction tasks in both content-based and non-content-based HINs (DBLP, IMDB and BlogCatalog). The experimental outputs demonstrate the effectiveness of proposed model which outperforms recent state-of-the-art HIN representation learning models.

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