# Subtyping brain diseases from imaging data

Junhao Wen  Center for Biomedical Image Computing and Analytics, Perelman
School of Medicine, University of Pennsylvania, Philadelphia, USA  Erdem Varol
Department of Statistics, Center for Theoretical Neuroscience, Zuckerman
Institute, Columbia University, New York, USA  Zhijian Yang  Center for
Biomedical Image Computing and Analytics, Perelman School of Medicine,
University of Pennsylvania, Philadelphia, USA  Gyujoon Hwang  Center for
Biomedical Image Computing and Analytics, Perelman School of Medicine,
University of Pennsylvania, Philadelphia, USA  Dominique Dwyer  Department of
Psychiatry and Psychotherapy, Ludwig-Maximilian University, Munich, Germany
Anahita Fathi Kazerooni  Center for Biomedical Image Computing and Analytics,
Perelman School of Medicine, University of Pennsylvania, Philadelphia, USA
Paris Alexandros Lalousis  Institute for Mental Health and Centre for Human
Brain Health, School of Psychology, University of Birmingham, Birmingham,
United Kingdom  Christos Davatzikos  Corresponding author: Christos
Davatzikos<EMAIL_ADDRESS>Center for Biomedical
Image Computing and Analytics, Perelman School of Medicine, University of
Pennsylvania, Philadelphia, USA

###### Abstract

The imaging community has increasingly adopted machine learning (ML) methods
to provide individualized imaging signatures related to disease diagnosis,
prognosis, and response to treatment. Clinical neuroscience and cancer imaging
have been two areas in which ML has offered particular promise. However, many
neurologic and neuropsychiatric diseases, as well as cancer, are often
heterogeneous in terms of their clinical manifestations, neuroanatomical
patterns or genetic underpinnings. Therefore, in such cases, seeking a single
disease signature might be ineffectual in delivering individualized precision
diagnostics. The current chapter focuses on ML methods, especially semi-
supervised clustering, that seek disease subtypes using imaging data. Work
from Alzheimer’s Disease and its prodromal stages, psychosis, depression,
autism, and brain cancer are discussed. Our goal is to provide the readers
with a broad overview in terms of methodology and clinical applications.

Keywords: Neuroimaging, machine learning, semi-supervised clustering,
heterogeneity

## 1\. Introduction

There is growing clinical evidence that structural and functional brain
development and aging take heterogeneous paths within different subsets of the
human population [51, 55, 78]. This heterogeneity has been relatively ignored
in case-control studies analyses, yielding a limited understanding of the
diversity of underlying biological processes that might give rise to similar
clinical phenotypes. The advent of high throughput neuroimaging technologies
and the concentrated efforts of the collection of large-scale datasets [49,
61] provide a unique opportunity to dissect the structural and functional
heterogeneity of brain disorders in finer details and in an unbiased data-
driven manner. A developing body of work that leverages ML and neuroimaging
seeks disease subtypes of neuropsychiatric and neurodegenerative disorders,
including Alzheimer’s disease (AD) [74, 75, 76, 83, 85, 88], schizophrenia [7,
19], and late-life depression [77].

Subtyping brain diseases is a clustering problem where the goal is to break
down the set of patients into distinct and relatively homogeneous subgroups
(i.e., subtypes). While this has been actively investigated in the computer
science community, subtyping neuroimaging data is endowed with a unique set of
obstacles, such as the “curse of dimensionality” and the confounding nuisance
effects, such as global demographics and scanner differences. Furthermore,
brain development and pathologies often progress along a continuum, e.g., from
healthy state to preclinical stages to full-fledged disease [84], thereby
modeling directly in the patient domain may lead to a biased clustering
solution. Thus to tackle these problems, some recent efforts have focused on
developing semi-supervised [15, 74, 76, 83] and unsupervised clustering
methods [85, 88]. Early studies mainly focused on unsupervised clustering
methods, such as K-means [33] or hierarchical clustering [13], to derive data-
driven subtypes using imaging data. However, such approaches directly
partition the patients based on similarities/dissimilarities, potentially
biased by confounding factors, such as demographics or heterogeneity caused by
unrelated pathological processes. More recently, semi-supervised clustering
methods [15, 74, 76, 83] have been proposed to tackle this problem from a
novel angle. To seek a pathology-oriented clustering solution, semi-supervised
approaches dissect disease heterogeneity by the “1-to-k” mapping between the
reference group (i.e., healthy control (CN)) and the subgroups of the patient
group (i.e., the k subtypes). This approach presumably zooms into the
heterogeneity of pathological processes rather than unwanted heterogeneity in
general. Furthermore, confounding variations, such as demographics, are often
ruled out in these approaches.

