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RESEARCH ARTICLE

Brain-wide connectome inferences using

functional connectivity MultiVariate Pattern

Analyses (fc-MVPA)

Alfonso Nieto-CastanonID

1,2

*

1Department of Speech, Language, and Hearing Sciences, Boston University, Boston, Massachusetts,

United States of America, 2Department of Brain and Cognitive Sciences, Massachusetts Institute of

Technology, Cambridge, Massachusetts, United States of America

*alfnie@bu.edu

Abstract

Current functional Magnetic Resonance Imaging technology is able to resolve billions of

individual functional connections characterizing the human connectome. Classical statistical

inferential procedures attempting to make valid inferences across this many measures from

a reduced set of observations and from a limited number of subjects can be severely under-

powered for any but the largest effect sizes. This manuscript discusses fc-MVPA (functional

connectivity Multivariate Pattern Analysis), a novel method using multivariate pattern analy-

sis techniques in the context of brain-wide connectome inferences. The theory behind fc-

MVPA is presented, and several of its key concepts are illustrated through examples from a

publicly available resting state dataset, including an analysis of gender differences across

the entire functional connectome. Finally, Monte Carlo simulations are used to demonstrate

the validity and sensitivity of this method. In addition to offering powerful whole-brain infer-

ences, fc-MVPA also provides a meaningful characterization of the heterogeneity in func-

tional connectivity across subjects.

Author summary

The human connectome comprises billions of functional connections between distant

brain areas. In recent years, analyses of functional Magnetic Resonance Imaging (fMRI)

data have provided large amounts of information exploring the differences in the human

connectome across individuals, developmental trajectories, or mental states. However, sci-

entists’ ability to derive strong conclusions from the analysis of these data are often hin-

dered by the sheer number of connections analyzed, where only connections that show

exceptionally large effects are able to stand out against that vast background. This leads to

results that tend to overemphasize similarities and mask out differences that are either

weaker or distributed across multiple individual connections, potentially misleading con-

ceptual models of the human connectome. This manuscript discusses a novel method for

the analysis of the human connectome (functional connectivity Multivariate Pattern Anal-

ysis) that addresses these limitations and enables strong conclusions from fMRI data by

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OPEN ACCESS

Citation: Nieto-Castanon A (2022) Brain-wide

connectome inferences using functional

connectivity MultiVariate Pattern Analyses (fc-

MVPA). PLoS Comput Biol 18(11): e1010634.

https://doi.org/10.1371/journal.pcbi.1010634

Editor: Daniele Marinazzo, Ghent University,

BELGIUM

Received: June 30, 2022

Accepted: October 4, 2022

Published: November 15, 2022

Peer Review History: PLOS recognizes the

benefits of transparency in the peer review

process; therefore, we enable the publication of

all of the content of peer review and author

responses alongside final, published articles. The

editorial history of this article is available here:

https://doi.org/10.1371/journal.pcbi.1010634

Copyright: ©2022 Alfonso Nieto-Castanon. This is

an open access article distributed under the terms

of the Creative Commons Attribution License,

which permits unrestricted use, distribution, and

reproduction in any medium, provided the original

author and source are credited.

Data Availability Statement: This manuscript

analyses are based on a publicly available resting

state dataset (Cambridge 1000-connectomes

dataset, n=198; www.nitrc.org/projects/fcon_1000;

doi:10.1073/pnas.0911855107), and all methods

combining classical statistics with modern pattern analysis techniques. This technique is

exemplified using a publicly available database of resting state data to characterize some of

the main aspects of the human connectome that differ across individuals, and to identify

specific differences in the human connectome across gender.

This is a PLOS Computational Biology Methods paper.

Introduction

Functional connectivity Magnetic Resonance Imaging (fcMRI) is used to characterize the state

(e.g. during rest or during individual cognitive tasks) of the human connectome, the set of all

functional connections within the brain. In its most basic form, the entire human connectome

state can be represented in a way that is limited only by the spatial resolution of the MRI acqui-

sition sequence as a matrix of voxel-to-voxel functional connectivity values. Human connec-

tome research is often motivated by the attempt to characterize similarities and discrepancies

in these functional connectivity matrices across subjects or across experimental conditions,

performing inferences that extrapolate from the limited data available in a study sample to

properties of the human connectome in a larger population. However, this form of uncon-

strained brain-wide connectome inferences can suffer from a curse of dimensionality. A

mass-univariate approach analyzing each functional connection between every pair of voxels

in the brain may consist of over 60 billion individual statistical tests (the total number of pair-

wise functional connections among approximately 250,000 isotropic 2mm voxels within gray

matter areas). This poses considerable difficulties. First, analytically, as an appropriate correc-

tion for multiple comparisons across this abundance of tests results in exceedingly low sensi-

tivity. For example, simple Bonferroni or False Discovery Rate corrections [1,2] would require

at least one individual connection below a p<10

−12

significance level in order to resolve FWE-

corrected significance at the analysis level, limiting the sensitivity and applicability of these

analyses (e.g. [3]). Second, computationally, as each voxel-to-voxel correlation matrix would

require approximately 400Gb of memory or storage space for each individual subject and

experimental condition of interest, making storing and working with these matrices extraordi-

narily demanding. Third, practically, as the potential wealth of information of voxel-to-voxel

connectivity results makes reporting and interpreting the results of these analyses a significant

challenge in itself.

Existing approaches have addressed these issues by either narrowing the focus of the analy-

ses to connectivity with one or a few a priori seed areas (e.g. connectivity with amygdala) and

then performing seed-based connectivity analyses (SBC), or by limiting the analysis units from

voxels to larger parcels or Regions of Interest (ROIs) and then performing ROI-to-ROI con-

nectivity analyses (RRC). The first approach (SBC) reduces the multiple-comparison problem

by focusing on individual (or linear combinations of) rows of the functional connectivity

matrices, disregarding all other possible effects beyond those involving at least one of these a

priori seed areas. The main advantage of this approach is its simplicity, as it can take advantage

of the same cluster-level inferential procedures that have been proven effective in standard

analyses of functional activation, such as Gaussian Random Field theory inferences [4], per-

mutation/randomization analyses [5] or Threshold Free Cluster Enhancement (TFCE) [6].

The main disadvantage of this approach is a high chance of potential false negatives, as other

effects not involving the chosen seed areas may be missed.

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described in this manuscript are publicly available

as part of CONN (RRID:SCR_009550, www.nitrc.

org/projects/conn).

Funding: This research was supported by the

National Institute on Deafness and Other

Communication Disorders (R01 DC007683, R01

DC002852, R01 DC016270), National Institute of

Neurological Disorders and Stroke (U01

NS117836) and National Institute of Mental Health

(U01 MH108168).

Competing interests: The authors have declared

that no competing interests exist.

The second approach (RRC) is able to perform brain-wide connectome inferences with suf-

ficient sensitivity by drastically reducing the multiple-comparison problem, typically focusing

on no more than a few hundred ROIs, often defining an entire parcellation of the brain (e.g.

Harvard-Oxford atlas). In addition, specialized false positive control approaches, such as Func-

tional Network Connectivity [7], Network Based Statistics [8], Spatial Pairwise Clustering [9],

Threshold Free Cluster Enhancement [6], or Multivariate cNBS [10] can be used to further

increase the sensitivity of these analyses. Nevertheless, ROI-to-ROI analyses suffer from

reduced spatial specificity arising from the a priori selection of parcels of interest, and their

conclusions can be particularly sensitive to the choice of ROIs. Advances in connectivity-

based parcellations (e.g. [11]) or subject-specific functional ROIs (e.g. [12]) can be useful to

partially alleviate these concerns.

An alternative approach uses Principal Component Analyses (PCA) or Independent Com-

ponent Analyses (ICA) to assess differences in functional networks, or sets of functionally cor-

related areas, across groups [13]. Similar to seed-based approaches, PCA and ICA are able to

drastically reduce the multiple-comparison problem by focusing on individual networks, each

comprising a group of functional-related areas, and then evaluating measures of within- and

between- network connectivity. One advantage of this approach, compared to SBC, is that

these networks do not need to be defined a priori and can be instead estimated directly from

the functional data. In the context of brain-wide connectome inferences, nevertheless, these

methods suffer from similar shortcomings as SBC, namely the potential of false negatives,

where finer functional connectivity differences that are not present at the level of entire net-

works may be missed.

This paper proposes functional connectivity Multivariate Pattern Analysis (fc-MVPA), an

alternative approach to the analysis of the brain-wide connectome at the resolution of individ-

ual voxels, that overcomes the difficulties of brain-wide connectome analyses using multivari-

ate pattern analysis techniques. Like other MVPA approaches in neuroimaging, fc-MVPA

follows a general searchlight procedure (e.g. [14]), but instead of focusing on the pattern of

activation surrounding each voxel, fc-MVPA considers separately for each voxel the entire

multivariate pattern of functional connections between this voxel and the rest of the brain.

Most MVPA methods focus on the relationship between properties of these multivariate pat-

terns, characterizing a subject’s mental state, and either static (e.g. patients vs. controls) or

dynamic properties of the experimental design (e.g. pre- vs. after- intervention, task vs. rest,

etc.), while varying in how exactly these relationships are modeled or analyzed. Classical

MVPA analyses (e.g. [15,16]) attempt to estimate, from these or other searchlight patterns,

properties of the experimental paradigm. These MVPA analyses are often referred to as back-

ward models [17], and typically use machine learning classification models embedded in a

cross-validation framework to decode information about a subject’s mental state from their

activation patterns. In this popular class of MVPA models searchlight patterns act as indepen-

dent/explanatory variables, while known subject or experimental properties act as dependent/

outcome variables. Unlike those forms of MVPA, fc-MVPA instead uses a forward model of

the data, attempting to estimate the shape of these searchlight patterns from known subject or

experimental properties, switching the role of dependent/independent variables. In addition to

being advantageous in terms of the interpretability of model weights, forward models also

enable us to frame brain-wide connectome inferences in the context of the General Linear

Model (GLM), one of the most widely used inferential statistical methods in neuroimaging,

and use powerful multivariate inferences [10] to directly address researchers’ hypotheses. Spe-

cifically, this approach allows us to make statistical inferences about individual voxels in the

brain regarding the shape of their functional connectivity patterns (e.g. is the shape of the func-

tional connectivity pattern between a voxel and the rest of the brain different in patient vs.

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control subjects?), and then repeat these analyses across all voxels within the brain extending

these inferences to the entire connectome (e.g. is the shape of functional connectivity patterns

different in patient vs. control subjects anywhere in the brain?).

