Fitting sparse multidimensional data with low-dimensional terms

Abstract
An algorithm that fits a continuous function to sparse multidimensional data is presented. The algorithm uses a representation in terms of lower-dimensional component functions of coordinates defined in an automated way and also permits dimensionality reduction. Neural networks are used to construct the component functions.

Title of program: RS_HDMR_NN
Catalogue Id: AEEI_v1_0

Nature of problem
Fitting a smooth, easily integratable and differentiatable, function to a very sparse (~2-3 points per dimension) multidimensional (D >= 6) large (~10 4 -10 5 data) dataset.

Versions of this program held in the CPC repository in Mendeley Data
AEEI_v1_0; RS_HDMR_NN; 10.1016/j.cpc.2009.05.022

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要

本文提出一种将连续函数拟合至稀疏多维数据集的算法。该算法采用自动定义的坐标低维分量函数形式进行表征，同时支持降维操作，且通过神经网络（Neural Networks）构建各分量函数。

程序名称：RS_HDMR_NN
目录编号：AEEI_v1_0

问题性质
将平滑、易于积分与求导的函数拟合至超高稀疏度（每维度仅约2~3个数据点）、维度D≥6且样本量为10⁴~10⁵的大规模多维数据集。

本程序在Mendeley数据平台的CPC程序库内的版本信息如下：
AEEI_v1_0; RS_HDMR_NN; 10.1016/j.cpc.2009.05.022

本程序源自贝尔法斯特女王大学所持有的CPC程序库（1969-2019年馆藏）