The traditional least squares support vector machine (LSSVM) is generally used to solve non-sparse problems. A sparse and parameter optimization method of LSSVM based on genetic algorithm was proposed. The basic idea of sparse was to give a probability value to each training sample

and if its probability value was less than 0.5 then the corresponding training sample was not a support vector. Samples that was not support vectors were treated as test samples. So

the set of total training samples was divided into the set of test samples and the set of training sample remained. A fitness function including sparse rate

training error and test error was defined. The first N dimensions of the population individual specified corresponding probability of each sample

the next m dimensions specified parameters to be optimized. All parameters including probabilities were optimized globally by mutation

selection

and crossover operations. A model of LSSVM was established by using the corresponding training sample remained and optimized parameters of the individuals with minimum fitness. The proposed method was applied to the soft sensor of 4-CBA concentration in the PX oxidation process. Simulation results with industrial data showed that by using the proposed method sparse rate was up to 87%

kernel parameters were identified automatically

and the sparse model had better generalization capability than that of the model before sparse.