Data Fusion Methodology and Applications

Marina Cocchi

• Publisher: Elsevier
• Year: 2019
• ISBN:
  9780444639851
• Topic: Physical Sciences
• Subtopic: Analytic Chemistry

Data Fusion Methodology and Applications explores the data-driven discovery paradigm in science and the need to handle large amounts of diverse data. Drivers of this change include the increased availability and accessibility of hyphenated analytical platforms, imaging techniques, the explosion of omics data, and the development of information technology. As data-driven research deals with an inductive attitude that aims to extract information and build models capable of inferring the underlying phenomena from the data itself, this book explores the challenges and methodologies used to integrate data from multiple sources, analytical platforms, different modalities, and varying timescales.

• Presents the first comprehensive textbook on data fusion, focusing on all aspects of data-driven discovery
• Includes comprehensible, theoretical chapters written for large and diverse audiences
• Provides a wealth of selected application to the topics included

Chapter 4

Numerical Optimization-Based Algorithms for Data Fusion

N. Vervliet ^{∗ , 1} and L. De Lathauwer ^{∗ , § ∗}KU Leuven, Department of Electrical Engineering ESAT/STADIUS, Kasteelpark Arenberg, Leuven, Belgium ^§Group Science, Engineering and Technology, KU Leuven - Kulak, Kortrijk, Belgium
¹ Corresponding author

Abstract

Combining various sources of information to discover hidden patterns is key in data analysis. These sources can often be represented as matrices and/or multiway arrays, or tensors, which can be factorized jointly, e.g., as sums of simple terms, to gain insight into the data. In this chapter, an overview of (the rationale behind) numerically well-founded optimization techniques based on a Gauss–Newton framework is given, which has superior convergence properties and allows all multilinear structure to be exploited. Prior knowledge in the form of parametric, box, or soft constraints as well as regularization can be incorporated easily. We show how matrices and/or tensors can be coupled through (partially) shared factors or through common underlying variables. The framework is further extended to more general divergences allowing more suitable statistical assumptions. Finally, as tensor problems become large scale quickly, owing to the curse of dimensionality, techniques used to alleviate or overcome this curse are discussed.

Keywords

Algorithms; Canonical polyadic decomposition; Constrained decomposition; Coupled decomposition; Data fusion; Gauss–Newton; Numerical optimization; Tensor decomposition

1. Introduction

Consider the two views of two point clouds in a 3D space in Fig. 4.1 . When looking at eit...

Table of contents

• Cover image
• Title page
• Copyright
• Table of Contents
• Contributors
• Preface
• Introduction:Ways and Means to Deal With Data From Multiple Sources
• A Framework for Low-Level Data Fusion
• General Framing of Low-, Mid-, and High-Level Data Fusion With Examples in the Life Sciences
• Numerical Optimization-Based Algorithms for Data Fusion
• Recent Advances in High-Level Fusion Methods to Classify Multiple Analytical Chemical Data
• The Sequential and Orthogonalized PLS Regression for Multiblock Regression
• ComDim Methods for the Analysis of Multiblock Data in a Data Fusion Perspective
• Data Fusion by Multivariate Curve Resolution
• Dealing With Data Heterogeneity in a Data Fusion Perspective
• Data Fusion Strategies in Food Analysis
• Image Fusion
• Data Fusion of Nonoptimized Models:Applications to Outlier Detection, Classification, and Image Library Searching
• Index