Aiming to provide the reader in the imaging and machine learning community
with a broad guideline in terms of methodology and clinical applications, we
organize the remainder of this chapter as follows. In Section 2, we provide a
brief overview of clustering methods, including unsupervised and semi-
supervised approaches. Section 3 discusses their applications in various
neurological and neuropsychiatric disorders and diseases. Section 4 concludes
the paper by discussing our main observations, methodological limitations, and
future directions.

## 2\. Methodological development using machine learning and neuroimaging

Machine learning and neuroimaging have brought unprecedented opportunities to
elucidate disease heterogeneity in various brain disorders and diseases [11].
Several trailblazing methodological papers have been recently published [83,
85, 88], challenging the conventional approach of patient stratification that
puts all patients into the same bucket. Among these, unsupervised [85, 88] and
semi-supervised clustering methods [83] sought to derive biologically data-
driven disease subtypes, but they anchor the modeling from distinct
perspectives. For conciseness, let us note that our imaging dataset contains q
healthy control (CN) samples
$\boldsymbol{X}_{r}=[\boldsymbol{x}_{1},\ldots,\boldsymbol{x}_{q}],\boldsymbol{X}_{r}\in\mathbb{R}^{p\times
q}$, representing our reference group, and n patient samples (PT)
$\boldsymbol{X}_{t}=[\boldsymbol{x}_{1},\ldots,\boldsymbol{x}_{m}],\boldsymbol{X}_{t}\in\mathbb{R}^{p\times
m}$, representing the target subtype population. We denote the whole
population as a matrix $\boldsymbol{X}$ that is organized by arranging each
image as a vector per column
$\boldsymbol{X}=[\boldsymbol{x}_{1},\ldots,\boldsymbol{x}_{q+m}],\boldsymbol{X}\in\mathbb{R}^{p\times(q+m)}$,
where p is the number of features per image. We use binary labels to
distinguish the patient and control groups, where 1 represents PT and -1 means
CN. Disease subtyping sought to find the number of clusters (k) in the patient
group that are neuroanatomically distinct while clinically relevant.

###  2.1 U nsupervised clustering

Many recent efforts to discover the heterogeneous nature of brain diseases
have investigated different unsupervised clustering algorithms [21, 36, 39,
46, 53, 57, 58, 60, 62, 64, 63, 71, 41, 85, 88]. Among these approaches, the
key clustering methods are often K-means, hierarchical clustering, and non-
negative matrix factorization (NMF) (Figure 1). In this subsection, we first
briefly go through these methods. Subsequently, we focus on two representative
models building on these unsupervised methods, i.e., Sustain [85] and latent
Dirichlet allocation [88].

Figure 1: Schematic diagram of representative unsupervised clustering methods,
K-means, NMF, and Hierarchical clustering.

#### 2.1.1. K-means clustering

K-means clustering aims to directly partition the n patients into k clusters.
Each patient belongs to the cluster with the nearest mean (i.e., cluster
centroid) quantified by a distance metric of choice (e.g., Euclidean
distance). Since searching the global minimum in clustering is computationally
difficult (NP-hard), local minima are searched in the K-means algorithm via an
iterative refinement approach. This usually involves two steps after giving an
initial set of k centroids: i) assignment step, assigning each data point to
the cluster with the nearest centroid with the least squared Euclidean
distance; ii) update step, recalculating means (centroids) for all data points
assigned to each cluster. The two steps iteratively continue until the
convergence, i.e., the assignments no longer change. More details regarding
the k-means algorithm are provided in Chapter 2, Section 12.1. Please refer to
[24, 65, 66] for representative studies using K-means for disease subtyping.

