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The purpose of graph embedding is to learn a lower-dimensional embedding function for graph data. Existing methods usually rely on maximum likelihood estimation (MLE), and often learn an embedding function through conditional mean estimation (CME). However, MLE is well-known to be vulnerable to the contamination of outliers. Furthermore, CME might restrict the applicability of the graph embedding methods to a limited range of graph data. To cope with these problems, this paper proposes a novel method for graph embedding called the *robust ratio graph embedding* (RRGE). RRGE is based on the ratio estimation between the conditional and marginal probability distributions of link weights given data vectors, and would be applicable to a wider-range of graph data than CME-based methods. Moreover, to achieve outlier-robust estimation, the ratio is estimated with the γ-cross entropy, which is a robust alternative to the standard cross entropy. Numerical experiments on artificial data show that RRGE is robust against outliers and performs well even when CME-based methods do not work at all. Finally, the performance of the proposed method is demonstrated on realworld datasets using neural networks.

- Publication
- IEICE TRANSACTIONS on Information Vol.E105-D No.10 pp.1812-1816

- Publication Date
- 2022/10/01

- Publicized
- 2022/07/04

- Online ISSN
- 1745-1361

- DOI
- 10.1587/transinf.2022EDL8033

- Type of Manuscript
- LETTER

- Category
- Artificial Intelligence, Data Mining

Kaito SATTA

Future University Hakodate

Hiroaki SASAKI

Future University Hakodate

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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Kaito SATTA, Hiroaki SASAKI, "Graph Embedding with Outlier-Robust Ratio Estimation" in IEICE TRANSACTIONS on Information,
vol. E105-D, no. 10, pp. 1812-1816, October 2022, doi: 10.1587/transinf.2022EDL8033.

Abstract: The purpose of graph embedding is to learn a lower-dimensional embedding function for graph data. Existing methods usually rely on maximum likelihood estimation (MLE), and often learn an embedding function through conditional mean estimation (CME). However, MLE is well-known to be vulnerable to the contamination of outliers. Furthermore, CME might restrict the applicability of the graph embedding methods to a limited range of graph data. To cope with these problems, this paper proposes a novel method for graph embedding called the *robust ratio graph embedding* (RRGE). RRGE is based on the ratio estimation between the conditional and marginal probability distributions of link weights given data vectors, and would be applicable to a wider-range of graph data than CME-based methods. Moreover, to achieve outlier-robust estimation, the ratio is estimated with the γ-cross entropy, which is a robust alternative to the standard cross entropy. Numerical experiments on artificial data show that RRGE is robust against outliers and performs well even when CME-based methods do not work at all. Finally, the performance of the proposed method is demonstrated on realworld datasets using neural networks.

URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.2022EDL8033/_p

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@ARTICLE{e105-d_10_1812,

author={Kaito SATTA, Hiroaki SASAKI, },

journal={IEICE TRANSACTIONS on Information},

title={Graph Embedding with Outlier-Robust Ratio Estimation},

year={2022},

volume={E105-D},

number={10},

pages={1812-1816},

abstract={The purpose of graph embedding is to learn a lower-dimensional embedding function for graph data. Existing methods usually rely on maximum likelihood estimation (MLE), and often learn an embedding function through conditional mean estimation (CME). However, MLE is well-known to be vulnerable to the contamination of outliers. Furthermore, CME might restrict the applicability of the graph embedding methods to a limited range of graph data. To cope with these problems, this paper proposes a novel method for graph embedding called the *robust ratio graph embedding* (RRGE). RRGE is based on the ratio estimation between the conditional and marginal probability distributions of link weights given data vectors, and would be applicable to a wider-range of graph data than CME-based methods. Moreover, to achieve outlier-robust estimation, the ratio is estimated with the γ-cross entropy, which is a robust alternative to the standard cross entropy. Numerical experiments on artificial data show that RRGE is robust against outliers and performs well even when CME-based methods do not work at all. Finally, the performance of the proposed method is demonstrated on realworld datasets using neural networks.},

keywords={},

doi={10.1587/transinf.2022EDL8033},

ISSN={1745-1361},

month={October},}

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TY - JOUR

TI - Graph Embedding with Outlier-Robust Ratio Estimation

T2 - IEICE TRANSACTIONS on Information

SP - 1812

EP - 1816

AU - Kaito SATTA

AU - Hiroaki SASAKI

PY - 2022

DO - 10.1587/transinf.2022EDL8033

JO - IEICE TRANSACTIONS on Information

SN - 1745-1361

VL - E105-D

IS - 10

JA - IEICE TRANSACTIONS on Information

Y1 - October 2022

AB - The purpose of graph embedding is to learn a lower-dimensional embedding function for graph data. Existing methods usually rely on maximum likelihood estimation (MLE), and often learn an embedding function through conditional mean estimation (CME). However, MLE is well-known to be vulnerable to the contamination of outliers. Furthermore, CME might restrict the applicability of the graph embedding methods to a limited range of graph data. To cope with these problems, this paper proposes a novel method for graph embedding called the *robust ratio graph embedding* (RRGE). RRGE is based on the ratio estimation between the conditional and marginal probability distributions of link weights given data vectors, and would be applicable to a wider-range of graph data than CME-based methods. Moreover, to achieve outlier-robust estimation, the ratio is estimated with the γ-cross entropy, which is a robust alternative to the standard cross entropy. Numerical experiments on artificial data show that RRGE is robust against outliers and performs well even when CME-based methods do not work at all. Finally, the performance of the proposed method is demonstrated on realworld datasets using neural networks.

ER -