Iterative Optimization Clustering Algorithm Based on Manifold Distance

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Iterative Optimization Clustering Algorithm Based on Manifold Distance

更新时间：2025-07-09

- Iterative Optimization Clustering Algorithm Based on Manifold Distance
- Vol. 43, Issue 5, Pages: 76-79(2009)
- 作者机构：
  
  西安交通大学机械工程学院,西安,710049
- 作者简介：
- 基金信息：
- DOI：
  CLC： TP181
- Online First：10 May 2009，
  
  Published：2009
- 稿件说明：
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Iterative Optimization Clustering Algorithm Based on Manifold Distance[J]. 2009, 43(5): 76-79.
DOI：

Iterative Optimization Clustering Algorithm Based on Manifold Distance[J]. 2009, 43(5): 76-79. DOI：

摘要

针对传统欧氏距离测度描述复杂结构的数据分布会失效的问题

引入能有效反映样本集固有的全局一致性信息的流形距离作为样本间相似度度量测度

并设计了反映类内相似度大、类间相似度小的聚类目标的准则函数

把数据聚类转化成准则函数优化问题

提出了一种迭代优化的聚类算法.通过4个人工数据集的仿真试验结果表明

新方法的参数很少且实现简单

由于实现过程中没有引入随机操作

因此结果比较确定.与标准k均值算法相比

新方法能够自动确定聚类数目

对于样本空间分布复杂的聚类问题具有良好的分类效果.

Abstract

Aiming at the problem that classical Euclidean distance metric may be invalid when it is used to measure the complicated data structures

a manifold distance based on similarity metric and being able to measure the geodesic distance along the manifold is introduced

and a criterion function used to express the clustering target is designed

where the samples in the same cluster are somehow more similar than samples in different one. Accordingly

the clustering problem is converted to function optimization problem

and an iterative optimization clustering algorithm is proposed. The steps of the algorithm are discussed in detail. Simulation results on four artificial datasets with different manifold structures show that the new algorithm is more straightforward due to the less pre-defined parameters and it is a deterministic algorithm due to the lack of random operations. A comparison with k-means clustering algorithms indicates the ability to determine the cluster number automatically and identify complex non-convex clusters.

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references

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SU Muchu, CHOU C H. A modified version of the k-means algorithm with a distance based on cluster symmetry [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(6): 674-680.

ZHOU Dengyong, BOUSQUET O, LAL T N, et al. Learning with local and global consistency [C]∥Advances in Neural Information Processing Systems:16. Cambridge, USA: MIT Press, 2004:321-328.

TENENBAUM J B, DE SILVA V, LANGFORD J C. A global geometric framework for nonlinear dimensionality reduction [J]. Science, 2000, 290(550): 2319-2323.

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MACQUEEN J B.Some methods for classification and analysis of multivariate observations[C]∥The 5th Berkeley Symposium on Mathematical Statistics and Probability. Berkeley, USA: Univ of Calif Press, 1967: 281-297.

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