In an information explosion era, the large scale and structure complexity of datasets become problems in approximation calculation. Dynamic computing is an efficient approach to solve these problems. With the development of existing updating method applied to the dynamic approximation in multi-granular rough sets, a vector matrix based method for computing and updating approximations in Variable Precision Multi-Granulation Rough Sets (VPMGRS) was proposed. Firstly, a static algorithm for computing approximations based on vector matrix for VPMGRS was presented. Secondly, the searching area for updating approximations in VPMGRS was reconsidered, and the area was shrunk according to the properties of VPMGRS, effectively improving the time efficiency of the approximation updating algorithm. Thirdly, according to the new searching area, a vector matrix based algorithm for updating approximations in VPMGRS was proposed based on the static algorithm for computing approximations. Finally, the effectiveness of the designed algorithm was verified by experiments.

Since it was not ideal for Extreme Learning Machine (ELM) to deal with non-linear data, and the parameter randomization of ELM was not conducive for generalizing the model, an improved version of ELM algorithm was proposed. The parameters of ELM were optimized by Adaptive Chaotic Particle Swarm Optimization (ACPSO) algorithm to increase the stability of the algorithm and improve the accuracy of ELM for gene expression data classification. The simulation experiments were carried out on the UCI gene data. The results show that Adaptive Chaotic Particle Swarm Optimization-Extreme Learning Machine (ACPSO-ELM) has good stability and reliability, and effectively improves the accuracy of gene classification over existing algorithms, such as Detecting Particle Swarm Optimization-Extreme Learning Machine (DPSO-ELM) and Particle Swarm Optimization-Extreme Learning Machine (PSO-ELM).