Manifold-Regularized Multitask Fuzzy System Modeling With Low-Rank and Sparse Structures in Consequent Parameters

Multitask modeling methods for Takagi–Sugeno–Kang (TSK) fuzzy systems exhibit better generalization ability attributed to the utilization of the knowledge of intertask correlation. However, existing methods usually ignore the balance between the sharing of the common knowledge across multiple tasks and the preservation of the task-specific characteristics of each rule. To this end, we propose a novel manifold-regularized multitask modeling method for TSK fuzzy system by introducing low-rank and sparse structures into consequent parameters across multiple tasks. Specifically, we decompose the consequent parameters into two components—a task–shared component that represents similar structure across multiple tasks, and a task-specific component that encodes the sparse characteristics of the individual tasks. This can be implemented by imposing low-rank constraints on the task-shared component and applying the sparse constraints on the task-specific component. A new manifold regularization is further devised to reflect the feature-feature relation, which provides prior knowledge in multitask learning. An efficient augmented Lagrange multiplier is developed to solve the optimization problem. The experimental results demonstrate that the proposed model significantly outperforms the existing methods.

I. Introduction

Fuzzy inference systems (FISs) are developed based on fuzzy logic and fuzzy inference. They are specialized in describing the uncertainty of knowledge and expression, and are able to approximate uncertain nonlinear systems better than conventional machine learning models [1]–[3]. Various models have been developed as a result of recent advances in FIS. Among them, the Takagi–Sugeno–Kang (TSK) fuzzy system is the most popular one that provides an effective framework to reduce nonlinear systems into multiple local linear structures [4]–[8].