Introduction Tensors mathematics Tucker model and examples PARAFAC model and examples PARAFAC VS Tucker Model selection

Introduction

Multiway data

To build multiway models, we need multiway data structures Common data structures consist of rows and columns (2D) A multiway data structure consists of a minimum of multiple 2D matrices that can be made into multiway models

1D: Vector 2D: Matrix 3D: Tensor

Tensors - The building blocks of Multiway models

Multiway models consist of "building blocks" called tensors

Tensor fancy mathematics definition: · An algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space

A simple definition: · A tensor is an N-dimensional array used to represent data, where N is the number of axes or modes

Examples of domains where multiway data structure is applicable

• Psychology
• Chemometrics
• Bioinformatics
• Computer vision

However, the multiway data structure is often ignored in favor of traditional 2D data analysis!