多变量线性偏最小二乘回归模型的优化方法及其在体育计量中的运用

Optimization of Multivariable Linear Partial Least Square Regression Model and Its Application in Sports Measurement

为了更有效地解决体育计量中多变量系统的线性回归建模问题,提出利用遗传算法(GA)与偏最小二乘回归(PLS回归)相结合,对多变量系统进行特征选择的方法,即采用GA筛选多变量系统中的变量信息,通过利用PLS回归的误差平方和变换为适应度评价函数,筛选回归建模的最优特征变量子集完成种群进化,最终以最优个体为确定PLS回归模型。为进一步提高模型的泛化能力,提出了基于最小一乘准则和模拟退火算法(SA)的求解方案,对PLS回归模型系数进行重新优化。实验结果表明:这种特征选择方法能有效地实现简化PLS回归方程,同时提高了所建模型的解释能力;回归系数经优化后的PLS回归模型,具有更好的泛化能力和稳健性。

A multivariable system based on genetic algorithm （GA） and partial least square （PLS） regression is developed to solve the problem of linear regression of multivariable systems in sports measurement in this paper. With GA screening variables in multivariable systems and converting error sum of square of PLS regression to fitness function, it selects the best feature subsets of regression model to finish the evolution, then determines PLS regression model on optimal individual. To further improve the generalization of the model, a scheme based on the least absolute deviation and SA （simulated annealing algorithm） in this paper is also proposed to re-optimize the coefficients of PLS regression model. Experimental results show that this algorithm can effectively simplify PLS regression equations, and improve the explanation ability of the present model. PLS regression model with optimized coefficients hasbetter generalization and stability.