基于DC规划的鲁棒模糊核聚类算法

Robust Kernel-Based Fuzzy Clustering Using Difference of Convex Functions Programming

对以径向基核函数和欧拉核函数为代表的鲁棒模糊核聚类算法进行非凸优化,以改善聚类算法目标函数非凸导致的局部解问题.采用凸差规划(DCP)将目标函数转化为2个凸函数之差的形式,减缓局部解的不良性,提高聚类性能.采用凸差算法(DCA)优化求解DCP问题,能快速搜索到相对更优的解,并保持聚类的鲁棒性.在UCI数据集上的实验验证基于DCP的鲁棒模糊核聚类算法对大规模数据集表现出相对更优的聚类性能.

A nonconvex optimization approach is presented for the robust kernel-based clustering algorithms represented by the radial basis function and the Euler kernel function. The presented approach can handle local optimum problem caused by the non-convexity of the objective function. Difference of convex functions programming （DCP） is applied to escape the local optimum. The clustering accuracy is improved by transforming the objective function into the difference of the two convex functions. The fast and robust algorithm, difference of convex functions algorithm （DCA）, is employed to optimize DCP. Consequently, a more robust and optimal solution can be searched by DCP and DCA. Experiments on several UCI datasets show the superiority of the algorithms based on DCP, especially on the large-scale datasets.