Code implementing fc-MVPA, as described in this manuscript, is available in SPM’s

CONN functional connectivity toolbox [18,19] and it has already been evaluated and shown to

provide valuable insights on a variety of research topics (e.g. [20–45]). Despite this, a rigorous

discussion of this method’s approach, validity, and applications has been missing. This manu-

script aims to correct that record by presenting a detailed mathematical description of the fc-

MVPA method, highlighting its relationship to other multivariate statistical inferential proce-

dures, illustrating some of fc-MVPA key concepts and applications through examples, and

demonstrating the method’s validity and sensitivity through Monte Carlo simulations.

In the first section, a general framework to perform univariate and multivariate statistical

inferences in the context of functional connectivity data is presented. This is followed by a sec-

tion describing the specifics of the fc-MVPA approach, where some of its central applications,

including brain-wide connectome inferences as well as the characterization of intersubject het-

erogeneity, are further illustrated with examples. Finally, the last section presents simulation

results demonstrating the method’s validity, and discussing some of the main factors affecting

sensitivity. All analysis examples in this manuscript are based on a publicly available resting

state dataset (Cambridge 1000-connectomes dataset, n = 198; www.nitrc.org/projects/fcon_

1000), and all methods are publicly available in SPM12 [46] (RRID:SCR_007037, www.fil.ion.

ucl.ac.uk/spm/software/spm12/) and CONN [19] (RRID:SCR_009550, www.nitrc.org/

projects/conn).

Methods

Definition of functional-connectivity univariate and multivariate analyses

(fc-MUA, fc-MVA)

For any subject nin a study, and any pair of voxels xand y, we consider the values r

n

(x,y) char-

acterizing the functional connectivity between these two voxels for this subject. Without loss

of generality, we are going to consider r

n

(x,y) to represent Pearson correlation coefficients

between these two voxels BOLD timeseries (but all of the following descriptions would equally

apply to any arbitrary connectivity or similarity measure between pairs of elements in any

high-dimensional set). In a study we desire to make inferences regarding the properties of

these connectivity measures in the population from which the study subjects are being drawn.

For example, we may ask, based on our current study data, whether there are any connectivity

differences when comparing patients to control subjects, or whether functional connectivity

strength correlates with age, or whether it is modulated by some experimental condition. To

that end we could use a forward model of the data defining for each individual connection a

separate General Linear Model (GLM) of the form:

functional connectivity Mass-Univariate Analyses (fc-MUA)

8x;y rnðx;yÞ ¼ gnbðx;yÞ þ εnðx;yÞ sðx;yÞ

Null hypothesis : Cbðx;yÞ ¼ 0ð1Þ

(note on notation: in this document’s equations we use regular fonts to refer to scalars,

bolded lower case fonts for vectors, and bolded capital fonts for matrices; see glossary of terms

in the supplementary materials S1 Table for details about the interpretation and dimensional-

ity of all terms in these equations.) In Eq (1)g

n

is a predictor vector for each subject n

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characterizing known factors in our experimental design, such as group membership or behav-

ioral measures (also known as the model design matrix), b(x,y) is an unknown vector of regres-

sion coefficients, estimated from the data and characterizing the effect of each modeled

predictor on the outcome functional connectivity measures (e.g. the average connectivity

strength within each group), ε

n

(x,y) represents an error term sampled independently for each

subject from a random Gaussian field with zero mean and unit variance (GLM asymptotic

normality assumption), and σ(x,y) is an intersubject variance term that depends on position x

but is otherwise constant across subjects (GLM homoscedasticity assumption). The General

Linear Model uses Ordinary Least Squares (OLS) to computed an unbiased estimate of the vec-

tor bfrom the data (Gauss-Markov theorem). After estimating these regressor coefficients, we

can specify a null-hypothesis of the form Cb(x,y) = 0 for any given between-subjects contrast

C(e.g. a null hypothesis might evaluate whether functional connectivity differs between

patients and controls) and use a classical hypothesis testing framework to evaluate this hypoth-

esis. Hypothesis testing extrapolates from the observed properties of b, estimated only from

our sample data, to the effects of the associated predictor terms in the larger population, allow-

ing us to make valid inferences about any hypothesis in this larger population. Null-hypotheses

are generally evaluated using a Likelihood Ratio Test (LRT) based on a Wilks Lambda distribu-

tion and associated T- and F- statistics [47]. These hypotheses are tested separately for each

pair of voxels xand y, resulting in a statistical parametric map F(x,y) of T- or F- statistics and

associated p- values, characterizing the likelihood of our observations under the null hypothe-

sis for every individual seed and target voxels.

We refer to this approach as mass-univariate (fc-MUA) because it is based on a separate

univariate test for each connection (for each pair of voxels xand y) in the entire brain-wide

connectome. As mentioned before, one of the main difficulties with fc-MUA in the context of

brain-wide connectome inferences is the extremely large number of connections evaluated

(one for every pair of voxels) leading to the need for very strong multiple comparison correc-

tions and reduced sensitivity to detect anything but the largest effects.

Compared to this mass-univariate approach, functional connectivity MultiVariate Analyses

(fc-MVA) use a searchlight approach where each individual analysis focuses on one individual

voxel-of-interest x, and perform an omnibus test of the connectivity between this voxel and

the rest of the brain using a multivariate GLM analysis of the form:

functional connectivity MultiVariate Analyses (fc-MVA)

8xrnðxÞ ¼ gnBðxÞ þ εnðxÞ ΣðxÞ

Null hypothesis : CBðxÞ PðxÞ ¼ 0ð2Þ

The term r

n

(x,y) in Eq 2 contains an entire map of connectivity values defined in vector

form (each element of this vector contains the connectivity value r

n

(x,y) for a different target

voxel y), fully characterizing the functional connectivity pattern for subject nbetween the

seed-voxel xand the rest of the brain. B(x) is now an unknown predictors-by- voxels matrix of

regression coefficients, ε

n

(x) is a residual error vector sampled from a random multivariate

Gaussian distribution with zero mean and unit variance, and S(x) is a voxels-by-voxels semi-

positive definite matrix characterizing the spatial covariance in functional connectivity pat-

terns, which again may depend on position xbut is otherwise constant across subjects. As

before, the General Linear Model uses Ordinary Least Squares (OLS) to estimate the matrix of

regressor coefficients Bfrom the data. In the context of hypothesis testing, Cand P(x) repre-

sent the between-subjects and between-voxels contrast matrices, respectively, characterizing

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which aspects of the matrix of regression coefficients we would like to evaluate. Any arbitrary

hypothesis of the form C

t

B(x)P(x) = 0, may be evaluated separately for each searchlight voxel

xusing a statistical parametric map F(x), computed using a Satterthwaite approximation [48]:

F xð Þ ¼ b

c

trðHðxÞÞ

trðWðxÞÞ Fkc;kb ð3Þ

bNrankðGÞ

crankðGCtÞ

ktrðWðxÞÞ2

trðW2ðxÞÞ

where band care error and hypothesis degrees of freedom, respectively, and the matrices W

and Hare the error and hypothesis sum of squares and products, respectively:

WðxÞ ¼ PtðxÞðRðxÞ GBðxÞÞtðRðxÞ GBðxÞÞPðxÞ ð4Þ

HðxÞ ¼ PtðxÞBtðxÞCtðCðGtGÞ1CtÞ1CBðxÞPðxÞ

BðxÞ ¼ ðGtGÞ1GtRðxÞ

RðxÞ ½rt

1ðxÞrt

2ðxÞ...rt

NðxÞt

G ½gt

1gt

2. . . gt

Nt

Eq 3 results in a statistical parametric map F(x) with values that follow, under the null

hypothesis, a standard Fdistribution with kc and kb degrees of freedom. This allows us to com-

pute associated p- values characterizing the likelihood of our observations under the null

hypothesis for every individual searchlight voxel.

The between-voxels contrast matrix P(x) in Eq 2 serves to focus the analyses on a particular

subspace of interest characterizing specific features of the functional connectivity maps r

n

(x).

The choice of P(x) affords great flexibility in the specific form of fc-MVA analyses that can

possibly be implemented. For example, in the simplest possible scenario, we may choose P(x)

to be a constant one-dimensional projector, such as a unit-norm vector with positive weights

over a single voxel or a small area, which would allow us to focus only on the connectivity with

one a priori voxel or region of interest. Interestingly, in this scenario fc-MVA reduces exactly

to a standard seed-based connectivity (SBC) analysis, producing statistical parametric maps F

(x) that characterize the connectivity between the chosen voxel or area and the rest of the

brain. In contrast, in perhaps the most general scenario, we may instead choose P(x) to also be

constant but now equal to the identity matrix, jointly and equally considering all target voxels.

This allows us to simultaneously estimate and evaluate any/all aspects of the functional con-

nectivity maps r

n

(x).

Between these two extrema, there are many reasonable alternatives. For example, a spatial

basis P(x) that would focus on low spatial-frequency components of connectivity profiles (e.g.

[49]), one that would focus only on local connectivity with neighboring areas (e.g. a multivari-

ate Local Connectivity measure), or one that would focus only on connectivity with all voxels

within a fixed area (masked fc-MVA, e.g. connectivity with the cerebellum or any other large/

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heterogeneous area). In the next section we will discuss one particular form of fc-MVA analy-

ses that is based on a data-driven choice of spatial basis P(x) focusing on rich low-dimensional

representations of arbitrary functional connectivity patterns.

Definition of functional-connectivity multivariate pattern analyses (fc-

MVPA)

Functional connectivity multivariate pattern analyses (fc-MVPA) can be considered a particu-

lar case of functional connectivity multivariate analyses (fc-MVA), where the choice of spatial

basis P(x) attempts to achieve a balance between retaining high sensitivity to unknown or arbi-

trary effects while maintaining a good level of specificity to those features more representative

of the data at hand. In particular, representative features in fc-MVPA are chosen to have maxi-

mal intersubject variability and minimal overlap (i.e. orthogonal features). This is achieved by

first constructing the matrix R(x) by concatenating all of the maps r

n

(x) for a given seed-voxel

xacross all subjects, and then defining P(x) implicitly as the right- orthogonal basis from a Sin-

gular Value Decomposition (SVD) factorization of the connectivity matrix R(x):

SðxÞ DðxÞ PtðxÞ ¼ RðxÞ ð5Þ

where S(x) and P(x) are orthogonal matrices of left- and right- singular vectors of R(x), respec-

tively, and D(x) is a diagonal matrix containing the positive singular values of Rsorted in

decreasing order. The total number of singular vectors and values in Eq 5 is equal to the num-

ber of subjects N, but typically this dimensionality can be further reduced to a lower value

kNto only include the first few singular values and vectors that achieve a predefined predic-

tive or descriptive target (e.g. those dimensions capturing on average 50% or more of the total

covariance in the patterns of functional connectivity across subjects).