#### 2.1.2. NMF clustering

Non-negative matrix factorization (NMF) is a method that implicitly performs
clustering by taking advantage that complex patterns can be construed as a sum
of simple parts. In essence, the input data $\boldsymbol{X}_{t}$ is factorized
into two non-negative matrices $\boldsymbol{C}\in\mathbb{R}^{p\times k}$ and
$\boldsymbol{L}\in\mathbb{R}^{k\times m}$, for which we refer to the component
matrix and loading coefficient matrix, respectively. This method has been
widely used as an effective dimensionality reduction technique in signal
processing and image analysis [42]. By its nature, the $\boldsymbol{L}$ matrix
can be directly used for clustering purposes, which is analogous to K-means if
we impose an orthogonality constraint on the $\boldsymbol{L}$ matrix.
Specifically, if $\boldsymbol{L}_{kj}>\boldsymbol{L}_{ij}$ for all $i\neq k$,
this clusters the data point $x_{n}$ into the k-th cluster. The vectors of the
$\boldsymbol{C}$ matrix indicate the cluster centroids. Please refer to [41]
for a representative study using NMF for disease subtyping.

#### 2.1.3. Hierarchical clustering

Hierarchical clustering aims to build a hierarchy of clusters, including two
types of approach: agglomerative and divisive [13]. In general, the merges and
splits are determined greedily and presented in a dendrogram. Similarly, a
measure of dissimilarity between sets of observations is required. Most
commonly, this is achieved by using an appropriate metric (e.g., Euclidean
distance) and a linkage criterion that specifies the dissimilarity of sets as
a function of the pairwise distances of observations. Please refer to [34, 38,
53, 57, 63] for representative studies using the hierarchical clustering for
disease subtyping.

#### 2.1.4. Representative unsupervised clustering methods

Sustain [85] is an unsupervised clustering method for subtype and stage
inference. Specifically, Sustain formulates the model as groups of subjects
with a particular biomarker progression pattern as a subtype. The biomarker
evolution of each subtype is modeled as a linear z-score model, a continuous
generalization of the original event-based model [86]. Each biomarker follows
a piecewise linear trajectory over a common timeframe. The key advantage of
this model is that it can work with purely cross-sectional data, and derive an
imaging signatures of subtype and stage simultaneously.

A Bayesian latent Dirichlet allocation model [88] was proposed to extract
latent AD-related atrophy factors. This probabilistic approach hypothesizes
that each patient expresses one or more latent factors, and each factor is
associated with distinct but possibly overlapping atrophy patterns. However,
due to the nature of latent Dirichlet allocation methods, the input images
have to be discretized. Moreover, this method exclusively models brain atrophy
while ignoring brain enlargement. For example, larger brain volumes in basal
ganglia have been associated with one subtype of schizophrenia [7].

###  2.2 S emi-supervised clustering

Semi-supervised clustering methods dissect the subtle heterogeneity of
interest under the principle of deriving data-driven and neurobiologically
plausible subtypes (Figure 2). In essence, the “1-to-k” mapping between the
reference CN group and the PT group, thereby teasing out clusters that are
likely driven by distinct pathological trajectories, instead of by global
similarity/dissimilarity in data, which is the core momentum of conventional
unsupervised clustering methods.

Figure 2: Schematic diagram of semi-supervised clustering methods. Figure is
adapted from [77]

In the following subsections, we briefly discuss four semi-supervised
clustering methods. These methods employ different techniques to seek this
“1-to-k” mapping. In particular, CHIMERA [15] and Smile-GAN [83] utilize
generative models to achieve this mapping, while HYDRA [74] and MAGIC [76] are
built on top of discriminative models.

The central principle of semi-supervised clustering methods is to seek the
”1-to-k” mapping from the reference domain to the patient domain. • CHIMERA: a
generative approach that leverages the Coherent Point Drift algorithm and maps
the data distribution of the CN group to the PT group, thereby enabling to
subtype by the distinct k regularized transformations. • Smile-GAN: a
generative approach based on GANs to learn multiple distinct mappings by
generating PT from CN. Simultaneously, a clustering model is trained
interactively with mapping functions to assign PT into the corresponding
subtype memberships. • HYDRA: a discriminative approach which leverages
multiple linear support vector machines to construct a polytope that clusters
the patients depending on the patterns of differences between the CN group and
the PT group. • MAGIC: a generalization of HYDRA that aims to dissect disease
heterogeneity at multiple imaging scales for a scale-consistent solution.

#### 2.2.1. CHIMERA

CHIMERA employs a generative probabilistic approach, considers all samples as
points in the imaging space, and infers the clusters from the transformations
between the CN and PT distributions. It hypothesizes that the PT distribution
can be generated from the CN distribution under k sets of transformations,
each reflecting a distinct disease process.

