TSK Fuzzy System for Multi-View Data Discovery Underlying Label Relaxation and Cross-Rule & Cross-View Sparsity Regularizations

Industry 4.0 places special emphasis on the use of intelligent models to discover patterns in data. In this article, we propose a novel Takagi-Sugeno-Kang (TSK) fuzzy system with low model complexity for multiview data pattern discovery. Compared with the classic TSK fuzzy systems, the proposed one has three merits: First, we introduce a transformation matrix to relax the strict binary label matrix of the training set so that the margins between classes become more discriminative. Second, we introduce two kinds of sparsity regularizations, i.e., cross-rule and cross-view, to reduce indiscriminative fuzzy rules and consequent parameters so that the model complexity is significantly reduced. Third, we introduce the alternating direction method of multipliers to optimize the objective function so that we have compact closed-form solutions in each iteration. Extensive experiments on different kinds of multiview image datasets indicate the promising performance for data pattern discovery with low model complexity.