Conceptually, this particular choice of basis in fc-MVPA has a very important benefit, as

the resulting eigenpatterns, defined as the columns of the resulting matrix P(x), have a mean-

ingful interpretation as those patterns that best characterize the observed heterogeneity across

subjects in functional connectivity with an individual seed voxel. In particular the squared

eigenvalues

ξðxÞ diagðD2ðxÞÞ=traceðRðxÞ RtðxÞÞ ð6Þ

represent the portion of the total intersubject covariance R(x)R

t

(x) in connectivity maps that

lies within the dimensions characterized by each individual eigenpattern, and by the nature of

SVD these values are maximal (i.e. there is no other k-dimensional subspace containing a

larger percentage of the total covariance of the data than the subspace spanned by the first k

eigenpatterns, for any value k).

In this context, the values s

n

(x), which we will refer to in this manuscript as eigenpattern

scores, and which are defined as the rows of the left-singular matrix S(x), define an optimal lin-

ear low-dimensional representation of the original data r

n

(x) for each subject, meaning that we

can always linearly reconstruct the high-dimensional data r

n

(x) from its low-dimensional

representation s

n

(x) with minimal error.

Mathematically, this approach is similar to functional PCA [50] or to the group-level

dimensionality reduction step in ICA [13] which helps reduce noise, simplify the analyses, and

increase the interpretability of the resulting ICA components, but the main difference is that

in fc-MVPA dimensionality reduction is performed separately for each individual seed-voxel

x. Because the dimensionality reduction step in fc-MVPA is only tasked with characterizing

the heterogeneity in functional connectivity patterns between one individual voxel xand the

rest of the brain, while in PCA/ICA the dimensionality reduction step is tasked with

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simultaneously characterizing the heterogeneity in functional connectivity patterns between

all pairs of voxels, the former can achieve a considerably more compact representation, where

fewer components will explain a larger portion of that heterogeneity (as will be illustrated in

the next section). In addition, the ability to obtain such low-dimensional characterization in a

way that is specific to each anatomical location offers a considerably richer representation of

intersubject heterogeneity compared to other similar but global approaches, such as PCA or

ICA.

In the context of brain-wide connectome analyses, using a simple change of basis allows us

to simplify the fc-MVA multivariate general linear model and null hypothesis in Eq 2. In par-

ticular, by right-multiplying Eq 2 by the matrix P(x)D

−1

(x) we develop an equivalent lower-

dimensional fc-MVPA general linear model and hypothesis of the form:

functional connectivity MultiVariate Pattern Analyses (fc-MVPA)

8xsnðxÞ ¼ gn~

BðxÞ þ εnðxÞ ~

ΣðxÞ

Null hypothesis : C~

BðxÞ ¼ 0ð7Þ

This is exactly the same model as in Eq 2 but expressed only within a lower-dimensional

subspace represented by the eigenpattern scores s

n

(x), instead of the original higher-dimen-

sional connectivity maps r

n

(x). In this context, the eigenpattern scores s

n

(x) represent what has

also been referred to as Multivariate Connectivity maps (MCOR) [51], a voxel-specific low-

dimensional multivariate representation of the pattern of functional connectivity between a

voxel and the rest of the brain. Similarly, ~

BðxÞand ~

ΣðxÞin Eq 7 are also equal to their Eq 2

counterparts simply projected onto the subspace defined by P(x). The reduced dimensionality

allows us to simplify the computational implementation of these analyses considerably. For

example, the eigenpattern scores s

n

(x) can now be simply stored as multiple whole-brain vol-

umes, with one volume or image per component and per subject, and shared across multiple

second-level analyses. This is in contrast with the considerably larger vectors r

n

(x)which can-

not be easily stored (e.g. one whole-brain volume per subject and per target voxel y). In addi-

tion, the eigenpattern scores s

n

(x) are defined independently of the predictor vectors g

n

, so

they not only offer a model-free characterization of the heterogeneity in the data, but the same

eigenpattern scores can also be used in multiple different group-level analyses of the same

data. Last, the reduced dimensionality of Eq 7 also allows the covariance ~

Σ2ðxÞacross eigenpat-

tern scores to be fully estimable from a limited number of samples, whereas the original covari-

ance S(x) across voxels in Eq 2 could very rarely be so estimated with full rank. Because of this,

the effect of the within-subjects covariance in the resulting null hypothesis Fstatistics at each

individual searchlight voxel does not need to be approximated (e.g. using Satterthwaite

approximation as in Eq 3), allowing us to rely instead on a more sensitive Likelihood Ratio sta-

tistic (LRT) of the form [52]:

F xð Þ ¼ d

ac 1l1=e

l1=eFac;dð8Þ

l¼jWj

jWþHj

arankðPðxÞÞ

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bNrankðGÞ

crankðGCtÞ

dbacþ1

2

eac

2þ1

eﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ

a2c24

a2þc25

r

where λis Wilks’ Lambda statistic, ais typically equal to k, the number of selected eigenpat-

terns (1<a<b), bis the error degrees of freedom, cis the hypothesis degrees of freedom, and

Wand Hare the same error and hypothesis sum of square matrices as in Eq 4 computed over

the subspace P(x). As before, the resulting F(x) values follow, under the null hypothesis, a stan-

dard Fdistribution with ac and bdegrees of freedom, for each individual searchlight voxel x.

To summarize, Fig 1 illustrates the idealized fc-MVPA procedure. For every searchlight

voxel xwe first compute the functional connectivity maps r

n

(x) between this voxel and the rest

of the brain for every individual subject (Fig 1 top left), and use Eq 5 to compute a reduced set

of eigenpattern scores s

n

(x) best characterizing relevant spatial features of these maps across

subjects (represented in Fig 1 top right). Once each subject’s functional connectivity profiles

are represented in terms of their lower-dimensional associated eigenpattern scores s

n

(x),

group-level functional connectivity analyses proceed normally by entering these scores into a

standard General Linear Model (Eq 7). This model evaluates at this searchlight location xany

hypothesis of the form C~

BðxÞ ¼ 0using LRT (Eq 8), allowing us to make inferences about

the shape of the functional connectivity maps that these scores represent. Last, this procedure

is then simply repeated for each searchlight voxel x, sequentially constructing a statistical

parametric map F(x) characterizing the results of this inferential procedure across the entire

brain.

The general fc-MVPA procedure may be seen as computationally prohibitive, particularly

for whole-brain analyses using relatively small voxel sizes (e.g. isotropic 2mm voxels), since the

computational load scales quadratically with the total number of voxels under consideration, it

appears to require the computation of entire voxel-to-voxel connectivity matrices, and it effec-

tively performs close to 200,000 whole-brain PCA analyses (one per seed voxel) characterizing

the intersubject heterogeneity of seed-based connectivity maps. Despite this, there are several

mathematical tricks that can be used to reduce the complexity of the necessary computations

by several orders of magnitude. In particular, in S1 Appendix we describe how to more effi-

ciently compute the eigenpattern scores s

n

(x) directly from the original BOLD timeseries in a

way that will instead scale only linearly with the number of voxels, and without the need at any

point to compute or store entire voxel-to-voxel connectivity matrices. In the analysis examples

below we use this approach to efficiently compute fc-MVPA analyses on hundreds of subjects

with minimal computation effort.

Results and discussion

Fc-MVPA brain-wide connectome inferences: interpretation and examples

Group-level analyses of the eigenpattern scores s

n

(x) enable statistical inferences at the level of

individual searchlight voxels evaluating the form or shape of the connectivity patterns with

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each voxel. In particular, for any individual hypothesis (e.g. group A = group B) the fc-MVPA

procedure will produce a statistical parametric map F(x) evaluating that hypothesis separately

at each individual searchlight voxel x. In order to test brain-wide connectome hypotheses it is

still necessary to control the resulting maps F(x) for multiple comparisons across the total

number of tests evaluated (one test per voxel). Fortunately, this can be done using the same

nonparametric cluster-level inferential procedures that are common in standard analyses of

Fig 1. Schematic representation of functional connectivity multivariate pattern analyses (fc-MVPA). For each

voxel, fc-MVPA analyses compute the functional connectivity maps between this seed/source voxel and the entire

brain (Top-left; r

n

(x) in Eq 2) separately for each individual subject. Each subject functional connectivity map is then

characterized by a lower dimensional eigenpattern scores (dots in top-right graph; s

n

(x) in Eq 5). This representation is

chosen in a way that captures as well as possible the observed voxel-specific variability in functional connectivity maps

across subjects. A multivariate test is then performed on the resulting lower-dimensional eigenpattern scores to

ascertain potential between- or within- subjects effects of interest (e.g. differences between subjects or between

conditions in functional connectivity at the original seed/source voxel). This process is then repeated for every source

voxel to identify regions that show brain-wide between- or within- subjects differences in functional connectivity.

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functional activation, such as cluster-mass or TFCE statistics based on permutation / randomi-

zation analyses [5,6,53]. These approaches allow us to compute statistics as well as associated

familywise error corrected p-values for individual clusters of contiguous searchlight voxels in

the statistical parametric map F(x), supporting cluster-level inferences with meaningful false

positive control (e.g. controlling the likelihood of observing or more false positive clusters

across the entire brain below 5%, for a familywise control procedure, or controlling the rate of

false positive clusters below 5% among all significant clusters, for a False Discovery Rate con-

trol procedure).

Another important choice that remains when using fc-MVPA in the context of brain-wide

connectome inferences is to select k, the dimensionality of s

n

(x) or the number of eigenpattern

scores used to represent functional connectivity at each voxel. As it will be discussed in more

detail in the Simulations section below, there is no “correct” choice of this parameter, and fc-

MVPA inferences remain valid for all possible values of this parameter. Nevertheless it is

important that this choice is made a priori and justified (e.g. from prior literature), and, if dif-

ferent values are tested/evaluated, the results of all these different evaluations should be

reported (rather than reporting only the value that produces the best results for a particular

analysis, which would inflate the chance of false positives). Regarding the sensitivity of fc-

MVPA inferences, choosing a low value of kcan be expected to improve sensitivity to detect

relatively large or widespread effects of interest such as inter-network connectivity differences,

while choosing a higher value of kcan improve our ability to detect relatively smaller or mar-

ginal effects such as connectivity with smaller areas or subnetworks. In the absence of assump-

tions about the extent of the expected effects, a reasonable balance is to scale the choice of k

with the dataset size (e.g. suggested 5:1, 10:1, or 20:1 ratio between N:k, the number of subjects

in the analysis and the number of eigenpattern scores retained [54–56]), in order to maintain a

reasonable sensitivity to identify large effects in small samples, and comparatively finer details

in the analysis of larger samples. As with any other preprocessing or analysis choices, as long

as the choice of kis made a priori, statistical inferences will remain valid. If, on the other hand,

the value of kis selected a posteriori as the one that produced the “best” results among several

possible values evaluated, an appropriate multiple-comparison correction should be used for

statistical inferences (e.g. using a Bonferroni corrected cluster-level threshold p-FWE<0.05/10

if the results were selected among 10 different choices of kvalues, or using split or cross-valida-

tion procedures such as choosing kas the value that produces the “best” results in one half of

the subjects and then basing statistical inferences on the analysis of the other half using the

selected kvalue). For new analyses, and in the absence of any other rationale (e.g. based on

prior literature, N:k ratios, or expected extent of effects) we recommend using a value of

k= 10, as that seems to suffice to cover a large proportion of the intersubject variability in

functional connectivity profiles (e.g. see fc-MVPA eigenpatterns section below). In all cases we

encourage researchers to evaluate and report the robustness of their results to different choices

of this parameter (e.g. as exploratory post-hoc analyses, without a need for additional multiple

comparison corrections), as that will help other researchers build upon those results in future

analyses and the field converge toward useful conventions.

