Research On Manifold Regularization Fuzzy System

Takagi Sugeno Kang(TSK)fuzzy system could utilize linear model to solve nonlinear model.Because this reason,TSK fuzzy system is widely popular in many fields.However,like most supervised machine learning models,TSK fuzzy system requires enough information.But in many real-world applications,training samples are often limited,and the model can not fully mine the information from the data,thus leading to overfitting problems.Existing TSK fuzzy system mothed pay more attentions to the structure research of fuzzy system model and ignore the problem of insufficient training information in real application.So,it is easy to over fit the model.Manifold learning can further mine the structural information of samples Therefore,we introduce manifold learning into fuzzy systems to propose two new TSK fuzzy system models.The main research work of this paper is as follows:Firstly,to solve this problem,we propose a TSK fuzzy system modeling method using two manifold regularization.This method firstly proposes a manifold regularization based on the geometric distribution of the samples in the sample space,which constrain the geometric distribution of the samples into output space.Then,the manifold regularization based on the correlation between the features in the dictionary space is proposed,which guide the correlation between parameters in the learning process.Experiments on several real datasets show the effectiveness of the proposed method.Then,to solve the problem that the existing multitask fuzzy system methods only focus on the knowledge of inter-task correlation and ignore the preservation of the task-specific characteristics.This paper proposes a new manifold regularized multi task fuzzy system modeling with low rank and sparse structures in consequent parameters.This method firstly proposes a manifold regularization method based on the feature-feature relation in the multitask sub-dictionary space.This method further decomposes the consequent parameters into two components – the low-rank structure shared by multiple tasks and the task-specific component that encodes the sparse characteristics of the individual tasks to balance the sharing of the common knowledge across multiple tasks and the preservation of the task-specific characteristics.Experiments demonstrate the effectiveness of the proposed method.