基于最小二乘支持向量机的TSK模糊模型

为了提高模糊系统处理高维问题的推广能力, 本文提出用最小二乘支持向量回归机(LSSVR)的思想设计TSK模糊模型.TSK模糊模型的传统算法普遍存在过学习问题, 为此我们在目标函数中考虑了结构风险从而避免了过学习现象.并且，我们将模糊系统的参数寻优问题转化为一个二次规划问题进行求解.由于该规划问题的求解与输入数据维数无关，适用于处理高维数据.算法分为两步：首先用Gustafsonk-Kessel (GK)算法确定模糊规则的前件；然后用最小二乘支持向量算法确定模糊规则的后件，这里的核函数是由模糊聚类确定的, 经证明它是Mercer核.三个著名数据的实验结果表明，与TSK模糊系统的传统算法相比，本文所提的算法提高了TSK模糊系统处理高维问题的推广能力；与LSSVR相比，，本文所提的算法具有良好的鲁棒性.

TSK Fuzzy Model Base on Least squares Support Vector Machines

To design a TSK fuzzy system with good generalization ability in high dimensional feature space, a novel learning algorithm based on the least squares support vector regression (LSSVR) is presented in this paper. The structural risk is considered in the goal function to avoid overfitting in traditional algorithms and then the parameter estimation of a TSK fuzzy system is converted to a quadratic optimization problem. The solution of this optimization problem has no relationship with the dimension of the input vector so that the proposed method is suit for the high dimension problem. Our proposed algorithm is divided into two steps. First, the antecedent fuzzy sets are derived from clusters obtained by the Gustafson-Kessel (GK) algorithm. The number of clusters is determined by the singular value decomposition (SVD) algorithm. Then, the corresponding consequent parameters of the TSK model can identified by the proposed support vector least squares algorithm. In the proposed algorithm, the fuzzy kernel generated by fuzzy clustering is proved to be a mercer kernel. Experimental results of three well-known dataset show that the proposed method has better generalization ability than the traditional techniques of TSK model and has a better robustness than LSSVR.