Research On Data Multi-classification Method Based On Non-local Operators

Data classification is an important part of research in the fields of data mining,computer vision,and machine learning.Among them,semi-supervised classification,which is based on a few number of known labels to obtain all data labels,is also called transductive learning in the field of machine learning,and it is the basis of current supervised learning.Based on the non-local Potts model,the discrete variational method of non-local operator based on graph has become an effective method for multi-data classification.This model uses the same number of label functions to classify the data,and introduces simplex constraints to avoid the problem of missing and repeating classification,which is computationally complex and inefficient.This thesis has carried out a systematic study on these two issues.The main innovations are as follows:1.An improved Potts model with no simplex constraints is proposed.Due to the existence of simplex constraints,each label function is no longer independent.With the help of computer vision research in recent years,in this thesis,the feature functions of all data types with fewer label functions is designed,naturally satisfies the original simplex constraints,reduces the complexity of the model,reduces the solving scale of the problem,and improves the computational efficiency.2.A vectorization model for improving the Potts model is proposed.The variational model of data multi-classification problem is a typical multivariate optimization problem.Alternate optimization is its main solution,but multivariate alternating optimization is not conducive to regional competition.Therefore,based on the idea of multivariate coupling,this thesis proposes a vectorization model of the improved Potts model,which realizes the simultaneous evolution of multivariables,improves the computational efficiency and simplifies the design of programming.This method also facilitates the design of parallel algorithms.3.The proposed improved Potts model and its vectorization model based on ADMM projection method are designed.The ADMM(Alternating Direction Method of Multipliers)is designed by introducing auxiliary variables,Lagrange multipliers and penalty parameters,that is,transforming the original problem into a series of subproblems of alternative optimization.This subproblem can be solved by simple Gauss-Seidel iteration,generalized soft threshold formula and projection method,which simplifies the calculation and improves the optimization calculation efficiency.In order to prove the feasibility and effectiveness of the improved model and algorithm proposed in this thesis,numerical experiments were carried out on several standard data sets and the efficiency of the classification algorithm is compared with the traditional Potts model.The proposed model and its calculation methods can be easily extended to other schemes for the evolution of label functions.