Model Identification Based on Sparse or Non-Uniform Datasets using Tensor Product Function Manipulations

This paper presents an approach for creating tensor product (TP) models based on sparse or non-uniform samples representing arbitrary datasets, and for manipulating the resulting TP structure to further identify the models behind the datasets. Given the usefulness of TP models in merging together closed algebraic formulae and tensor representations, it is argued that the proposed approach can be applied towards understanding the underlying complexity of a given dataset, while iteratively arriving at a model for the process that generated it. The key idea behind the approach is demonstrated using a dataset on sound pressure levels generated by different-sized airfoils in a wind tunnel.

I. Introduction

Tensor Product (TP) models can be seen as discrete sampling-based structures that are transformed into a unique representation (consisting of tensor-matrix products) based on higher-order singular value decomposition (HOSVD) [1] . TP models represent a natural connection between matrix and tensor-algbraic concepts such as rank or dimensionality reduction on the one hand, and closed-form equations on the other. This property of TP models has made them a suitable representation in a wide variety of application areas where modeling accuracy and complexity reduction are equally important. [2] , [3] , [4] .