Mathematically, the transformation $\boldsymbol{T}$ is a convex combination of
the k linear transformations that map a CN subject in the reference space to
the target space:
$\boldsymbol{x}_{i}^{r}\in\mathbb{R}^{q}\rightarrow\boldsymbol{x}_{i}^{t}=\boldsymbol{T}(x_{i})=\sum_{j=1}^{k}\xi_{j}\boldsymbol{T}_{j}(x_{i})$,
where $\xi_{j}$ is the probability that a PT belongs to the j-th subtype.
Ideally, if the disease subtypes were distinct, $\xi_{j}$ should take value 1
for the transformation corresponding to this specific disease subtype and
value 0 otherwise. At its core, the Coherent Point Drift algorithm [52], a
generative probabilistic approach, is used to estimate the transformation
$\boldsymbol{T}$. Specifically, the CN sample point is mapped to the PT domain
and regarded as a centroid of a spherical Gaussian cluster, whereas the
patient points are treated as independent and identically distributed data
generated by a Gaussian Mixture Model (GMM) with equal weights for each
cluster. The goal is to maximize the data likelihood during the distribution
matching while also taking into account covariate confounds (e.g., age and
gender). The Expectation-Maximization approach is adopted to optimize the
resulting energy objective. Clustering inference is straightforward after the
optimized transformation $\boldsymbol{T}_{j}$ is achieved, i.e., a patient can
be assigned the subtype membership corresponding to the largest likelihood.

#### 2.2.2. Smile-GAN

Smile-GAN is a novel generative deep learning approach based on Generative
Adversarial Networks (GAN). The reader may refer to Chapter 5 for generic
information about GANs. Smile-GAN aims to learn a mapping function, $f$, from
joint CN domain $\mathcal{X}$ and subtype domain $\mathcal{Z}$ to the PT
domain $\mathcal{Y}$, by transforming CN data $\bm{x}$ to different
synthesized PT data $\bm{y^{\prime}}=f(\bm{x},\bm{z})$ that are
indistinguishable from real PT data, $\bm{y}$, by the discriminator, $D$.
Mapping function, $f$, is regularized for inverse consistencies, with a
clustering function, $g:\mathcal{Y}\rightarrow\mathcal{Z}$, trained
interactively to reconstruct $\bm{z}$ from synthesized PT data
$\bm{y^{\prime}}$. The clustering function, $g$, can also be directly used to
cluster both training and unseen test data after the training process.

More specifically, three different data distributions are denoted as
$\mathbf{x}\sim p_{\text{CN}}$ (for controls), $\mathbf{y}\sim p_{\text{PT}}$
(for patients) and $\mathbf{z}\sim P_{\text{Sub}}$ (for a subtype),
respectively, where $\mathbf{z}\sim P_{\text{Sub}}$ is sampled from a discrete
uniform distribution and encoded as a one-hot vector with dimension $K$
(number of clusters). Mapping function,
$f:\mathcal{X}*\mathcal{Z}\rightarrow\mathcal{Y}$, and clustering function,
$g:\mathcal{Y}\rightarrow\mathcal{Z}$, are learned through the following
training procedure ($l_{c}$ denotes the cross-entropy loss):

$\displaystyle f,g=\arg\min_{f,g}\max_{D}L_{\text{GAN}}(D,f)+\mu
L_{\text{change}}(f)+\lambda L_{\text{cluster}}(f,g)$ (1)

where

$\displaystyle L_{\text{GAN}}(D,f)$ $\displaystyle=\mathbb{E}_{\mathbf{y}\sim
p_{\text{PT}}}[\log(D(\bm{y}))]$ $\displaystyle+\mathbb{E}_{\mathbf{z}\sim
p_{\text{Sub}},\mathbf{x}\sim p_{\text{CN}}}[1-\log(D(f(\bm{x},\bm{z})))]]$
(2) $\displaystyle L_{\text{change}}(f)$
$\displaystyle=\mathbb{E}_{\mathbf{x}\sim p_{\text{CN}},\mathbf{z}\sim
p_{\text{Sub}}}[||f(\bm{x},\bm{z})-\bm{x}||_{1}]$ (3) $\displaystyle
L_{\text{cluster}}(f,g)$ $\displaystyle=\mathbb{E}_{\mathbf{x}\sim
p_{\text{CN}},\mathbf{z}\sim
p_{\text{Sub}}}[l_{c}(\bm{z},g(f(\bm{x},\bm{z})))]$ (4)

