一种基于矩阵低秩近似的聚类集成算法

摘要

As an important extension to conventional clustering algorithms ,cluster ensemble techniques became a hotspot in machine learning area .In this paper ,cluster ensemble problem was first viewed as a direct problem of seeking the best subspace . And then ,we formally described the problem as an optimization problem with constraint according to linear algebra ,and further transformed into a matrix low rank approximation problem by relaxing the discrete constraint .Lastly ,a set of orthonormal basis of the best subspace was attained by solving the singular value decomposition problem of the hypergraph′s weighted adjacent matrix . Hereby ,a matrix low rank approximation-based algorithm was proposed ,which called K-means algorithm to cluster objects accord-ing to their coordinates in the low dimensional space and obtained the final clustering result .Experiments on baseline datasets demonstrate the effectiveness of the proposed algorithm ,and it outperforms other baseline algorithms .%首先将聚类集成问题归结为直观的最佳子空间的求解问题；随后根据线性代数理论将该问题描述为带约束条件的优化问题，通过放松离散约束条件进一步约简为矩阵低秩近似问题；最后通过求解超图的加权邻接矩阵的奇异值分解问题获得最佳子空间的一组标准正交基。据此，设计了一个基于矩阵低秩近似的算法，该算法根据每个对象在低维空间下的坐标使用K均值算法进行聚类，从而得到最终的结果。在多组基准数据集上的实验结果表明：较之于传统的聚类集成算法，本文的算法获得了更好的聚类结果，且效率较高。