Last, regarding the interpretation of fc-MVPA results, when reporting statistical inferences

from fc-MVPA brain-wide connectome analyses, those inferences should be if possible framed

regarding the patterns of connectivity between each voxel or cluster and the rest of the brain.

For example, when using fc-MVPA to evaluate the difference in connectivity between two

groups of subjects, if the fc-MVPA procedure above produces one supra-threshold cluster

with corrected significance level below p <.05 that should be interpreted as indicating that the

pattern of connectivity between this cluster and the rest of the brain is (significantly) different

between the two groups. The fc-MVPA method does not afford further spatial specificity in

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the resulting statistical inferences, but it is still useful to report measures of effect-size charac-

terizing the patterns of connectivity within each individual significant cluster, as a way to sug-

gest possible interpretations and future analyses.

Effect-sizes in GLM analyses are typically represented by linear combinations of the esti-

mated regressor coefficients B, and, specifically in the context of hypothesis testing, linear

combinations of the form cB, as these measures quantify the extent of the observed departures

from the null hypothesis (cB= 0). The interpretation of effect-sizes in GLM depends naturally

on the choice of hypothesis being evaluated. For example, for a GLM two-sample t-test com-

paring connectivity between two groups, effect-sizes of the form cBwould represent the dif-

ference in connectivity (e.g. average differences in r- values) between the two groups, while for

a GLM regression analysis evaluating the association between some behavioral measure and

connectivity strength, effect-sizes of the form cBwould represent the slope of the regression

line approximating the observed associations. Note that in both cases an effect-size of zero

would represent the null hypothesis (of no differences or no associations, respectively). In the

analysis of the statistical parametric map F(x), for any significant cluster O(group of contigu-

ous suprathreshold voxels with a cluster-level corrected p-value below the chosen family-wise

error threshold), we recommend reporting the effect-sizes hcj~

Bseparately for each mean-

ingful between-subjects contrast c

j

(e.g. individual rows of the contrast matrix C). Effect sizes

can be reported as a vector of eigenpattern weights (h

eig

(O)), or as a whole-brain projected

map (h

map

(O)):

fc-MVPA effect-sizes at location O

heigðOÞ Xx2Ocj~

BðxÞ ð9Þ

hscoresðOÞ X

x2O

cj~

BðxÞ StðxÞ ¼ X

x2O

heigðxÞ StðxÞ

hmapðOÞ X

x2O

cj~

BðxÞ DðxÞ PtðxÞ ¼ X

x2O

hscoresðxÞ RðxÞ

The effect-size measure h

eig

(O) is a vector, with one element per eigenpattern, estimated

separately at each location O. It represents the effect-size of a group-level analysis contrast of

interest cj~

BðxÞevaluated separately for each individual eigenpattern (columns of ~

B). For

example, if the group-level analysis was a two-sample t-test comparing connectivity between

two subject groups, then the k-th element in the h

eig

(O) effect-size vector will evaluate what is

the difference in the k-th eigenpattern scores at location Obetween these two groups.

Similarly, and perhaps more directly interpretable, the effect-size measure h

map

(O) repre-

sents the same contrast but is now evaluated separately at each individual voxel. In the example

above, the value of h

map

(O) at a particular voxel will represent the difference in functional con-

nectivity between Oand this voxel between the two subject groups analyzed. It should be

noted that a very similar whole-brain projected map of effect-sizes h

map

(O) can also be com-

puted from the voxel-level effect-sizes of a post hoc analysis that would evaluate the same

group-level model as in Eq 7 but this time focusing on the seed-based connectivity maps (SBC)

associated with seeds defined from each individual significant cluster O. As in any post-hoc

analysis, p-values derived from these SBC post-hoc analyses will be partially inflated due to

selection bias and should not to be used to make secondary inferences regarding individual

connections within the reported patterns. Despite this limitation, post-hoc SBC analyses on

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the same dataset offer a simple and perfectly valid alternative approach for reporting fc-MVPA

effect sizes within each significant cluster, while, when performed on an independent dataset,

they also offer a natural method to further probe specific aspects of these connectivity patterns.

For those interested, the resulting h

map

(O) effect-sizes following this approach can be shown

to be equal to those derived from Eq 9 in the limit when the number of eigenpatterns retained

equals the total number of subjects in the study, simplifying the variable h

scores

(O) to a constant

vector independent of the location O:

h1

scoresðOÞ ¼ cj ðGtGÞ1Gtð10Þ

Effect-size measures such as those described in Eqs 9and 10 represent post-hoc estimates,

and as such they should always be understood to contain a certain amount of bias. Their appli-

cation is mainly for interpretation purposes and for hypothesis building. In other contexts,

when the accuracy of these estimates may be essential, a cross-validation approach may be

used where, for example, the clusters Omay be computed from an initial General Linear

Model (Eqs 7and 8) that includes only data from a subset of subjects, while the effect-size esti-

mates (Eqs 9and 10) may be computed using a second GLM that includes data from a sepa-

rate/independent subset of subjects.

As an illustration of fc-MVPA brain-wide connectome inferences, we analyzed gender dif-

ferences in resting state functional connectivity using the Cambridge 1000-connectomes data-

set (n = 198, see S2 Appendix for a description of this dataset preprocessing and fc-MVPA

analysis methods [57–66]). The question that these analyses ask is whether there are any differ-

ences across the entire voxel-to-voxel functional connectome between male and female sub-

jects. To answer this question, we performed fc-MVPA analyses focusing on the first 10

eigenpatterns (an approximate 20:1 subjects to eigenpattern ratio), entering the corresponding

eigenpattern scores into a second-level group analysis evaluating a multivariate ANCOVA test

with gender as a between-subjects factor and subject motion (average framewise displacement)

as a control variable. The resulting statistical parametric maps were thresholded using Thresh-

old Free Cluster Enhancement [6] (TFCE, with default H = 1, E = 0.5 values) at a familywise

error corrected 5% false positive level.

The results, shown in Fig 2 show a large number of areas with significant gender-related dif-

ferences in connectivity (p-FWE <.05, shown as yellow and black areas in the center image).

Given the abundance of areas showing significant gender effects, for illustration purposes we

focused our description only on a subset of cortical regions showing some of the strongest

effects (TFCE>200; p-FWE <.001, highlighted in black in Fig 2 center image). For each clus-

ter in this reduced subset, we computed effect-size maps h

map

(O) characterizing the pattern of

gender-related differences in connectivity with each cluster (displayed in Fig 2 as a circular

array of brain displays), with yellow indicating higher connectivity with this cluster in male

compared to female subjects, and blue indicating higher connectivity in female compared to

male subjects.

Some of the strongest effects were visible in the bilateral Occipital Pole visual areas. A left

hemisphere cluster centered at MNI coordinates (-22,-94,+4) mm showed a pattern of

increased connectivity with Default Mode Network (DMN) and increased anticorrelations

with Salience Network (SN) areas in male subjects (see Fig 2 Occipital Pole plot). A similar pat-

tern (not shown) was present in another cluster in right hemisphere Occipital Pole areas

(+28,-82,+2). Similarly, there were significant gender effects in several DMN areas, such as

Medial Prefrontal Cortex (+6,+54,-12) and Precuneus (+18,-72,+32), showing a similar pattern

of stronger connectivity with visual and sensorimotor areas (shown in yellow in Fig 2 Medial

Frontal Cortex and Precuneus plots) in male subjects compared to stronger connectivity

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(weaker anticorrelations) with SN and attention areas in female subjects (shown in blue in

same plots).

In the left hemisphere, Inferior Frontal Gyrus pars triangularis (-54,+22,+14) showed a pat-

tern of stronger connectivity in female subjects with frontoparietal network areas and with

Inferior Temporal Cortex (shown in blue in Fig 2 Inferior Frontal Gyrus plot).

In the right hemisphere, there was a cluster of regions in the Temporal Parietal Occipital

Junction that also showed strong gender-related differences in connectivity. Lateral superior

Postcentral Gyrus (+36,-32,+48) showed a mixed pattern of increased integration with other

Fig 2. Fc-MVPA results evaluating gender-related differences in connectivity. Central figure shows left- and right- hemisphere medial (bottom) and lateral

(top) views of the main fc-MVPA results showing areas with significant gender-related differences in functional connectivity (highlighted in yellow and black,

TFCE statistics p-FWE<0.05). Among all significant results a reduced subset showing some of the strongest effects are highlighted in black, and the effect-sizes

within these areas (pattern of differences in connectivity with each area between male and female subjects) are shown in the additional circular plots (yellow

indicating higher connectivity in male compared to female subjects, and blue indicating higher connectivity in female compared to male subjects).

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Dorsal Attention areas in female subjects, compared to increased connectivity with Central

Sulcus, including somatosensory and motor areas in male subjects. A cluster in superior Angu-

lar Gyrus centered at coordinates (+50,-54,+42) mm showed increased integration with medial

prefrontal and posterior cingulate areas in female subjects, and increased integration with lat-

eral prefrontal and reduced anticorrelations with insular areas in male subjects. Relatedly, a

cluster in the mid Insular Cortex (+38,+10,+2) showed a similar pattern of higher connectivity

with angular Gyrus and other DMN areas in male subjects. Another relatively proximal cluster

in the Anterior Supramarginal Gyrus (+60,-26,+30) also showed increased local associations

with superior postcentral areas in male subjects. Posterior Superior Temporal Gyrus (+48,-26,-

2) showed a pattern of higher connectivity (mixed with reduced anticorrelations) with fronto-

parietal areas in female subjects (shown in blue in Fig 2 Superior Temporal Gyrus plot), com-

pared to a similar pattern of stronger local connectivity in male subjects (shown in yellow in

same plot).