The objective consists of adversarial loss $L_{\text{GAN}}$, regularization
terms $L_{\text{change}}$ and $L_{\text{cluster}}$. Adversarial loss forces
the synthesized PT data to follow similar distributions as real PT data. The
discriminator $D$, trying to identify synthesized PT data from real PT data,
attempts to maximize the loss while the mapping $f$ attempts to minimize
against it. Both regularization terms serve to constrain the function class
where the mapping function $f$ is sampled from so that it is truly meaningful
while matching the distributions. Minimization of $L_{\text{change}}$
encourages sparsity of regions captured by $f$, with the assumption that only
some regions are changed by disease effect. Optimizing $L_{\text{cluster}}$
ensures that the input sub variable $\bm{z}$ can be reconstructed from
synthesized PT data $\bm{y^{\prime}}$, so that the mutual information between
$\bm{z}$ and $\bm{y}^{\prime}$ are maximized, and distinct imaging patterns
are synthesized when $\bm{z}$ takes different values. Further regularization
is also imposed by forcing mapping function f and clustering function g to be
Lipschitz continuous. More importantly, thanks to the inverse consistencies
led by $L_{\text{cluster}}$, function $g$ can directly output cluster
probabilities and cluster labels when given unseen test PT data.

#### 2.2.3. HYDRA

In contrast to the generative approaches used in CHIMERA and Smile-GAN, HYDRA
leverages a widely used discriminative method, i.e., support vector machines
(SVM), to seek this “1-to-k” mapping. The novelty is that HYDRA extends
multiple linear SVMs to the non-linear case in a piecewise fashion, thereby
simultaneously serving for classification and clustering. Specifically, it
constructs a convex polytope by combining the hyperplane from k linear SVMs,
separating the CN group and the k subpopulation of the PT group. Intuitively,
each face of the convex polytope can be regarded to encode each subtype,
capturing a distinct disease effect.

The convex polytope is estimated by sequentially solving each linear SVM as a
sub-problem under the principle of the sample weighted SVM [8]. The
optimization stops when the sample weights become stable, i.e., the polytope
is stably established. The objective of maximizing the polytope’s margin can
be summarized as:

$\displaystyle\min_{\\{\bm{w}_{j},b_{j}\\}_{(j=1)}^{k}}\sum_{(j=1)}^{k}\frac{||\bm{w}_{j}||_{2}^{2}}{2}+\mu\sum_{i|y_{i}=+1}\frac{1}{k}\max\\{0,1-\bm{w}_{j}^{T}\bm{X}_{i}^{T}-b_{j}\\}$
$\displaystyle+\mu\sum_{i|y_{i}=-1}s_{i,j}\max\\{0,1+\bm{w}_{j}^{T}\bm{X}_{i}^{T}+b_{j}\\}$
(5)

where $\bm{w}_{j}$ and $b_{j}$ are the weight and bias for each hyperplane,
respectively. $\mu$ is a penalty parameter on the training error, and
$\boldsymbol{S}$ is the subtype membership matrix of dimension $m*k$ deciding
whether a patient sample i belongs to subtype j. The cluster membership is
inferred as follows:

$\displaystyle\bm{S}_{i,j}=\Big{\\{}\begin{matrix}1,j=\operatorname*{arg\,max}_{j}(\bm{w}_{j}^{T}\bm{X}^{T}+b_{j})\\\
0,otherwise\end{matrix}$ (6)

#### 2.2.4. MAGIC

MAGIC was proposed to overcome one of the main limitations that HYDRA faced.
That is, a single-scale set of features (e.g., atlas-based regions of
interest) may not be sufficient to derive subtle differences, compared to
global demographics, disease heterogeneity, since ample evidence has shown
that the brain is fundamentally composed of multi-scale structural or
functional entities. To this objective, MAGIC extracts multi-scale features in
a coarse-to-fine granular fashion via stochastic orthogonal projective non-
negative matrix factorization (opNMF) [70], a very effective unbiased, data-
driven method for extracting biologically interpretable and reproducible
feature representations. Together with these multi-scale features, HYDRA is
embedded into a double-cyclic optimization procedure to yield robust and
scale-consistent cluster solutions.

