求解大规模矛盾方程组的最小二乘支持向量机算法

A least square support vector machine algorithm for solving huge contradictory equations

房价预测、共享单车出租数量预测、空气污染情况预测等常涉及矛盾方程组求解,对其数值求解方法研究具有重要的理论意义与应用价值。当矛盾方程组规模过大时,用传统的最小二乘法求解,不仅计算量大,而且由于误差积累使最终结果的准确性不高。鉴于此,采用机器学习中的最小二乘支持向量机(least squares support vector machine,LS-SVM)算法求解大规模矛盾方程组,并分别针对线性、非线性、单变量、多变量矛盾方程组进行了数值求解。数值结果表明,数据类型和数据量的变化对结果的影响不大,因此只要选取适当的参数就可建立合适的模型,得到高精度的预测结果。

Contradictory equations often appear in the predictions of housing price, the number of shared bike rentals, air pollution and other problems. It is of important theoretical significance and practical application value to conduct research on the related numerical method. When the number of contradictory equations is huge, it is too difficult to use the traditional least square method to solve the problem due to the accumulation of errors. In view of this, this paper adopts the least square support vector machine(LS-SVM) algorithm, which is suitable for machine learning of big data process, to solve the huge contradictory equations, and applies the algorithm to problems with practical application background.Experimental results show that the linear, nonlinear, univariate and multivariable contradictory equations can be solved numerically, the change of data type and data volume does not affect the results much, and the appropriate model can be built to obtain high accuracy results as long as the appropriate parameters are selected.