基于Grassmann流形的谱聚类分析算法

在标准谱聚类分析算法中,基于欧氏空间的度量不能完全反映数据集合复杂的空间分布特性,导致聚类结果不够准确。而使用流形空间能够更准确的描述数据之间的几何结构关系。在基于规范化拉普拉斯矩阵的谱聚类算法基础上,研究Grassmann流形的光滑曲面的空间表达方式,应用适合度量数据点之间距离的特性,提出基于Grassmann距离度量的改进的谱聚类分析算法,在流形空间上分析待聚类数据点之间的相似性。实验结果表明,该算法不仅能够对分布在相同或不同子空间上的数据进行有效聚类,而且能够对具有复杂几何结构的数据集合进行分析,在流形空间上进行有效聚类。

Spectrum clustering analysis algorithm based on Grassmann manifold

In the standard spectrum clustering algorithm, the metric based on Euclidean space cannot represent the complicate space distribution feature of some data set, which might lead to the clustering result inaccuracy.While the geometric relationship between data can be described more precise by manifold space.The special expression on curved surface is researched, the feature which is more fit for measuring the distance between data is applied, and an improved spectrum clustering analysis algorithm based on the distance metric under Graasmann manifold is proposed.The similarity between data is analyzed under manifold space.The experimental results show that the proposed algorithm can cluster data set either belonging the same or different subspace more accurately, furthermore, it can cluster data set with more complicate geometric structure under manifold space efficiently.