Last, Medial Precentral Gyrus areas (+16,-26,+40) showed relatively higher integration with

SN or ventral attention network in female subjects. In contrast, lateral Precentral Gyrus areas

(+54,-4,+22) showed higher integration with the same networks in male subjects, while in

female subjects this area showed stronger local correlations (shown in blue in Fig 2 Precentral

Gyrus plot).

From a validation and generalization perspective, it is interesting to question whether the

same or similar results would have been observed if, instead of using 10 eigenpattern scores,

based on a conservative suggestion to maintain an approximately 20:1 ratio between subjects

and eigenpatterns, we would have chosen a different number. To that end we repeated the pre-

vious group-level analyses evaluating gender differences in connectivity but now using differ-

ent number of eigenpattern scores, ranging from 1 to 100, and compared the resulting fc-

MVPA statistic parametric maps F(x).

The results (Fig 3 top) show very similar F(x) statistics when varying the number of eigen-

patterns around the k = 10 value selected for our original analyses. In addition, the distribution

of resulting statistics across the entire brain (Fig 3 bottom) shows high sensitivity across the

entire range of evaluated k values, consistent with the sensitivity simulations in the sections

below, and with average sensitivity peaking at k = 50 (approximately a 4:1 ratio in subjects to

eigenpatterns) for detecting gender effects in this dataset. While there were several areas like

superior Postcentral Gyrus where the statistics peaked at relatively low number of eigenpat-

terns, suggesting that the effects in these areas may be best represented by the first few fc-

MVPA eigenpatterns (i.e. they may be better described in terms of common/large sources of

variability across subjects), there were also many areas where the F(x) statistics peaked when

using a large number of eigenpatterns (e.g. 50 or above), suggesting that there may still be

widespread gender differences in functional connectivity beyond those highlighted in our orig-

inal analyses and described in Fig 2 that are better expressed in some of the higher-order fc-

MVPA eigenpatterns (i.e. representing more subtle or less common sources of intersubject

variability).

Fc-MVPA eigenpatterns P(x): interpretation and examples

In addition to enabling brain-wide connectivity inferences, fc-MVPA estimates a model-free

representation of the observed intersubject variability in functional connectivity in terms of

the resulting eigenpatterns P(x), which can be useful on its own. In this context, the eigenpat-

terns, defined as the columns of the voxel-specific matrix P(x), represent a set of mutually

orthogonal spatial patterns, different for each voxel, that best characterize the diversity across

subjects in functional connectivity between this voxel and the rest of the brain. By convention

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they are sorted in descending order based on the proportion of the total intersubject covari-

ance explained by each eigenpattern.

In practice, while it is straightforward to compute and store the eigenpattern scores s

n

(x),

storing the entire set of eigenpatterns P(x) can be particularly demanding as it consists of a set

of orthogonal whole-brain maps for each individual voxel. Luckily it is simple to define P(x)

analytically at any individual voxel xfrom its associated eigenpattern scores as:

PðxÞ / Xnrt

nðxÞ snðxÞ ð11Þ

which can be generalized to define characteristic eigenpatterns over small homogeneous areas

by integrating the corresponding voxel-specific eigenpatterns:

fc-MVPA eigenpatterns at location O

PðOÞ / X

nX

x2O

rt

nðxÞ snðxÞ ð12Þ

This can also be useful in the context of a cross-validation framework where it may be nec-

essary to compute eigenpattern scores s

n

(x) for a new, yet unseen, set of subjects. This can be

done using Eq 12 to first characterize P(x) from the original data, and then Eq 5b to compute

s

n

(x) from the new subjects’ connectivity maps.

In general, reporting and describing the fc-MVPA eigenpatterns in Eq 12 over a small area,

along with the proportion of the total covariance explained by each eigenpattern at this area,

allows to gain a better understanding of the main factors affecting intersubject heterogeneity

in functional connectivity between this area and the rest of the brain.

For example, from the analysis of the same resting state data of 198 subjects in the Cam-

bridge dataset, the map ξ

1

(x) shown in Fig 4 (bottom) describes the proportion of the total

Fig 3. Selecting different number of fc-MVPA eigenpatterns. Difference in fc-MVPA statistic parametric maps evaluating gender

differences in connectivity, when varying k, the number of fc-MVPA eigenpatterns used in the analysis, from k = 1 (left) to k = 100

(right). For reference, the original results shown in Fig 2 used k = 10 (highlighted here inside black box). Top: Statistic parametric maps

with color coding showing voxel-level -log

10

(p) values for four different choices of k (from 5 to 20). The results show consistent statistic

parametric maps across different kvalues. Bottom: Distribution of fc-MVPA statistics across all gray matter voxels with kranging from 1

to 100, compared to null hypothesis distribution (shown in leftmost ‘null’ histogram). The results indicate high sensitivity across the

entire range of evaluated kvalues, with sensitivity peaking at around k = 50 (close to a 4:1 ratio in subjects to eigenpatterns) for detecting

widespread gender effects in this dataset.

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intersubject covariance explained by each voxel’s first eigenpattern. In this sample, ξ

1

(x) values

range between 5% and 42% across different voxels. The values ξ

1

(x) associated with the first

eigenpattern are particularly interesting because they provide a simple measure of the overall

intersubject homogeneity of the connectivity maps at each voxel (with higher values indicating

higher homogeneity), as the first eigenpattern can often be expected to lie in the direction of

the average pattern of connectivity with that voxel (as illustrated in the analyses below). Over-

all, this sample ξ

1

(x) map shows high contrast between gray matter areas and other tissue clas-

ses, with higher values within gray matter areas, particularly those located along cortical gyra,

and relatively lower values for areas located deeper into cortical sulci. Some of the regions that

show the highest homogeneity include Medial Prefrontal, Posterior Cingulate, or Lateral Parie-

tal areas, part of the Default Mode Network (DMN), as well as anterior Insula and other

Salience Network (SN) areas. In contrast, cerebellar, subcortical, and Limbic Network areas

are some of the regions that show the most heterogeneous functional connectivity profiles

across subjects (lowest ξ

1

(x) values).

Looking at the contribution of additional eigenpatterns beyond the first one, Fig 4 (top)

shows histograms of the values ξ

k

(x), the percentage of the total intersubject covariance

Fig 4. Percentage of total covariance associated with each fc-MVPA eigenpattern. Top: histogram of ξ

k

(x)|1i100 values, percentage of

the total covariance explained by each of the first 100 eigenpatterns. Histograms are further broken down by the most likely tissue class (gray

matter in black, CSF areas in grey, and white matter in white) at each individual voxel as defined by SPM’s tissue probability map templates.

Bottom: spatial map ξ

1

(x) showing the proportion of the total intersubject covariance explained by each voxel’s first eigenpattern (a measure

of the overall intersubject homogeneity in functional connectivity patterns at each voxel; seetext for details).

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explained by each of the first 100 eigenpatterns. The distribution shows a strongly anisotropic

covariance (for reference, the dashed line simulates the expected percent covariance values

associated with each eigenpattern if the intersubject covariance was isotropic, with equal

covariance along all subject dimensions and approximate 100-voxel spatial resels). In general,

approximately 20 eigenpatterns are associated with higher-than-average covariance values.

The first 5 eigenpatterns combined explain a range between 18% and 51%, 10 eigenpatterns

between 28% and 57%, and 20 eigenpatterns between 39% and 64%, of the total intersubject

covariance (from a maximum of 197 eigenpatterns that could be theoretically computed from

this sample).

While ξ

k

(x) maps allow us to explore how the degree of anisotropy varies across different

areas, it is often also of interest to display the actual eigenpatterns P(x) at some particular rep-

resentative locations, in order to better understand the shape of that intersubject covariance.

Fig 5 shows the first 5 eigenpatterns at 14 example locations. These 14 locations were manually

chosen to illustrate some of the similarities and differences across different locations in inter-

subject variations of functional connectivity patterns. They were selected among the set of all

local maxima of the cumulative P5

k¼1xkðxÞmaps (shown in Fig 5 center image for reference)

trying to cover most of the larger clusters observed there. As this figure illustrates, the first

eigenpattern across different locations (shown in the leftmost portion of each individual-

region display in Fig 5) often reflects a pattern mimicking the average connectivity between

each location and the rest of the brain. For example, the first eigenpattern at the Posterior Cin-

gulate gyrus, a region part of the Default Mode Network (DMN), reflects an arrangement very

similar to the expected pattern of positive and negative associations with the DMN, and the

same arrangement appears in the first eigenpattern at other distant but related locations, such

as Frontal Medial Cortex. Similarly, the first eigenpattern at Anterior Insula or Anterior Cin-

gulate also shows similar profiles mimicking Salience or Ventral Attention Network connectiv-

ity. In contrast, second- and higher- order eigenpatterns, even from regions that are part of the

same network, show noticeable differences in their profiles, possibly indicating nonoverlap-

ping sources of intersubject variability beyond simple within-network connectivity variations.

Other regions, in contrast, show eigenpatterns that reflect perhaps competing contributions.

For example, in Paracingulate Gyrus the first eigenpattern reflects sources of variability in con-

nectivity with nearby DMN areas while the second eigenpattern possibly reflects variability in

connectivity with Anterior Cingulate and Medial Prefrontal regions.

From a validation perspective, it is interesting to note that the covariance explained by the

first few fc-MVPA eigenpatterns and represented by the ξ

k

(x) values is always, by nature of the

fc-MVPA SVD procedure, larger than what could be achieved by any other alternatively-

defined eigenpatterns. In particular, it is larger than the spatial patterns that would result from

a standard ICA or PCA decomposition of the same functional data. In order to highlight this,

we computed on this dataset a Principal Component Analysis in CONN using the same conca-

tenative approach and dimensionality reduction steps as in Calhoun et al. [13] to produce a set

of representative components sorted by decreasing explanatory power (shown in Fig 6 bot-

tom). We then computed, for each of these components, the covariance in functional connec-

tivity with each individual voxel along those dimensions, and plotted histograms of the

resulting cumulative variance as a function of the number of components retained (Fig 6 top).

As expected, the covariance explained cumulatively by the first kfc-MVPA eigenpatterns at

each individual voxel (shown in gray in Fig 6 top) is always equal to or larger than the covari-

ance explained cumulatively by the same number of PCA components (shown in black in the

same plots). While this is a necessary consequence of the SVD properties as used in the context

of fc-MVPA, it is important to note that in particular this implies that if we would like to

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characterize the functional connectivity pattern at each voxel using a reduced fixed number of

scores, then the representation produced by the fc-MVPA eigenpattern scores would always be

more efficient (it would better approximate the functional connectivity data) than an equally-

sized multivariate representation produced by characterizing each voxel connectivity in terms

of network-level properties (at least for the general class of linear transformations projecting

each connectivity pattern onto multiple networks, including those resulting from Principal

Fig 5. First 5 fc-MVPA eigenpatterns, characterizing the principal components of the localintersubject heterogeneity in functional connectivity maps. The

central display shows the cumulative total covariance in functional connectivity patterns explained by the first 5 eigenpatterns at each voxel (colormap values range

between 22%/black to 50%/white). The first five eigenpatterns at 14 manually-defined example locations are shown in a circular display. In each of these plots,

eigenpatterns range from first/left to fifth/right, and each eigenpattern is shown projected to a left hemisphere lateral (top plot) and medial (bottom plot) views, on a

relative color scale ranging from blue (highest negative values for each eigenpattern) to yellow (highest positive values).

