计算数学
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计算数学  2019, Vol. 41 Issue (1): 1-11    DOI:
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子空间聚类的重建模型及其快速算法
夏雨晴1, 张振跃2
1. 浙江大学 数学科学学院, 杭州 310027;
2. 浙江大学 数学科学学院;CAD&CG国家重点实验室, 杭州 310027
RECONSTRUCTION MODEL AND FAST ALGORITHM FOR SUBSPACE CLUSTERING
Xia Yuqing1, Zhang Zhenyue2
1. School of Mathematics Science, Zhejiang University, 310027 Hangzhou, China;
2. School of Mathematics Science and State Key Laboratory of CAD & CG, 310027 Hangzhou, China
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摘要 有限样本的子空间数据聚类建模及其大规模计算是子空间学习面临的主要问题.现有的大多数模型都不适合大规模计算.本文提出了一个新的优化模型,结合谱投影反馈和辅助信息优化.在提升模型的学习能力的同时,采用高效的分片符号更新算法,可以适合大规模计算.我们用较大规模的模拟例子和实际例子,分析检验了新的优化模型及其快速算法的优于现有其他模型与算法的有效性.
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关键词子空间聚类   谱投影   辅助矩阵   分片符号更新算法     
Abstract: Effective models and scalable algorithms are two key issues of subspace learning from limited samples. State-of-the-art methods usually suffer from their rapidly increasing costs when the data scale becomes large. This paper proposes a new reconstruction model that utilizes spectral projection and auxiliary information from samples for improving its capacity for subspace learning. A fast algorithm based on active piece-wise sign updating is then proposed for efficiently solving the problem in large scale. Comprehensive experiments on both synthetic and real-world datasets are reported to demonstrate the effectiveness and efficiency of the proposed model and the performance better than the existing algorithms for subspace learning.
Key wordsSubspace Clustering   Spectral Projection   Auxiliary Matrix   Active Piecewise Sign Updating   
收稿日期: 2018-09-26;
基金资助:

国家自然科学基金(11571312,91730303)和中国国家重点基础研究发展计划(2015CB352503)资助项目.

引用本文:   
. 子空间聚类的重建模型及其快速算法[J]. 计算数学, 2019, 41(1): 1-11.
. RECONSTRUCTION MODEL AND FAST ALGORITHM FOR SUBSPACE CLUSTERING[J]. Mathematica Numerica Sinica, 2019, 41(1): 1-11.
 
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