Non-local Variational Model Of Data Multi-classification Problem On Graph And Its Fast Algorithm Research

Data classification is of importance in data mining and machine learning.It is also fundamental in modern enterprise management,business policy decision,has a lot of applications in computer vision,pattern recognition,social network analysis,business intelligence,etc.With rapid development of big data techniques,more and more efficient models and algorithms of multi-class classification are required.This thesis focuses on semi-supervised multi-class classification models and algorithms based on little labeled data samples using non-local discrete differential operators on graph to support data analysis in different areas.Main work and innovations in this paper are as follows:For two-class semi-supervised classifacation problem,the discrete nonlocal operators on graph are analyzed systematically.A series of nonlocal discrete variational models are proposed,and the corresponding ADMM(Alternating Direction Method of Multipliers)algorithms are designed.The accuracies of classification problems with equality and inequality constraints are compared systematically.This works are helpful for further studies in this area.For multi-class semi-supervised classifacation problem,the Potts model and algorithms for balanced multi-class classification are studied.By setting up the equivalent vector regularization model,the computation efficiency of the traditional Potts model is greatly improved by introducing a series of auxiliary variables.The model is transformed into an alternate optimization method,and the corresponding ADMM algorithm is designed.For multi-class semi-supervised classifacation problem,a scheme for multiclass characteristic function with fewer labeled functions is proposed.Inspired by Chan-Vese model proposed in computer vision,m labeled functions are designed to express 2~mcharacteristic functions for semi-supervised balance multi-class classification model,and the computational efficiency is improved by using vector regularization and ADMM method.In order to improve the computational efficiency,the projection method of constraint processing is adopted in this paper,which greatly reduces the quantity of Lagrange multipliers and penalty parameters.This strategy can not only simplify the variational model but also improve the computational efficiency and accuracy.The proposed models and fast algorithms are verified through mass of numerical experiments using some standard datasets and artificial datasets.