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Fig 6. Comparison between PCA and MVPA components. Top: Median (dots) and 25%-75% percentile range (vertical lines) of the total

covariance in functional connectivity patterns at each voxel explained cumulatively by the first kcomponents from a functional connectivity

Principal Component Analysis (black dots and lines), and by the first kfc-MVPA eigenpatterns (light gray dots and lines), from the analysis

of the same sample dataset (Cambridge, n = 198 dataset). Bottom: First five principal components from PCA (first row) and from fc-MVPA

(second and third row, first five eigenvariates shown only at two sample locations: posterior cingulate and anterior insula). Each row shows

individual components sorted from first/left to fifth/right, projected to a left hemisphere lateral view (top image) and medial view (bottom

image), on a relative color scale ranging from blue (highest negative values for each component) to yellow (highest positive values). Larger

explanatory power of fc-MVPA components compared to PCA (shown on top figure) stems largely from the ability of fc-MVPA

components to adapt to the specificity of the functional connectivity patterns at each individual location (as exemplified in the bottom

figures by the differences and commonalities between the components describing posterior cingulate vs. anterior insula connectivity

patterns).

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Component or Independent Component Analyses of the same data). This, naturally, also sup-

ports the use of fc-MVPA eigenpattern scores in the context of brain-wide connectome infer-

ences as a rich low-dimensional representation of the functional connectivity patterns for each

subject.

Simulations: validity and sensitivity of fc-MVPA statistics

In order to evaluate the validity and sensitivity of the general fc-MVPA inferential approach,

we constructed a set of simplified simulations. All of the simulations consider a dataset with 50

subjects. Each subject’s BOLD data encompass 50 timepoints and 1,000 voxels. For each voxel,

the simulated BOLD timeseries contained a mixture of noise (independent samples from a

Gaussian distribution for each timepoint, computed separately for each voxel and subject, and

spatially convolved with a Gaussian filter with FWHM 10 voxels) and signal (independent

samples from a Gaussian distribution for each timepoint, computed separately for each subject

and shared across all voxels where the signal was present). The signal was only present in one

half of the subjects and, among those subjects, only within 10% of all contiguous voxels. For

each individual simulation Eq 5 was used to estimate the projection matrix P(x) at each indi-

vidual voxel, and Eqs 7&8were used to evaluate between-group differences in the patterns of

connectivity between this voxel and all other voxels, using a 50-by-2 design matrix Gcharac-

terizing the two groups of subjects and a between-subjects contrast vector C= [–1 1] evaluat-

ing the difference in functional connectivity between the two groups.

For each individual simulation, we computed the statistical parameter map F(x) and the

associated map of raw/uncorrected voxel-level p-values evaluating the null hypothesis sepa-

rately for two different voxels: one where the signal was present (so the connectivity between

that voxel and all of the other voxels is expected to differ between the two subject groups), and

one where the signal was not present (so the connectivity between that voxel and all other vox-

els is not expected to differ between the two subject groups). We run 10,000 simulations, and

from their results, we computed summary Receiver Operating Characteristic (ROC) curves

describing the true positive rate (probability of a voxel showing a significant between-group

difference in connectivity) as a function of different prescribed false positive rates (p-value

threshold used to determine significance), for each of these two representative voxels. The

results from the first voxel, where the signal was present, were used to obtain estimates of the

sensitivity of voxel-level fc-MVPA connectome inferences (sensitivity analyses), and the results

from the second voxel, where the signal was not present, were used to obtain estimates of the

validity of this inferential procedure (validity analyses).

Each of the above sets of 10,000 simulations was repeated 50 times, each time using a differ-

ent number of eigenpatterns retained (ranging between 1 and 50) in Eq 5. In addition, all of

the above simulations were repeated under six different scenarios in order to further evaluate

the robustness of the obtained sensitivity and validity estimates in the presence of: a) varying

levels of spatial cross-correlation of BOLD noise (FWHM set to 1, and 25 voxels); b) varying

numbers of timepoints in BOLD scanning sessions (10, and 100 samples); and c) varying num-

bers of subjects in the study (10, and 100 subjects).

The results of the validity analyses are shown in Fig 7. The reported voxel-level p-values

(shown in the x-axis labeled as false positive rate) from fc-MVPA inferences matched very pre-

cisely the empirically observed false positive rates (shown in z-axis labeled as positive rate),

with all tested conditions showing accurate diagonal ROC curves. Differences between

reported voxel-level p- values and observed false positive rates were below ±0.22% in 50% of

all simulations, and below ±0.98% in 99% of all simulations. When controlling voxel-level

false positives at a 5% level, and across a total of 386 sets of different conditions evaluated, the

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empirical false positive rate observed across the 10,000 fc-MVPA analyses within each set ran-

ged between 4.5% and 5.4% (Fig 7 top right). Statistics remained valid across the entire range

of eigenpatterns tested up to the point where the number of eigenpatterns (ain Eq 8) equals

the error degrees of freedom (bin Eq 8, equal to the number of subjects minus the number of

Fig 7. Validation of fc-MVPA voxel-level inferences. Analysis of Receiver Operating Characteristic curves evaluating between-group

differences in functional connectivity under the null hypothesis (when there are no true differences in the population). Top left: surfaces,

and highlighted thick black lines, show, for a chosen combination of false positive threshold (false positive rate x-axis) and number of

eigenpatterns (ky-axis), the resulting proportion of false positive results (positive rate z-axis), where the fc-MVPA procedure would falsely

conclude there is a significant difference in connectivity between the groups. The red line marks the observed rate of false positives when

fixing the prescribed false positive rate threshold at a fixed 5% level (graphically, the intersection of each ROC surface and a vertical plane

with constant false positive rate = 0.05), matching the expected 5% level. Top Right: Observed false positive rates (y-axis) when using fc-

MVPA statistical analyses controlled at a p <.05 level across the reference simulations (‘reference’) and simulations evaluating different

conditions (FWHM = 0, FHWM-25, N = 10, N = 100, Nt = 10, Nt = 100). The average (black dots) and histogram (gray surfaces) of the

observed false positive rates across these simulations all indicate an appropriate match to the expected/prescribed false positive level (5%).

Bottom: evaluating validity under different conditions: (A) low spatial autocorrelation (FWHM = 0); (B) large spatial autocorrelation

(FWHM = 25 voxels); (C) low number of subjects (N = 10); (D) high number of subjects (N = 100); (E) short scanning session (Nt = 10);

(F) long scanning session (Nt = 100).

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model regressors, or 48 in our simulations) where the data covariance becomes rank deficient

and the likelihood ratio test assumptions no longer hold.

The results of the sensitivity analyses are shown in Fig 8. Generally, sensitivity was large

across the entire range of eigenpatterns tested, only decreasing markedly as the number of

Fig 8. Sensitivity of fc-MVPA voxel-level inferences. Analysis of Receiver Operating Characteristic curves evaluating between-group

differences in functional connectivity. Top Left: surfaces, and highlighted thick black lines, show, for a chosen combination of false positive

threshold (false positive rate x-axis) and number of eigenpatterns (ky-axis), the resulting proportion of true positive results (positive rate z-

axis), where the fc-MVPA procedure would correctly conclude there is a significant difference in connectivity between the groups in our

reference simulations. Top Right: Observed true positive rates (y-axis) when using fc-MVPA statistical analyses controlled at a p <.05 level

across the reference simulations (‘reference’) and simulations evaluating different conditions (FWHM = 0, FHWM = 25, N = 10, N = 100,

Nt = 10, Nt = 100). The average (black dots) and histogram (gray surfaces) of the observed true positive rates, or proportion of significant

results, across these simulations indicate that sensitivity is typically higher when using low or intermediate numbers of eigenpatterns, with

poorer sensitivity when the number of timepoints for functional connectivity estimation is low (Nt = 10), or when the number of subjects

included in the analysis is low (N = 10). Bottom: evaluating sensitivity under different conditions: (A) no spatial autocorrelation

(FWHM = 0); (B) large spatial autocorrelation (FWHM = 25 voxels); (C) low number of subjects (N = 10); (D) high number of subjects

(N = 100); (E) short scanning session (Nt = 10); (F) long scanning session (Nt = 100).

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eigenpatterns approached their maximum possible value. For example, sensitivity at a p <.05

level was above 80% in the main simulations (with 50 subjects) as long as the number of eigen-

patterns was kept below 42, below 92 in the simulations with 100 subjects, and below 4 in the

simulations with 10 subjects. While optimal sensitivity will naturally vary on multiple factors,

including the size and nature of the effects that we are trying to evaluate, several trends in sen-

sitivity were apparent from different scenarios evaluated. In particular, the degree of spatial

autocorrelation in the functional data (simulations A-B in Fig 8) appeared to have a relatively

small effect on sensitivity, while the number of subjects in the study (simulations C-D) and the

duration of the scanning session (simulations E-F) both had a larger impact. For example,

when fixing the number of eigenvariates to 5, sensitivity to detect a group effect was above

99% at a p <.05 level in the simulations with 50 or 100 subjects, but sensitivity dropped to

56% when the number of subjects was only 10. Similarly, sensitivity at a p <.05 level was

above 99% when the number of simulated timepoints (or equivalently, the number of effective

degrees of freedom of the BOLD timeseries in a study after the denoising and bandpass filter-

ing procedure) was above 50, but it dropped to 92% when the number of simulated timepoints

was only 10.

Conclusions

This manuscript presented the theory and motivation behind functional connectivity Multi-

variate Pattern Analyses (fc-MVPA), both in the context of brain-wide connectome inferences,

as well as a model-free characterization of the heterogeneity in functional connectivity across

subjects. Fc-MVPA extends or complements other MVPA approaches commonly used in neu-

roimaging in three different ways: first, to characterize a subject’s mental state, instead of the

patterns of activation surrounding each voxel considered by many MVPA applications, fc-

MVPA considers the patterns of connectivity between each voxel and the rest of the brain; sec-

ond, instead of a backward model focusing on decoding known properties of a subject or of

the experimental paradigm, fc-MVPA uses a forward model focusing on testing a researcher’s

hypothesis about the subject’s connectivity state across the entire connectome (brain-wide

connectome inferences); and third, in addition to the above inferential framework, fc-MVPA

also provides a model-free characterization of the sources of intersubject heterogeneity in con-

nectivity patterns.

