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
Klasifikasi berpasangan mempunyai banyak aplikasi termasuk ramalan rangkaian, resolusi entiti dan penapisan kolaboratif. Kernel berpasangan telah dicadangkan untuk tujuan tersebut oleh beberapa kumpulan penyelidikan secara bebas, dan telah digunakan dengan jayanya dalam beberapa bidang. Dalam makalah ini, kami mencadangkan alternatif yang cekap yang kami panggil a Isirong Cartesian. Walaupun isirong berpasangan sedia ada (yang kita rujuk sebagai isirong Kronecker) boleh ditafsirkan sebagai matriks bersebelahan wajaran graf produk Kronecker bagi dua graf, isirong Cartesian boleh ditafsirkan sebagai graf Cartesian, yang lebih jarang daripada graf produk Kronecker. Kami membincangkan sempadan generalisasi bagi dua kernel berpasangan dengan menggunakan analisis nilai eigen bagi matriks kernel. Juga, kami menganggap N-sambungan bijak bagi dua biji berpasangan. Keputusan eksperimen menunjukkan kernel Cartesian jauh lebih pantas daripada kernel Kronecker, dan pada masa yang sama, bersaing dengan kernel Kronecker dalam prestasi ramalan.
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Salinan
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
Salinan
@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},}
Salinan
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 -