A step gravitational search algorithm for function optimization and STTM’s synchronous feature selection-parameter optimization

The support tensor train machine (STTM) can make full use of the correlation of tensor data structures, while the parameter training is inefficient and feature redundancy is large. For this, a step gravitational search algorithm (SGSA) is proposed and used for synchronous feature selection and parameter optimization of STTM in this paper. Since the single population structure of the gravitational search algorithm is difficult to balance exploration and exploitation effectively, a new dual population structure is defined by the step function. Subpopulation Pop1 focuses on exploration, and a Kbest-Elite hybrid learning strategy is designed to avoid the rapid decline of exploration ability due to the rapid reduction of the size of Kbest set as well as the gravitational constant G. Subpopulation Pop2 focuses on exploitation, and a position update strategy that integrates Cauchy distribution and Gaussian distribution is designed to make Pop2 always have a certain exploration ability. Finally, use SGSA to solve the synchronous feature selection and parameter optimization problem of STTM (the resulting model is denoted as SGSA-STTM). The algorithm’s optimization performance test results show that SGSA can obtain relatively best results on most test functions compared with other state-of-the-art algorithms. The classification performance test on fMRI datasets shows that SGSA-STTM can remove more than 40% of redundant features on most datasets, which can effectively improve the efficiency of the algorithm, and the classification accuracy for the StarPlus fMRI dataset and the CMU Science 2008 fMRI dataset reached 60 and 70%, respectively.