多视角聚类的数值方法研究

Reaearch of a Numerical Method for Multi-View Clustering

针对Zhang等提出的多视角子空间聚类方法,本文给出了一种求解该非凸优化问题的方法并对其提出的算法进行了新的分析和改进。得到的主要结果包括:(1)选择一个好的近似解作为初始点,提高了算法的收敛速度和对全局最优解的收敛概率。(2)用MM思想重新推导出Zhang的方法,由此证明了一个新的收敛性定理;(3)改进了Wen提出的基于流形的正交约束算法并用于求解多视角子空间聚类模型,在算法中加入了初始点,大大提高了运行速度。通过对合成数据和实际数据的实验,验证了算法的有效性。

Aiming at the multi-view subspace clustering method proposed by Zhang et al.,this paper presents a method to solve the non-convex optimization problem,and makes a new analysis and improvement on the algorithm proposed by them.The main results include:(1)The convergence speed and probability of the global optimal solution are improved by selecting agood approximate solution as the initial point;(2)A new proof idea for optimization method is provided by using MM method;(3)The orthogonal constraint algorithm based on Wen’s manifold is improved and used to solve the multiview subspace clustering model.In addition,initial points are added into the algorithm,which greatly improves the running speed.Experiments on synthetic data and real data demonstrate the effectiveness of the algorithm.