.png){kind=icon}
返回
Graph characteristics from the heat kernel trace
.png){kind=icon}
PRE
AI
DOI：10.1016/j.patcog.2008.12.029.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
Graph structures have been proved important in high level-vision since they call be used to represent structural and relational arrangements of objects in a scene. One of the problems that arises in the analysis of structural abstractions of objects is graph clustering. In this paper, we explore how permutation invariants computed from the trace of the heat kernel can be used to characterize graphs for the purposes of measuring similarity and clustering. The heat kernel is the Solution of the heat equation and is a compact representation of the path-length distribution oil a graph. The trace of the heat kernel is given by the sum of the Laplacian eigenvalues exponentiated with time. We explore three different approaches to characterizing the heat kernel trace as a function of time. Our first characterization is based on the zeta function, which from the Mellin transform is the moment generating function of the heat kernel trace. Our second characterization is unary and is found by computing the derivative of the zeta function at the origin. The third characterization is derived from the heat content, i.e. the sum of the elements of the heat kernel. We show how the heat content call be expanded as a power series in time, and the coefficients of the series can be computed using the Laplacian spectrum. We explore the use of these characterizations as a means of representing graph structure for the purposes of clustering, and compare them with the use of the Laplacian spectrum. Experiments with the synthetic and real-world databases reveal that each of the three proposed invariants is effective and outperforms the traditional Laplacian spectrum. Moreover, the heat-content invariants appear to consistently give the best results in both synthetic sensitivity studies and on real-world object recognition problems. (C) 2009 Elsevier Ltd. All rights reserved.
Keyword:
Heat kernel trace
Graph invariants
Image clustering and recognition
AI总结
对已上传原文的论文进行重点信息的提取，主要内容包括：简要概述、研究摘要、背景介绍、关键亮点、图文解析、展望与总结。
期刊
IF:
7.6
论文数:
1.3W
被引数:
4.5W
机构
引用论文
.png){kind=icon}
分享收藏
Tinnitus Retraining Therapy (TRT) as a Method for Treatment of Tinnitus and Hyperacusis Patients耳鸣再训练疗法 (TRT) 作为治疗耳鸣和高亢患者的方法
PREAI
分享收藏
查看更多内容