改进的POTTS模型及其数据多分类直推学习算法  

Improved POTTS Model and its Data Multi-classification Direct Learning Algorithm

作　　者：赵方丽 潘振宽 徐止磊 郑世秀 ZHAO Fang-li;PAN Zhen-kuan;XU Zhi-lei;ZHENG Shi-xiu(College of Computer Science and Technology,Qingdao University,Qingdao Shandong 266071,China)

机构地区：[1]青岛大学计算机科学技术学院

出　　处：《计算机仿真》2019年第5期310-315,359,共7页Computer Simulation

基　　金：国家自然科学基金(61772294)

摘　　要：借助于图上离散非局部算子,计算机视觉领域图像分割的Potts模型可直接应用于数据多分类直推学习,但为受多种约束的能量泛函极值问题。采用传统的惩罚函数方法将受约束优化问题转化为无约束优化问题的求解涉及多个难以设定的惩罚参数。通过用较少的标记函数设计每类数据的特征函数自然满足原有的Simplex约束避免了对这类约束的惩罚。通过直接投影方法保证了直推学习中预设标记点精确约束进一步减少了能量泛函中惩罚项及惩罚参数的数量。对平衡分类约束和变量分裂引起的约束通过设计ADMM(Alternating Direction Method of Multipliers)方法降低了对惩罚参数的过分依赖。通过对多个标准数据集进行数值实验验证了所提出模型和算法的有效性。The Potts model for image segmentation in computer vision can be extended to multi-class data classification/transductive learning via discrete non-local operators on graph,but it leads to a constrained energy minimization problem with multiple constraints.Traditionally,this problem is solved through transformation of a constrained problem into an unconstrained one by penalty function methods with some parameters which are hard to tune.This paper proposed a modified Potts model and ADMM(Alternating Direction Method of Multipliers) to avoid the selections of multiple parameters for easy implementation.This paper designed a new scheme for characteristic functions for different sub-datasets using fewer label functions to fulfill naturally the simplex constraint of original Potts model.This paper used a simple projection method to ensure the predefined labels exactly,avoiding the data terms due to penalty.In order to overcome the problems of dependences of penalty parameters,this paper designed the ADMM method to enforce the balance classification constraints and the constraints due to linear splitting variables.Finally,numerous experiments on standard datasets are presented to demonstrate the efficiency of the proposed model and algorithm.

关 键 词：图 离散非局部算子 数据多分类 算法约束 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]