基于Finsler几何的k-means算法

doi:10.3969/j.issn.0253-2778.2014.07.005

中国科学技术大学学报 ›› 2014, Vol. 44 ›› Issue (7): 570-575.DOI: 10.3969/j.issn.0253-2778.2014.07.005

基于Finsler几何的k-means算法

许晴，李凡长，邹鹏

苏州大学计算机科学与技术学院，江苏苏州 215006

收稿日期:2014-03-21 修回日期:2014-06-15 接受日期:2014-06-15 出版日期:2023-05-11 发布日期:2014-06-15
通讯作者: 李凡长
作者简介:许晴，女，1990年生，硕士生. 研究方向：机器学习. E-mail: 20124227022@suda.edu.cn
基金资助:
国家自然科学基金(61033013,60775045)，东吴学者计划，苏州大学敬文书院“3I工程”重点项目资助.

The k-means algorithm based on Finsler geometry

XU Qing, LI Fanzhang, ZOU Peng

School of Computer Science and Technology, Soochow University, Suzhou 215006, China

Received:2014-03-21 Revised:2014-06-15 Accepted:2014-06-15 Online:2023-05-11 Published:2014-06-15

摘要/Abstract

摘要： 针对k-means算法存在的相似性度量、准则函数优化效果不理想及多维流形数据分析性能效果不好等问题，引入Finsler几何中的Finsler度量，提出了一种基于Finsler几何的k-means算法，并在UCI数据集和ORL人脸数据库上与传统k-means算法及SBKM算法进行了比较，实验结果验证了该算法的可行性和有效性.

关键词: Finsler几何, Finsler度量, k-means算法, 相似性度量, 准则函数

Abstract: The problems with the k-means algorithm that the optimization effect of similarity measure and criterion function is not ideal and the analysis performance of multi-dimensional manifold data is ineffective, a modified version based on Finsler geometry was proposed, which introduces Finsler metric. Experimental results in comparison with traditional k-means algorithm and SBKM algorithm on UCI data sets and ORL face image sets show the feasibility and effectiveness of the algorithm.

Key words: Finsler geometry, Finsler metric, k-means algorithm, similarity measure, criterion function

中图分类号:

TP311

许晴，李凡长，邹鹏. 基于Finsler几何的k-means算法[J]. 中国科学技术大学学报, 2014, 44(7): 570-575.

XU Qing, LI Fanzhang, ZOU Peng. The k-means algorithm based on Finsler geometry[J]. Journal of University of Science and Technology of China, 2014, 44(7): 570-575.

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基于Finsler几何的k-means算法

The k-means algorithm based on Finsler geometry

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