Estimation of monthly evaporative loss using relevance vector machine, extreme learning machine and multivariate adaptive regression spline models
Estimation of monthly evaporative loss using relevance vector machine, extreme learning machine and multivariate adaptive regression spline models
复制标题
DOI：
10.1007/s00477-015-1153-y
复制
发表时间：
2016-08-01
影响因子：
4.2
通讯作者：
Kim, Dookie
中科院分区：
文献类型：
--
作者：
Deo, Ravinesh C.;Samui, Pijush;Kim, Dookie
蒸发损失(E)的预测对于水资源管理、农业实践、生态系统管理和水文工程中的水文过程的理解是至关重要的。利用入射太阳辐射(S)、最高气温(T(Max))、最低气温(T(Min))、大气水汽压(Vp)和降水量(P)这五个预报变量，开发了三种机器学习算法，即相关性向量机(RVM)、极限学习机(ELM)和多元自适应回归样条法(MARS)来预测E。RVM模型基于具有适当先验的线性模型的贝叶斯公式，从而产生稀疏表示。ELM模型是基于随机选择输入权重的单层前向神经网络的计算高效算法，而MARS模型建立在灵活的回归算法基础上，该算法通常将解空间划分为预测变量的区间，并将样条基函数拟合到每个区间。利用随机抽样过程，将预测器数据分为训练阶段(70%的数据)和测试阶段(剩余30%的数据)。建立了月E的预报方程。RVM模型采用径向基函数，ELM模型由5个输入和10个隐含神经元组成，采用径向基激活函数，MARS模型采用15个基函数。当T(Max)作为输入时，对MARS模型的预测数据集之间的方差分解产生了最大的广义交叉验证统计量(千分之0.03)，其次是S和VP定义的相对较低的值(千分之0.028，0.019)。这证实了E的预测利用了来自T(Max)的预测特征的最大贡献，并通过敏感性分析检验得到了重点验证。模型性能统计的相关系数分别为0.979(均方根)、0.977(榆树)和0.974(MARS)，均方根误差分别为9.306、9.714和10.457，平均绝对误差分别为0.034、0.035和0.038。尽管总体预测技巧差异不大，但RVM模型对E的预测似乎更准确。因此，RVM模型可以作为一种很有前途的机器学习工具用于蒸发损失的预测。
The forecasting of evaporative loss (E) is vital for water resource management and understanding of hydrological process for farming practices, ecosystem management and hydrologic engineering. This study has developed three machine learning algorithms, namely the relevance vector machine (RVM), extreme learning machine (ELM) and multivariate adaptive regression spline (MARS) for the prediction of E using five predictor variables, incident solar radiation (S), maximum temperature (T (max)), minimum temperature (T (min)), atmospheric vapor pressure (VP) and precipitation (P). The RVM model is based on the Bayesian formulation of a linear model with appropriate prior that results in sparse representations. The ELM model is computationally efficient algorithm based on Single Layer Feedforward Neural Network with hidden neurons that randomly choose input weights and the MARS model is built on flexible regression algorithm that generally divides solution space into intervals of predictor variables and fits splines (basis functions) to each interval. By utilizing random sampling process, the predictor data were partitioned into the training phase (70 % of data) and testing phase (remainder 30 %). The equations for the prediction of monthly E were formulated. The RVM model was devised using the radial basis function, while the ELM model comprised of 5 inputs and 10 hidden neurons and used the radial basis activation function, and the MARS model utilized 15 basis functions. The decomposition of variance among the predictor dataset of the MARS model yielded the largest magnitude of the Generalized Cross Validation statistic (a parts per thousand 0.03) when the T (max) was used as an input, followed by the relatively lower value (a parts per thousand 0.028, 0.019) for inputs defined by the S and VP. This confirmed that the prediction of E utilized the largest contributions of the predictive features from the T (max), verified emphatically by sensitivity analysis test. The model performance statistics yielded correlation coefficients of 0.979 (RVM), 0.977 (ELM) and 0.974 (MARS), Root-Mean-Square-Errors of 9.306, 9.714 and 10.457 and Mean-Absolute-Error of 0.034, 0.035 and 0.038. Despite the small differences in the overall prediction skill, the RVM model appeared to be more accurate in prediction of E. It is therefore advocated that the RVM model can be employed as a promising machine learning tool for the prediction of evaporative loss.