基于LS-SVM的时空变系数回归模型算法及仿真

LS-SVM Based Spatiotemporal Varying Coefficient Model Algorithm and Simulation

时空模型在涉及时空数据的自然科学以及社会科学各个领域都有着重要的研究价值。然而,目前广泛应用的绝大部分传统的时空模型存在假设前提较为严格,灵活性及适应性较差的缺点。提出的模型通过将LS-SVM估计算法应用在时空变系数模型并构造相应的时空核函数,实现机器学习算法较高的灵活性及适应性的同时又保留了传统回归框架的可解释性。仿真结果表明,上述模型对于复杂时空回归系数以及误差项方差的估计能力较为精准且稳定,在时空线性及非线性趋势混合的情形下,依然能较为准确地还原真实的系数曲面。

Spatiotemporal varying coefficient model possesses considerable value in the field of natural science and social science that involve spatiotemporal.However,most of the existed classic models are based on strict hypothesis and lack flexibility as well as adaptability.In this paper,a new model that applies LS-SVMestimation algorithm on spatially and temporally varying coefficient model was proposed and a correspond spatiotemporal kernel function was constructed to achieve flexibility and adaptability of the machine learning algorithm without losing the interpretability of classic regression framework.Simulation experiment indicates that the proposed model possesses high accuracy and stability on the estimation of complex spatiotemporal regression coefficients and error variance.The proposed model can also reproduce the real coefficient surface accurately even while mixing both spatiotemporal linear and nonlinear trends.