MAGIC encapsulates the two previous proposed methods (i.e., opNMF and HYDRA)
and optimizes the clustering objective for each single-scale feature as a sub-
optimization problem. To fuse the multi-scale clustering information and
enforce the clusters to be scale-consistent, it adopts a double-cyclic
procedure that transfers and fine-tunes the clustering polytope. First, i)
inner cyclic procedure: let us remind that HYDRA decides the clusters based on
the subtype membership matrix ($\bm{S}$). MAGIC first initializes the $\bm{S}$
matrix with a specific single-scale feature set, i.e., $L_{i}$, then the
$\bm{S}$ matrix is transferred to the next set of feature set $L_{i+1}$ until
the predefined stopping criterion is achieved (i.e., the clustering solution
across scales are stable). Secondly, ii) outer cyclic procedure: the inner
cyclic procedure was repeated by initializing with each single-scale feature
set. Finally, to determine the final subtype assignment, we perform a
consensus clustering by computing a co-occurrence matrix based on all the
clustering results and then perform spectral clustering [54].

## 3\. Application to brain disorders

Brain disorders and diseases affect the human brain across a wide age range.
Neurodevelopmental disorders, such as autism spectrum disorders (ASD), are
usually present from early childhood and affect daily functioning [22].
Psychotic disorders, such as schizophrenia, involve psychosis that is
typically diagnosed for the first time in late adolescence or early adulthood
[31]. Dementia and mild cognitive impairment (MCI) prevail both in late mid-
life for early-onset AD (usually 30 to 60 years of age) and most frequently in
late-life for late-onset AD (usually over 65 years of age) [50]. Brain cancers
in children and adults are heterogeneous and encompass over 100 different
histological types of tumors, based on cells of origin and other
histopathological features, and have substantial morbidity and mortality [56].
Ample clinical evidence encourages the stratification of the patients in these
brain disorders and cancers, potentially paving the road towards
individualized precision medicine.

This section collectively overviews previous work aiming to unravel imaging-
derived heterogeneity in ASD, psychosis, major depressive disorders (MDD), MCI
and AD, and brain cancer.

###  3.1 A utism Spectrum Disorder

ASD encompasses a broad spectrum of social deficits and atypical behaviors
[48]. Heterogeneity of its clinical presentation has sparked massive research
efforts to find subtypes to better delineate its diagnosis [44, 79]. Recent
initiatives to aggregate neuroimaging data of ASD, such as the ABIDE [14] and
the EU-AIMS [45], also have motivated large-scale subtyping projects using
imaging signatures [35].

Different clustering methods have been applied to reveal structural brain-
based subtypes, but primarily traditional techniques such as the K-means [9]
or hierarchical clustering [34]. Besides structural MRI, functional MRI [20]
and EEG [18] have also been popular modalities. For reasons discussed earlier,
normative clustering and dimensional analyses are better suited to parse a
patient population that is highly heterogeneous [72]. However, efforts in this
avenue have been primitive, with only a few recent publications using cortical
thickness [87]. Taken together, although more validation and replication
efforts are necessary to define any reliable neuroanatomical subtypes of ASD,
some convergence in findings has been noted [35]. First, most sets of ASD
neuroimaging subtypes indicate a combination of both increases and decreases
in imaging features compared to the CN group, instead of pointing in a uniform
direction. Second, most subtypes are characterized by spatially distributed
imaging patterns instead of isolated or focal patterns. Both findings
emphasize the significant heterogeneity in ASD brains and the need for better
stratification.

The search for subtypes in the ASD population has unique challenges. First,
the early onset of ASD implies that it is heavily influenced by
neurodevelopmental processes. Depending on the selected age range, the results
may significantly differ. Second, ASD is more prevalent in males, with three
to four male cases for one female case [43], which adds a layer of potential
bias. Third, individuals with ASD often suffer psychiatric comorbidities, such
as ADHD, anxiety disorders, obsessive-compulsive disorder, among many others
[29], which, if not screened carefully, can dilute or alter the true signal.

###  3.2 P sychosis

Psychosis is a medical syndrome characterized by unusual beliefs called
delusions and sometimes hallucinations of visions, sounds, smells, or body
sensations that are not present in reality. Symptoms, functioning, and
outcomes are highly heterogeneous across individuals, leading to long-standing
hypotheses of underlying brain subgroups. However, objective brain biomarkers
have largely not been discovered for any psychosis diagnosis, stage, or
clinically-defined subgroup [32, 59]. Neuroimaging studies are also affected
by brain heterogeneity [1, 37]. Recent research has thus focused on finding
structural brain subtypes using unbiased statistical techniques [7, 19, 40].

