The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
La classification par paires a de nombreuses applications, notamment la prédiction de réseau, la résolution d'entités et le filtrage collaboratif. Le noyau par paires a été proposé à ces fins par plusieurs groupes de recherche indépendants et a été utilisé avec succès dans plusieurs domaines. Dans cet article, nous proposons une alternative efficace que nous appelons un Noyau cartésien. Alors que le noyau par paire existant (que nous appelons noyau de Kronecker) peut être interprété comme la matrice d'adjacence pondérée du graphe produit de Kronecker de deux graphes, le noyau cartésien peut être interprété comme celui du graphe cartésien, qui est plus clairsemé que le graphique du produit Kronecker. Nous discutons des limites de généralisation des deux noyaux par paire en utilisant l'analyse des valeurs propres des matrices du noyau. Aussi, nous considérons le Nextensions par paires des deux noyaux. Les résultats expérimentaux montrent que le noyau cartésien est beaucoup plus rapide que le noyau de Kronecker et, en même temps, compétitif avec le noyau de Kronecker en termes de performances prédictives.
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Hisashi KASHIMA, Satoshi OYAMA, Yoshihiro YAMANISHI, Koji TSUDA, "Cartesian Kernel: An Efficient Alternative to the Pairwise Kernel" in IEICE TRANSACTIONS on Information,
vol. E93-D, no. 10, pp. 2672-2679, October 2010, doi: 10.1587/transinf.E93.D.2672.
Abstract: Pairwise classification has many applications including network prediction, entity resolution, and collaborative filtering. The pairwise kernel has been proposed for those purposes by several research groups independently, and has been used successfully in several fields. In this paper, we propose an efficient alternative which we call a Cartesian kernel. While the existing pairwise kernel (which we refer to as the Kronecker kernel) can be interpreted as the weighted adjacency matrix of the Kronecker product graph of two graphs, the Cartesian kernel can be interpreted as that of the Cartesian graph, which is more sparse than the Kronecker product graph. We discuss the generalization bounds of the two pairwise kernels by using eigenvalue analysis of the kernel matrices. Also, we consider the N-wise extensions of the two pairwise kernels. Experimental results show the Cartesian kernel is much faster than the Kronecker kernel, and at the same time, competitive with the Kronecker kernel in predictive performance.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E93.D.2672/_p
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@ARTICLE{e93-d_10_2672,
author={Hisashi KASHIMA, Satoshi OYAMA, Yoshihiro YAMANISHI, Koji TSUDA, },
journal={IEICE TRANSACTIONS on Information},
title={Cartesian Kernel: An Efficient Alternative to the Pairwise Kernel},
year={2010},
volume={E93-D},
number={10},
pages={2672-2679},
abstract={Pairwise classification has many applications including network prediction, entity resolution, and collaborative filtering. The pairwise kernel has been proposed for those purposes by several research groups independently, and has been used successfully in several fields. In this paper, we propose an efficient alternative which we call a Cartesian kernel. While the existing pairwise kernel (which we refer to as the Kronecker kernel) can be interpreted as the weighted adjacency matrix of the Kronecker product graph of two graphs, the Cartesian kernel can be interpreted as that of the Cartesian graph, which is more sparse than the Kronecker product graph. We discuss the generalization bounds of the two pairwise kernels by using eigenvalue analysis of the kernel matrices. Also, we consider the N-wise extensions of the two pairwise kernels. Experimental results show the Cartesian kernel is much faster than the Kronecker kernel, and at the same time, competitive with the Kronecker kernel in predictive performance.},
keywords={},
doi={10.1587/transinf.E93.D.2672},
ISSN={1745-1361},
month={October},}
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TY - JOUR
TI - Cartesian Kernel: An Efficient Alternative to the Pairwise Kernel
T2 - IEICE TRANSACTIONS on Information
SP - 2672
EP - 2679
AU - Hisashi KASHIMA
AU - Satoshi OYAMA
AU - Yoshihiro YAMANISHI
AU - Koji TSUDA
PY - 2010
DO - 10.1587/transinf.E93.D.2672
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E93-D
IS - 10
JA - IEICE TRANSACTIONS on Information
Y1 - October 2010
AB - Pairwise classification has many applications including network prediction, entity resolution, and collaborative filtering. The pairwise kernel has been proposed for those purposes by several research groups independently, and has been used successfully in several fields. In this paper, we propose an efficient alternative which we call a Cartesian kernel. While the existing pairwise kernel (which we refer to as the Kronecker kernel) can be interpreted as the weighted adjacency matrix of the Kronecker product graph of two graphs, the Cartesian kernel can be interpreted as that of the Cartesian graph, which is more sparse than the Kronecker product graph. We discuss the generalization bounds of the two pairwise kernels by using eigenvalue analysis of the kernel matrices. Also, we consider the N-wise extensions of the two pairwise kernels. Experimental results show the Cartesian kernel is much faster than the Kronecker kernel, and at the same time, competitive with the Kronecker kernel in predictive performance.
ER -