基于Sinc函数的回归算法

Sinc Function-Based Regression Algorithm

摘要: 本文引入采样定理中离散信号的重构思想，提出基于Sinc函数的线性与逻辑回归模型及其算法。为使回归函数的均方误差最小化，在数据的自变量域中设计出Sinc函数，然后直接重构出回归曲线。在基于Sinc函数的线性与逻辑回归模型推导与算法分析基础上，进行了充分的仿真实验验证。与传统线性回归相比，基于Sinc的回归算法在回归函数关系不明显时具有明显优势。最后，将基于Sinc的线性回归算法成功用于月最低气温预测。

Abstract: In this paper, the reconstruction of discrete signals in sampling theorem is introduced, and a linear and logistic regression model based on Sinc function is proposed. In order to minimize the mean square error of the regression function, Sinc function is designed in the independent variable do-main of data, and then the regression curve is reconstructed directly. On the basis of the linear and logistic regression model based on Sinc function and the algorithm analysis, a sufficient simulation experiment is carried out. And compared with the traditional linear regression, regression algorithm based on Sinc function has obvious advantages when the regression function is not obvious. Finally, the linear regression algorithm based on Sinc function is succeeding to predict the monthly minimum temperature.