Alignment and Supervised Learning with Functional Neuroimaging

190 Pages·2012·2.41 MB·English

by  Alexander Lorbert

Alignment and Supervised Learning
with Functional Neuroimaging Data
Alexander Lorbert
A Dissertation
Presented to the Faculty
of Princeton University
in Candidacy for the Degree
of Doctor of Philosophy
Recommended for Acceptance
by the Department of
Electrical Engineering
Adviser: Professor Peter J. Ramadge
November 2012
©
Copyright by Alexander Lorbert, 2012.
All rights reserved.
Abstract
Cortical alignment is an essential link in the processing chain for establishing neu-
rological relationships across multiple subjects. This thesis addresses multi-subject
corticalalignmentusingfunctionalmagneticresonanceimaging(fMRI)data. Starting
from a correlation-based alignment metric, we derive hyperalignment, a previously-
established method that has demonstrated significant improvement over anatomical
alignment through the use of a common, synchronous stimulus. We then introduce a
regularized form of hyperalignment, revealing qualitative connections with canonical
correlation analysis (CCA) and further improving hyperalignment.
Extending hyperalignment beyond inter-subject correlations, we then investigate
hyperalignment via intra-subject correlations, yielding a functional connectivity hy-
peralignment (FCH) problem. Weakened by severe identifiability issues from a lack of
synchrony, FCH grossly underperforms. We show, however, that with a small injec-
tion of synchrony, FCH can match the performance levels of anatomical alignment.
Next, we address the scalability of hyperalignment, where we focus on an efficient
means of hyperaligning the entire cortex. Reformulating the hyperalignment problem
in terms of a voxel-derived feature set, which generally increases dimensionality, we
form a kernelized hyperalignment procedure. Using positive definite kernels as gener-
alized measures of similarity, kernel hyperalignment proves robust and competitive.
Beyond alignment, this thesis presents two supervised learning methods fit for
fMRIdataanalysis. ThefirstislinearregressionwiththePairwiseElasticNet(PEN),
a regularization term that can encode local and sparse groupings of the linear weights.
WeusePENforbinaryclassificationwithsupportvectormachines(SVM)inthefMRI
setting, demonstrating its ability to automatically select a sparse set of spatially-
grouped voxels. The second method is VIBoost, a boosting-like algorithm emanating
from variational inference. The VIBoost algorithm can generate a binary classifier
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along with meaningful statistics about the label noise. Such statistics are vital when
there is a lack of ground truth, as in the case of fMRI data.
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Acknowledgements
God said to Solomon, “Because you want this, and have not asked
forwealth,property,andglory,norhaveyouaskedforthelifeofyour
enemy, or long life for yourself, but you have asked for the wisdom
and the knowledge to be able to govern My people over whom I have
made you king, wisdom and knowledge are granted to you, and I
grant you also wealth, property, and glory, the like of which no king
before you has had, nor shall any after you have.”
II Chronicles 1:11–12
Knowledge with wisdom—and its pursuit—is a blessing like no other. It is the
key to life’s greatest rewards, both physical and spiritual. My time at Princeton was
nothing less than a gift from God, to Whom I am most grateful. A small yet crucial
ingredient of all research hinges on the initial sparks of inspiration and creativity.
I have been the beneficiary of these divine gifts, and the flame kindled from these
sparks are manifest in this thesis.
Standing on the shoulders of giants is not easy—it is a logistical nightmare. Find-
ing a giant, scaling the giant and, lastly, balancing oneself requires great skill and
practice. My research adviser, Dr. Peter Ramadge, has spent the past five years
training me to hone this skill, and I thank him for all of the knowledge and know-how
he has imparted to me. He has taught me to how to question, analyze, diagnose and
solve complex, real-world problems. I have greatly benefited from his uncanny ability
to absorb a problem, navigate to its nucleus, and yield new and exciting results. I
am deeply grateful for all of his guidance, candor and encouragement.
During the past five years, I have had the privilege and honor to work and collabo-
rate with first-rate researchers. I am indebted to Dr. David Blei, Dr. Robert Schapire
and Dr. James Haxby for all of their time and insightful input they have provided.
I am grateful to have been part of an excellent research group and I thank them for
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all of their collaboration, creativity and diligence: Eugene Brevdo, Xu Chen, Bryan
Conroy, David Eis, Shannon Hughes, Zhen (James) Xiang, Yun Wang, Yongxin (Tay-
lor) Xi, Hao Xu and Pingmei Xu. I would also thank J. Swaroop Guntupalli, Dr. Ben
Singer, Victoria Kostina, and Dr. Bede Liu. My graduate life was so much easier