Psychosis studies have mainly focused on determining subtypes by clustering
brain structural data within the chronic schizophrenia population that has had
the illness for years, with results demonstrating two [7, 19], three [58], and
six [71] subgroups. Various clustering techniques have been used to achieve
these outcomes, including conventional approaches, such as k-means, in
addition to more advanced machine learning methods, such as semi-supervised
learning. A limitation of the work so far has been the lack of internal or
external validation. Still, in studies with robust internal validation methods
using metrics that choose the optimal cluster number based on the stability of
the solution (e.g., consensus clustering), subtypes cluster along the lines of
the severity of brain differences.

In a recent study, with the largest sample to date (n=671), clustered
individuals with chronic schizophrenia using HYDRA and multiple internal
validation procedures were applied (i.e., cross-validation resampling, split-
half reproducibility, and leave-site-out validation) [7]. A two-subtype
solution was found, with one subtype demonstrating widespread reductions and
the other showing the localized larger volume of the striatum that was not
associated with antipsychotic use. Interestingly, there were limited
associations with current psychosis symptoms in this work, but indications of
associations with education and illness duration in specific subtypes.

Functional imaging has also been used to define psychosis subgroups using
functional connectivity at rest [82] and effective connectivity during task
performance [5]. The research commonly has relatively low sample sizes with
little internal or external validation. Still, of these works, preliminary
results demonstrate that clusters can follow diagnostic divisions between
individuals with psychosis [5] and that specific networks (e.g.,
frontoparietal network) are associated with specific psychotic symptoms [5]
[82]. A recent advanced deep learning approach has also revealed clinical
separations along the lines of symptom severity [81]. Taken together with
brain structural results, it is possible that functional imaging maps onto
symptom states rather than underlying illness traits that are captured by
structural imaging. Further internal and external validation work is required
to investigate this hypothesis by characterizing, comparing, and ultimately
combining clustering solutions. A critical future direction will also be to
conduct longitudinal studies that track individuals over time. Such research
could lead the way towards clinical translation.

###  3.3 M ajor depressive disorder

MDD is a common, severe, and recurrent disorder, with over 300 million people
affected worldwide, and is characterized by low mood, apathy, and social
withdrawal, with symptoms spanning multiple domains [80]. Its vast
heterogeneity is exemplified by the fact that according to DSM-5 criteria, at
least 227 and up to 16,400 unique symptom presentations exist [26, 47]. The
potential causes for this heterogeneity vary from divergent clinical symptom
profiles to genetic aetiologies and individual differences in treatment
outcomes.

Despite neurobiological findings in MDD spanning cortical thickness, gray
matter volume (GMV), and fractional anisotropy (FA) measures, objective brain
biomarkers that can be used to diagnose and predict disease course and outcome
remain elusive [6, 47, 68]. Recently, there have been efforts to identify
neurobiologically based subtypes of depression using a bottom-up approach,
mainly using data from resting-state fMRI [47]. Several studies [24, 65, 66]
employed k-means clustering and group iterative multiple model estimation
respectively to identify two functional connectivity subtypes, while Tokuda et
al. [73] and Drysdale et al. [17] identified three and four subtypes
respectively using non-parametric Bayesian mixture models and hierarchical
clustering. These subtypes are characterized by reduced connectivity in
different networks, including the Default Mode Network (DMN), ventral
attention network, and frontostriatal and limbic dysfunction. Regarding
structural neuroimaging, one study has used K-means clustering on fractional
anisotropy (FA) data to identify two depression subtypes. The first subtype
was characterized by decreased FA in the right temporal lobe and the right
middle frontal areas and was associated with an older age at onset. In
contrast, the second subtype was characterized by increased FA in the left
occipital lobe and was associated with a younger age at onset [10].

Current research in the identification of brain subtypes in MDD has produced
results that are promising but confounded by methodological and design
limitations. While some studies have shown clinical promises such as
predicting higher depressive symptomatology and lower sustenance of positive
mood [65, 66], depression duration [24], and TMS therapy response [17], they
are confounded by limitations such as relatively small samples sizes, nuisance
variances such as age, gender, and common ancestry, lack of external
validation, and lack of statistical significance testing of identified
clusters. Furthermore, there has been a lack of ambition in the use of novel
clustering techniques. Clustering based on structural neuroimaging is limited
compared to other disease entities and is an avenue that future research
should consider. Future studies should also aim to perform longitudinal
clustering to elucidate the stability of identified brain subtypes over time
and examine their utility in predicting disease outcomes.

