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".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
쌍별 분류에는 네트워크 예측, 엔터티 해결, 협업 필터링 등 다양한 응용 분야가 있습니다. 이러한 목적을 위해 쌍별 커널은 여러 연구 그룹에서 독립적으로 제안되었으며 여러 분야에서 성공적으로 사용되었습니다. 본 논문에서는 효율적인 대안을 제안합니다. 데카르트 커널. 기존 쌍별 커널(크로네커 커널이라고 함)은 두 그래프의 크로네커 곱 그래프의 가중치 인접 행렬로 해석될 수 있는 반면, 데카르트 커널은 데카르트 그래프의 커널로 해석될 수 있습니다. 크로네커 제품 그래프. 커널 행렬의 고유값 분석을 사용하여 두 쌍의 커널의 일반화 범위에 대해 논의합니다. 또한, 우리는 N- 두 쌍의 커널을 확장한 것입니다. 실험 결과에 따르면 데카르트 커널은 크로네커 커널보다 훨씬 빠르며 동시에 예측 성능에서도 크로네커 커널과 경쟁할 수 있습니다.
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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},}
부
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 -