Monte Carlo simulations showed that fc-MVPA inferences remain valid for the entire

range of evaluated scenarios, including using any arbitrary number of eigenpattern scores, dif-

ferent sample sizes, and scanning session durations. Simulations and example analyses of gen-

der-related differences in functional connectivity illustrated the high sensitivity of fc-MVPA

inferential statistics to detect meaningful effects across the entire human connectome. In addi-

tion, an example analysis of fc-MVPA eigenpatterns in functional connectivity during resting

state showed rich and varied sources of intersubject heterogeneity in functional connectivity.

One of the main practical advantages of fc-MVPA in the context of brain-wide connectome

inferences, is that it combines the benefits of pattern analysis techniques, such as the increased

interpretability and reduced noise of lower-dimensional projections, with the benefits of a clas-

sical statistical framework, such as the ability to use popular approaches to group-level analyses

(e.g. GLM’s ANOVA and regression framework), novel multiple comparison techniques (e.g.

TFCE), and well understood statistical control procedures (e.g. ANCOVA in this manuscript

example analyses). Similarly, fc-MVPA eigenpattern representations offer a natural way to

extend common multidimensional reduction approaches in neuroimaging, such as ICA or

PCA, to begin considering the specificity of these lower-dimensional representations across

different brain areas. From its theoretical and practical advantages, we believe that fc-MVPA

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can be a powerful and hopefully useful tool for researchers to further explore the complexities

of the human connectome.

Supporting information

S1 Appendix. Efficient computation of multivariate patterns.

(DOCX)

S2 Appendix. Preprocessing and analysis of resting state functional data.

(DOCX)

S1 Table. Glossary of terms in manuscript equations.

(DOCX)

Author Contributions

Conceptualization: Alfonso Nieto-Castanon.

Formal analysis: Alfonso Nieto-Castanon.

Methodology: Alfonso Nieto-Castanon.

References

1. Benjamini Y, Hochberg Y. Controlling the false discovery rate: a practical and powerful approach to mul-

tiple testing. Journal of the Royal statistical society: series B (Methodological). 1995; 57(1):289–300.

2. Chumbley J, Worsley K, Flandin G, Friston K. Topological FDR for neuroimaging. Neuroimage. 2010;

49(4):3057–64. https://doi.org/10.1016/j.neuroimage.2009.10.090 PMID: 19944173

3. Marek S, Tervo-Clemmens B, Calabro FJ, Montez DF, Kay BP, Hatoum AS, et al. Reproducible brain-

wide association studies require thousands of individuals. Nature. 2022; 603(7902):654–660. https://

doi.org/10.1038/s41586-022-04492-9 PMID: 35296861

4. Worsley KJ, Marrett S, Neelin P, Vandal AC, Friston KJ, Evans AC. A unified statistical approach for

determining significant signals in images of cerebral activation. Human brain mapping. 1996; 4(1):58–

73. https://doi.org/10.1002/(SICI)1097-0193(1996)4:1<58::AID-HBM4>3.0.CO;2-O PMID: 20408186

5. Bullmore ET, Suckling J, Overmeyer S, Rabe-Hesketh S, Taylor E, Brammer MJ. Global, voxel, and

cluster tests, by theory and permutation, for a difference between two groups of structural MR images of

the brain. IEEE transactions on medical imaging. 1999; 18(1):32–42. https://doi.org/10.1109/42.750253

PMID: 10193695

6. Smith SM, Nichols TE. Threshold-free cluster enhancement: addressing problems of smoothing,

threshold dependence and localisation in cluster inference. Neuroimage. 2009; 44(1):83–98. https://doi.

org/10.1016/j.neuroimage.2008.03.061 PMID: 18501637

7. Jafri MJ, Pearlson GD, Stevens M, Calhoun VD. A method for functional network connectivity among

spatially independent resting-state components in schizophrenia. Neuroimage. 2008; 39(4):1666–81.

https://doi.org/10.1016/j.neuroimage.2007.11.001 PMID: 18082428

8. Zalesky A, Fornito A, Bullmore ET. Network-based statistic: identifying differences in brain networks.

Neuroimage. 2010; 53(4):1197–207. https://doi.org/10.1016/j.neuroimage.2010.06.041 PMID:

20600983

9. Zalesky A, Fornito A, Bullmore ET. On the use of correlation as a measure of network connectivity. Neu-

roimage. 2012; 60(4):2096–106. https://doi.org/10.1016/j.neuroimage.2012.02.001 PMID: 22343126

10. Noble S, Mejia AF, Zalesky A, Scheinost D. Improving power in functional magnetic resonance imaging

by moving beyond cluster-level inference. Proceedings of the National Academy of Sciences. 2022;

119(32):e2203020119. https://doi.org/10.1073/pnas.2203020119 PMID: 35925887

11. Gorbach NS, Schu¨tte C, Melzer C, Goldau M, Sujazow O, Jitsev J, et al. Hierarchical information-based

clustering for connectivity-based cortex parcellation. Frontiers in neuroinformatics. 2011; 5:18. https://

doi.org/10.3389/fninf.2011.00018 PMID: 21977015

12. Nieto-Castaño

´n A, Fedorenko E, Subject-specific functional localizers increase sensitivity and func-

tional resolution of multi-subject analyses. Neuroimage. 2012; 63(3):1646–69. https://doi.org/10.1016/j.

neuroimage.2012.06.065 PMID: 22784644

PLOS COMPUTATIONAL BIOLOGY

Brain-wide connectome inferences using fc-MVPA

PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1010634 November 15, 2022 25 / 28

13. Calhoun VD, Adali T, Pearlson GD, Pekar JJ. A method for making group inferences from functional

MRI data using independent component analysis. Human brain mapping. 2001; 14(3):140–151. https://

doi.org/10.1002/hbm.1048 PMID: 11559959

14. Kriegeskorte N, Goebel R, Bandettini P. Information-based functional brain mapping. Proc. Natl. Acad.

Sci. 2006; 103(10):3863–8. https://doi.org/10.1073/pnas.0600244103 PMID: 16537458

15. Norman KA, Polyn SM, Detre GJ, Haxby JV. Beyond mind-reading: multi-voxel pattern analysis of fMRI

data. Trends in cognitive sciences. 2006; 10(9):424–430. https://doi.org/10.1016/j.tics.2006.07.005

PMID: 16899397

16. Pereira F, Mitchell T, Botvinick M. Machine learning classifiers and fMRI: a tutorial overview.Neuro-

image. 2009; 45(1):S199–S209. https://doi.org/10.1016/j.neuroimage.2008.11.007 PMID: 19070668

17. Haufe S, Meinecke F, Go

¨rgen K, Da

¨hne S, Haynes JD, Blankertz B, et al. On the interpretation of weight

vectors of linear models in multivariate neuroimaging. Neuroimage. 2014; 87:96–110. https://doi.org/

10.1016/j.neuroimage.2013.10.067 PMID: 24239590

18. Whitfield-Gabrieli S, Nieto-Castanon A. Conn: a functional connectivity toolbox for correlated and antic-

orrelated brain networks. Brain connectivity. 2012; 2(3):125–41. https://doi.org/10.1089/brain.2012.

0073 PMID: 22642651

19. Nieto-Castanon A. CONN functional connectivity toolbox (RRID:SCR_009550), Version 21. Hilbert

Press; 2021. https://doi.org/10.56441/hilbertpress.2161.7292

20. Beaty RE, Benedek M, Barry Kaufman S, Silvia PJ. Default and executive network coupling supports

creative idea production. Scientific reports. 2015; 5(1):1–14.

21. Flodin P, Martinsen S, Altawil R, Waldheim E, Lampa J, Kosek E, et al. Intrinsic brain connectivity in

chronic pain: a resting-state fMRI study in patients with rheumatoid arthritis. Frontiers in human neuro-

science. 2016; 10:107. https://doi.org/10.3389/fnhum.2016.00107 PMID: 27014038

22. Thompson WH, Thelin EP, Lilja A, Bellander BM, Fransson P. Functional resting-state fMRI connectiv-

ity correlates with serum levels of the S100B protein in the acute phase of traumatic brain injury. Neuro-

Image: Clinical. 2016; 12:1004–12. https://doi.org/10.1016/j.nicl.2016.05.005 PMID: 27995066

23. Amad A, Seidman J, Draper SB, Bruchhage MM, Lowry RG, Wheeler J, et al. Motorlearning induces

plasticity in the resting brain—drumming up a connection. Cerebral Cortex. 2017; 27(3):2010–21.

https://doi.org/10.1093/cercor/bhw048 PMID: 26941381

24. Beaty RE, Silvia PJ, Benedek M. Brain networks underlying novel metaphor production. Brain and cog-

nition. 2017; 111: 163–70. https://doi.org/10.1016/j.bandc.2016.12.004 PMID: 28038366

25. Mo¨ller A, Nemmi F, Karlsson K, Klingberg T. Transcranial electric stimulation can impair gains during

working memory training and affects the resting state connectivity. Frontiers in human neuroscience.

2017; 11:364. https://doi.org/10.3389/fnhum.2017.00364 PMID: 28747878

26. Yankouskaya A, Stolte M, Moradi Z, Rotshtein P, Humphreys G. Integration of identity and emotion

information in faces: fMRI evidence. Brain and Cognition. 2017; 116:29–39. https://doi.org/10.1016/j.

bandc.2017.05.004 PMID: 28599147

27. Arnold Anteraper S, Guell X, D’Mello A, Joshi N, Whitfield-Gabrieli S, Joshi G. Disrupted cerebrocere-

bellar intrinsic functional connectivity in young adults with high-functioning autism spectrum disorder: a

data-driven, whole-brain, high-temporal resolution functional magnetic resonance imaging study. Brain

connectivity. 2019; 9(1):48–59. https://doi.org/10.1089/brain.2018.0581 PMID: 29896995

28. Argyropoulos GP, Loane C, Roca-Fernandez A, Lage-Martinez C, Gurau O, Irani SR. Network-wide

abnormalities explain memory variability in hippocampal amnesia. Elife. 2019;8. https://doi.org/10.

7554/eLife.46156 PMID: 31282861

29. Multani N, Taghdiri F, Anor CJ, Varriano B, Misquitta K, Tang-Wai DF, et al. Association between social

cognition changes and resting state functional connectivity in frontotemporal dementia, Alzheimer’s dis-

ease, Parkinson’s disease, and healthy controls. Frontiers in neuroscience. 2019; 13:1259. https://doi.

org/10.3389/fnins.2019.01259 PMID: 31824254

30. Schneider MA, Spritzer PM, Minuzzi L, Frey BN, Syan SK, Fighera TM. Effects of estradiol therapy on

resting-state functional connectivity of transgender women after gender-affirming related gonadectomy.