thanks to the administrative staff of the Electrical Engineering Department. I am
grateful for all of the support and assistance of Colleen Conrad, Sarah McGovern,
Roelie Abdi-Stoffers, Beth Jarvie and Dorothy Coakley. Finally, I would like to thank
my dissertation committee: Professors Peter Ramadge, David Blei, Sanjeev Kulkarni,
Bede Liu, and Paul Cuff.
I would now like to thank the people who believe in the exceptionality of this work
while exhibiting a high level of apathy toward its content—my family. I am thankful
for my siblings Adam, Jonathan and Miriam. They have always rooted for me and
have always kept me rooted. I would also like to thank my in-laws Shaul and Dalia.
From the moment I became their son-in-law, they have treated me like a son and
have always been available for advice, support and encouragement.
Life’s events, both momentous and mundane, have taught me two truths. First,
I cannot begin to quantify how much my parents have worked and sacrificed to help
me become the person I am today. Second, I can always be a better son. My parents,
Zahuv (of blessed memory) and Eta, have always been my rock of support and love.
I thank them with all of my heart knowing that I cannot thank them enough.
During my time at Princeton, God has blessed my wife and me with two beautiful
boys: Zahuv Nisim and Akiva. No matter what, Nisim and Akiva can always put a
smile on my face. I enjoy every moment with them as they play, sing, eat, and share
in witty conversation. I thank them for motivating me to be a better person.
In closing, I am deeply grateful to the woman who has given me my greatest and
most-humbling titles of husband and father. My wife Sareet has been by my side
for the past six years, from New York to Massachusetts to New Jersey. A spouse
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is unique in that it is the only chosen family member—and I could not have chosen
better. Sareet is loving, caring, dependable, diligent, insightful and funny. She is an
amazing wife, mother, friend and teacher. It is my hope that we have many more
happy and healthy years together.
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To my family.
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Contents
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
List of Symbols and Abbreviations . . . . . . . . . . . . . . . . . . . . . . xvi
1 Introduction 1
1.1 Why fMRI? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Overview of function-based alignment . . . . . . . . . . . . . . . . . . 2
1.3 fMRI datasets used in this thesis . . . . . . . . . . . . . . . . . . . . 4
1.4 Organization of this thesis . . . . . . . . . . . . . . . . . . . . . . . . 6
2 Background: Hyperalignment 7
2.1 Time-Series Hyperalignment . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Voxel selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Cross-similarity scoring . . . . . . . . . . . . . . . . . . . . . . 9
2.3 Inter-subject correlation . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 The optimization problem . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 TSH and ISC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Regularized Time-Series Hyperalignment 14
3.1 CCA and ISC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
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3.2 Regularization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3 Case study: movie segment identification . . . . . . . . . . . . . . . . 21
3.4 Conclusion and future work . . . . . . . . . . . . . . . . . . . . . . . 23
4 Functional Connectivity Hyperalignment 27
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Functional Connectivity Hyperalignment . . . . . . . . . . . . . . . . 29
4.3 Identifiability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.3.1 An illustrative example . . . . . . . . . . . . . . . . . . . . . . 31
4.3.2 Addressing identifiability with time calibration . . . . . . . . . 35
4.4 Case study: image classification & voxel count . . . . . . . . . . . . . 39
4.5 Conclusion and future work . . . . . . . . . . . . . . . . . . . . . . . 40
5 Kernel Hyperalignment 43
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
5.2 Kernel hyperalignment . . . . . . . . . . . . . . . . . . . . . . . . . . 45
5.3 Using the transformations . . . . . . . . . . . . . . . . . . . . . . . . 49
5.4 Case study: revisiting image classification . . . . . . . . . . . . . . . 52
5.5 Conclusion and future work . . . . . . . . . . . . . . . . . . . . . . . 54
6 The Pairwise Elastic Net 57
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.2 Pairwise elastic net . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.2.1 Selecting R . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.3 The grouping effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
6.4 Coordinate descent . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6.5 Rescaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.6 Case study: PEN and image classification . . . . . . . . . . . . . . . 74
6.7 Conclusion and future work . . . . . . . . . . . . . . . . . . . . . . . 79
x