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\begin{document}
\title{Object Oriented Data Analysis}

\author{J. S. Marron and Ian L. Dryden}


\pagenumbering{roman}
\maketitle



\lyxaddress{Department of Statistics and Operations Research, University of North
Carolina, Chapel Hill, NC 27599-3260, USA}

\lyxaddress{School of Mathematical Sciences, University of Nottingham, Nottingham,
NG7 2RD, UK}

\copyright \; 2021 by Taylor \& Francis Group, LLC. Except as permitted under
U.S. copyright law, no part of this book may be reprinted, reproduced,
transmitted, or utilized in any form by an electronic, mechanical,
or other means, now known or hereafter invented, including photocopying,
microfilming, and recording, or in any information storage or retrieval
system, without written permission from the publishers.

\bigskip{}



\chapter*{Dedication}

To our families for their ongoing strong support over the many years
it took to fully develop these ideas, and to the many colleagues who
have played a vital role in shaping this approach to data analysis.

\chapter*{Preface}

This book is intended as a resource for researchers in the development
of novel statistical and data science methodology. At the time of
this writing, \emph{Big Data} is a very popular area of study. While
Big Data does indeed present major statistical challenges, an even
greater challenge is dealing effectively with \emph{Complex Data}
which is the main motivation for \emph{Object Oriented Data Analysis}.
The latter is a framework that facilitates inter-disciplinary research
through new terminology for discussing the often many possible approaches
to the analysis of complex data. Such data are naturally arising in
a wide variety of areas. This book aims to provide ways of thinking
that enable the making of sensible choices. The main points are illustrated
with many real data examples, based on the authors' personal experiences,
which have motivated the invention of a wide array of analytic methods. 

A generally relevant comment is that most statistical problems can
be solved in many sensible ways. Simon Sheather elegantly summarized
that state of affairs (applicable to the many methods discussed in
this book) as: ``every dog has its day''. The point is that any
method that has been seriously advocated by someone has situations
where it gives excellent performance, but also situations where it
can be quite poor. The challenge is to understand the properties of
each well enough to guide good choices. The material in this book
will provide the reader with useful insights and a general framework
to assist in this process.

A fundamental theme throughout the book, that has not been deeply
explored elsewhere is \emph{modes of variation}. That provides a novel
terminology and framework for understanding many aspects of Object
Oriented Data Analysis.

While the mathematics goes far beyond the usual in statistics (including
differential geometry and even topology), the book is aimed at accessibility
by graduate students. There is deliberate focus on ideas over mathematical
formulas. An exception is the detailed linear algebra development
in Chapter \ref{chapP:PCA-Details}. While many references to various
aspects of OODA are given, it should be noted we have deliberately
not attempted to be comprehensive in those. Our aim instead is to
simply provide useful starting points that interested researchers
can use for their own bibliographic searches. 

The historical background of the Object Oriented Data Analysis terminology
is discussed in Section \ref{secC1:History-and-Terminology}.

Much of the material that went into this book, including data sets,
and the code to generate most of the graphics can be found in the
the web companion to this book at \citet{Marron2020OODAbookGitPage}.
Many of those require Marron's Matlab Software, available at: \citet{Marron2017MatlabSoftware}.
The companion website also contains further references and links to
other software packages.

\section*{Acknowledgments}

Many of the ideas and presentation style have been developed during
the teaching of a graduate course entitled Object Oriented Data Analysis,
taught roughly every other year at the University of North Carolina
since 2005. There were some important precursors, including a related
course taught at Cornell University in 2002. Two such courses were
offered at the Statistical and Mathematical Sciences Institute in
2010 and 2011 with lecturers (beyond the authors of this book) including
Hans-Georg M\"{u}ller, James O. Ramsay, and Jane-Ling Wang. The course
was also taught at the National University of Singapore in 2015.

Several events have played a pivotal role in the development of Object
Oriented Data Analysis. One was the Statistical and Mathematical Sciences
Institute program on ``Analysis of Object Data'' during 2010-2011,
with co-organizers Hans-Georg M\"{u}ller, James O. Ramsay and Jane-Ling
Wang. Another pivotal workshop was the November 2012 ``Statistics
of Time Warpings and Phase Variations'' at the Mathematical BioSciences
Institute, with co-organizers James O. Ramsay, Laura Sangalli and
Anuj Srivastava.

General research in this area by the authors has been supported over
the years by a number of grants from the National Science Foundation,
including DMS-9971649, DMS-0308331, DMS-0606577, DMS-0854908 and IIS-1633074,
and the Engineering and Physical Sciences Research Council grants
EP/K022547/1 and EP/T003928/1. 

The material on sounds as data objects was kindly provided by Davide
Pigoli. The authors are especially grateful to Stephan F. Huckemann,
John T. Kent, James O. Ramsay and Anuj Srivastava for providing formal
reviews of early drafts that fundamentally impacted the final version.
Additional useful comments on various drafts have been provided by
Iain Carmichael, Benjamin Elztner, Thomas Keefe, Carson Mosso, Vic
Patrangenaru, Stephen M. Pizer, Davide Pigoli and Piercesare Secchi.

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