Frontiers in neuroscience. 2019; 13:817. https://doi.org/10.3389/fnins.2019.00817 PMID: 31440128

31. Tortora D, Severino M, Di Biase C, Malova M, Parodi A, Minghetti D, et al. Early pain exposure influ-

ences functional brain connectivity in very preterm neonates. Frontiers in neuroscience. 2019; 13:899.

https://doi.org/10.3389/fnins.2019.00899 PMID: 31507370

32. Argyropoulos GP, Moore L, Loane C, Roca-Fernandez A, Lage-Martinez C, Gurau O, et al. Pathologic

tearfulness after limbic encephalitis: A novel disorder and its neural basis. Neurology. 2020; 94

(12):1320–35. https://doi.org/10.1212/WNL.0000000000008934 PMID: 31980582

33. Guell X, Arnold Anteraper S, Gardner AJ, Whitfield-Gabrieli S, Kay-Lambkin F, Iverson GL, et al. Func-

tional connectivity changes in retired rugby league players: a data-driven functional magnetic resonance

PLOS COMPUTATIONAL BIOLOGY

Brain-wide connectome inferences using fc-MVPA

PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1010634 November 15, 2022 26 / 28

imaging study. Journal of neurotrauma. 2020; 37(16):1788–96. https://doi.org/10.1089/neu.2019.6782

PMID: 32183583

34. Guell Paradis X, Anteraper SRA, Ghosh SS, Gabrieli JD, Schmahmann JD. Neurodevelopmental and

Psychiatric Symptoms in Patients with a Cyst Compressing the Cerebellum: an Ongoing Enigma. The

Cerebellum. 2020; 19(1):16–29 https://doi.org/10.1007/s12311-019-01050-4 PMID: 31321675

35. Kelly E, Meng F, Fujita H, Morgado F, Kazemi Y, Rice LC, et al. Regulation of autism-relevant behaviors

by cerebellar–prefrontal cortical circuits. Nature neuroscience. 2020; 23(9):1102–10. https://doi.org/10.

1038/s41593-020-0665-z PMID: 32661395

36. Westfall DR, Anteraper SA, Chaddock-Heyman L, Drollette ES, Raine LB, Whitfield-Gabrieli S, et al.

Resting-State functional connectivity and scholastic performance in preadolescent children: A data-

driven multivoxel pattern analysis (MVPA). Journal of Clinical Medicine. 2020; 9(10):3198.

37. Katsumi Y, Kondo N, Dolcos S, Dolcos F, Tsukiura T, Intrinsic functional network contributions to the

relationship between trait empathy and subjective happiness. NeuroImage. 2021; 227:117650. https://

doi.org/10.1016/j.neuroimage.2020.117650 PMID: 33338612

38. Mateu-Estivill R, Forne

´S, Lo

´pez-Sala A, Falco

´n C, Caldu

´X, Sopena JM, et al. Functional connectivity

alterations associated with literacy difficulties in early readers. Brain Imaging and Behavior. 2021; 15

(4):2109–20. https://doi.org/10.1007/s11682-020-00406-3 PMID: 33048291

39. Morris TP, Chaddock-Heyman L, Ai M, Anteraper SA, Nieto-Castanon A, Whitfield-Gabrieli S, et al.

Enriching activities during childhood are associated with variations in functional connectivity patterns

later in life. Neurobiology of Aging. 2021; 104:92–101. https://doi.org/10.1016/j.neurobiolaging.2021.04.

002 PMID: 33984626

40. Shaw SB, McKinnon MC, Heisz J, Becker S. Dynamic task-linked switching between brain networks–A

tri-network perspective. Brain and cognition. 2021; 151:105725. https://doi.org/10.1016/j.bandc.2021.

105725 PMID: 33932747

41. Cahart MS, Amad A, Draper SB, Lowry RG, Marino L, Carey C, et al. The effect of learning to drum on

behavior and brain function in autistic adolescents. Proceedings of the National Academy of Sciences.

2022; 119(23):e2106244119. https://doi.org/10.1073/pnas.2106244119 PMID: 35639696

42. Eckstein KN, Wildgruber D, Ethofer T, Bru¨ck C, Jacob H, Erb M, Correlates of individual voice and face

preferential responses during resting state. Scientific reports. 2022; 12(1):1–13.

43. Fitzgerald JM, Webb EK, Weis CN, Huggins AA, Bennett KP, Miskovich, TA, et al. Hippocampal rest-

ing-state functional connectivity forecasts individual posttraumatic stress disorder symptoms: A data-

driven approach. Biological Psychiatry: Cognitive Neuroscience and Neuroimaging. 2022; 7(2):139–49.

https://doi.org/10.1016/j.bpsc.2021.08.007 PMID: 34478884

44. Smith JL, Trofimova A, Ahluwalia V, Casado Garrido JJ, Hurtado J, Frank R, et al. The “vestibular neu-

romatrix”: A proposed, expanded vestibular network from graph theory in post-concussive vestibular

dysfunction. Human brain mapping. 2022; 43(5):1501–18. https://doi.org/10.1002/hbm.25737 PMID:

34862683

45. Walsh MJ, Pagni B, Monahan L, Delaney S, Smith CJ, Baxter L, et al. Sex-related brain connectivity

correlates of compensation in adults with autism: insights into female protection. Cerebral Cortex. 2022.

https://doi.org/10.1093/cercor/bhac069 PMID: 35212373

46. Penny WD, Friston KJ, Ashburner JT, Kiebel SJ, Nichols TE, editors. Statistical parametric mapping:

the analysis of functional brain images. Elsevier; 2011.

47. Nieto-Castanon A. General Linear Model. In: Handbook of functional connectivity Magnetic Resonance

Imaging methods in CONN. Hilbert Press; 2020. pp 63–82.

48. Satterthwaite FE. An approximate distribution of estimates of variance components. Biometrics bulletin.

1946; 2(6):110–4. PMID: 20287815

49. Nieto-Castanon A, Ghosh SS, Tourville JA, Guenther FH. Region of interest based analysis of func-

tional imaging data. Neuroimage. 2003; 19(4):1303–16. https://doi.org/10.1016/s1053-8119(03)00188-

5PMID: 12948689

50. Worsley KJ, Poline JB, Friston KJ, Evans AC. Characterizing the response of PET and fMRI data using

multivariate linear models. Neuroimage. 1997; 6(4):305–319. https://doi.org/10.1006/nimg.1997.0294

PMID: 9417973

51. Nieto-Castanon A. Functional Connectivity measures. In: Handbook of functional connectivity Magnetic

Resonance Imaging methods in CONN. Hilbert Press; 2020. pp 26–62.

52. Rao CR. An asymptotic expansion of the distribution of Wilk’s criterion. Bulletin of the international sta-

tistical institute. 1951; 33(2):177–80.

53. Winkler AM, Ridgway GR, Webster MA, Smith SM, Nichols TE. Permutation inference for the general

linear model. Neuroimage. 2014; 92:381–397. https://doi.org/10.1016/j.neuroimage.2014.01.060

PMID: 24530839

PLOS COMPUTATIONAL BIOLOGY

Brain-wide connectome inferences using fc-MVPA

PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1010634 November 15, 2022 27 / 28

54. Vittinghoff E, McCulloch CE. Relaxing the rule of ten events per variable in logistic and Cox regression.

American journal of epidemiology. 2007; 165(6):710–718. https://doi.org/10.1093/aje/kwk052 PMID:

17182981

55. Concato J, Peduzzi P, Holford TR, Feinstein AR, Importance of events per independent variable in pro-

portional hazards analysis I. Background, goals, and general strategy. Journal of clinical epidemiology.

1995; 48(12):1495–501.

56. Harrell FE Jr, Lee KL, Mark DB. Multivariable prognostic models: issues in developing models, evaluat-

ing assumptions and adequacy, and measuring and reducing errors. Statistics in medicine. 1996; 15

(4):361–387. https://doi.org/10.1002/(SICI)1097-0258(19960229)15:4<361::AID-SIM168>3.0.CO;2-4

PMID: 8668867

57. Andersson JLR, Hutton C, Ashburner J, Turner R, Friston K. Modelling geometric deformations in EPI

time series. NeuroImage. 2001; 13(5):903–19.

58. Henson RNA, Buechel C, Josephs O, Friston KJ. The slice-timing problem in event-related fMRI. Neu-

roImage. 1999; 9:125

59. Whitfield-Gabrieli S, Nieto-Castanon A, Ghosh SS. Artifact detection tools (ART). Cambridge, MA.

Release Version. 2011; 7(19):11.

60. Power JD, Mitra A, Laumann TO, Snyder AZ, Schlaggar BL, Petersen SE. Methods to detect, charac-

terize, and remove motion artifact in resting state fMRI. Neuroimage. 2014; 84:320–41. https://doi.org/

10.1016/j.neuroimage.2013.08.048 PMID: 23994314

61. Ashburner J, Friston KJ. Unified segmentation. NeuroImage. 2005; 26:839–51. https://doi.org/10.1016/

j.neuroimage.2005.02.018 PMID: 15955494

62. Friston KJ, Williams S, Howard R, Frackowiak RS, Turner R. Movement-related effects in fMRI time-

series. Magnetic resonance in medicine. 1996; 35(3):346–55. https://doi.org/10.1002/mrm.1910350312

PMID: 8699946

63. Behzadi Y, Restom K, Liau J, Liu TT. A component based noise correction method (CompCor) for

BOLD and perfusion based fMRI. Neuroimage. 2007; 37(1):90–101. https://doi.org/10.1016/j.

neuroimage.2007.04.042 PMID: 17560126

64. Chai XJ, Nieto-Castaño

´n A, O

¨ngu¨r D, Whitfield-Gabrieli S. Anticorrelations in resting state networks

without global signal regression. Neuroimage. 2012; 59(2):1420–28. https://doi.org/10.1016/j.

neuroimage.2011.08.048 PMID: 21889994

65. Nieto-Castanon A. FMRI denoising pipeline. In: Handbook of functional connectivity Magnetic Reso-

nance Imaging methods in CONN. Hilbert Press; 2020. pp 17–25.

66. Ciric R, Wolf DH, Power JD, Roalf DR, Baum GL, Ruparel K, et al. Benchmarking of participant-level

confound regression strategies for the control of motion artifact in studies of functional connectivity.

Neuroimage. 2017; 154:174–87. https://doi.org/10.1016/j.neuroimage.2017.03.020 PMID: 28302591

PLOS COMPUTATIONAL BIOLOGY

Brain-wide connectome inferences using fc-MVPA

PLOS Computational Biology | https://doi.org/10.1371/journal.pcbi.1010634 November 15, 2022 28 / 28