基于张量偏最小二乘法的高维输出预测模型

A Multi-dimensional Output Prediction Model Based on Tensor Partial Least Squares

针对输出为高维数据的预测问题,构建了一种基于张量偏最小二乘法的预测模型。该模型的输入和输出均为张量,可在不进行数据降维操作的前提下对多个输出同时预测。该方法以偏最小二乘法为基础,引入逐块Tucker分解和高阶奇异值分解,通过对输入和输出变量的分析,提取同时包含二者最大信息的潜在变量并计算残差,再通过残差计算新的潜在变量,循环直到残差小于给定范围为止。实验数据来源于心脏传导系统在正常和急性高糖环境下采集的电生理信息,通过最大正振幅、最大负振幅、频率、单次信号持续时间四个维度的输入同时预测急性高糖的浓度和作用时间,并将预测结果与传统的多向偏最小二乘法和多维偏最小二乘法相比较。实验结果表明,基于张量偏最小二乘法的预测模型预测精度最高。

A prediction model based on tensor partial least squares (TPLS) is built to solve the problem of high dimensional data.The input and output of the model are tensors,and multi-dimensional output can be predicted without dimensional reduction.Based on partial least squares, this method introduces block by block Tucker decomposition and high order singular value decomposition.Through the analysis of input and output variables,the potential variables containing the maximum information of both are extracted and the residual error is calculated.Then,the new potential variable is calculated through the residual error,and the loop runs until the residual error is less than the given range.The experimental data are derived from electrophysiological information of cardiac conduction systems in normal and acute hyperglycemic environments.The input is a four-dimensional tensor which contains maximum positive amplitude,maximum negative amplitude,frequency and single signal duration.The predictive output contains the concentrations and durations of acute hyperglycemia.The prediction results are compared with multi-way PLS and N-way PLS,which shows that the tensor PLS has the highest prediction accuracy.