非线性流形上的线性结构聚类挖掘

针对非线性数据流形的线性结构挖掘问题,提出一种基于Grassmann 流形和蚁群方法的聚类算法.为抑制噪声对线性结构探测的影响, 对含噪数据集进行算法处理最小单元提升,利用Grassmann 流形定义提升后单元间相似度,同时设计了一种类测地距离作为簇连通性约束. 为提高蚁群解的线性结构挖掘质量,提出了曲面复杂度最小方向定义,并将其作为信息素更新的启发信息引入. 在多个数据集上的实验和分析表明,与K-means、Geodesic K-means 以及有限混合模型(Finite mixture model, FMM) 等传统算法相比,本文算法具备挖掘非线性流形上线性结构的新特性,并且能够保证线性结构内部的连通性.

Exploring Linear Homeomorphic Clusters on Nonlinear Manifold

This paper proposed a new clustering alogorithm based on ant colony optimization and Grassmann manifold for exploring linear homeomorphic clusters on non-linear dataset manifold. The minimum processed units of algorithm were first lifted to suppress the influence of noise, and then the similarity of unit was measured according to Grassmann manifold and a geodesic-like distance was designed for ensuring the connectivity of cluster. To improve the quality of cluster generated by ant colony clustering, the direction of minimum surface complexity was defined and introduced into the pheromone update strategy as heuristic information. Experiments and analysis on several datasets have shown the successful performance on linear homeomorphic clustering compared to traditional clustering algorithms.