###  3.4 M CI and AD

AD, along with its prodromal stage presenting MCI, is the most common
neurodegenerative disease, affecting millions across the globe. Although a
plethora of imaging studies have derived AD-related imaging signatures, most
studies ignored the heterogeneity in AD. Recently, there has been a developing
body of effort to derive imaging signatures of AD that are heterogeneity-aware
(i.e., subtypes) [75, 76, 83, 85, 88].

Most previous studies leveraged unsupervised clustering methods such as
Sustain [85], NMF [41], latent Dirichlet allocation [88], and hierarchical
clustering [38, 53, 57, 63]. Other papers [16, 21, 25, 74, 83] utilized semi-
supervised clustering methods. Due to the variabilities of the choice of
databases and methodologies and the lack of ground truth in the context of
clustering, the reported number of clusters and the subtypes’ neuroanatomical
patterns differ and cannot be directly compared. The targeted heterogeneous
population of study also varies across papers. For instance, [74] focused on
dissecting the neuroanatomical heterogeneity for AD patients, while [16]
included AD plus MCI and [21] studied MCI only. However, some common subtypes
were found in different studies. First, a subtype showing a typical diffuse
atrophy pattern over the entire brain was witnessed in several studies [16,
38, 39, 60, 63, 64, 41, 74, 76, 83, 85]. Another subtype demonstrating nearly
normal brain anatomy was robustly identified [15, 21, 39, 53, 57, 64, 63, 76,
83]. Moreover, studies [16, 63, 64, 76, 83] also reported one subtype showing
atypical AD patterns (i.e., hippocampus or medial temporal lobe atrophy
spared).

Though these methods enabled a better understanding of heterogeneity in AD,
there are still limitations and challenges. First, due to demographic
variations and the existence of comorbidities, it is not guaranteed that
models cluster the data based on variations of the pathology of interest.
Semi-supervised methods might tackle this problem to some extent, but more
careful sample selection and further study with longitudinal data may ensure
disease-specificity. Second, spatial differences and temporal changes may
simultaneously contribute to subtypes derived through clustering methods.
Third, subtypes captured from neuroimaging data alone bring limited insight
into disease treatments, thereby a joint study of neuroimaging and genetic
heterogeneity may provide greater clinical value [77, 27].

###  3.5 B rain cancer

Brain tumors, such as glioblastoma (GBM), exhibit extensive inter and intra-
tumor heterogeneity, diffuse infiltration, and invasiveness of various immune
and stromal cell populations, which pose diagnostic and prognostic challenges,
and render the standard therapies futile [4]. Deciphering the underlying
heterogeneity of brain tumors, which arises from genomic instability of these
tumors, plays a key role in understanding and predicting the course of tumor
progression and its response to the standard therapies, thereby designing
effective therapies targeted at aberrant genetic alterations [2, 67]. Medical
imaging noninvasively portrays the phenotypic differences of brain tumors and
their micro-environment caused by molecular activities of tumors on a
macroscopic scale [12, 30]. It has the potential to provide readily accessible
and surrogate biomarkers of particular genomic alterations, predict response
to therapy, avoid risks of tumor biopsy or inaccurate diagnosis due to
sampling errors, and ultimately develop personalized therapies to improve
patient outcomes. An imaging subtype of brain tumors may provide a wealth of
information about the tumor, including distinct molecular pathways [23, 28].

Recent studies on radiomic analysis of multiparametric MRI (mpMRI) scans
provide evidence of distinct phenotypic presentation of brain tumors
associated with specific molecular characteristics. These studies propose that
quantification of tumor morphology, texture, regional microvasculature,
cellular density, or microstructural properties can map to different imaging
subtypes. In particular, one study [69] discovered three distinct clusters of
GBM subtypes through unsupervised clustering of these features, with
significant differences in survival probabilities and associations with
specific molecular signaling pathways. These imaging subtypes, namely solid,
irregular, and rim-enhancing, were significantly linked to different clinical
outcomes and molecular characteristics, including isocitrate dehydrogenase-1,
O6-methylguanine–DNA methyltransferase, epidermal growth factor receptor
variant III, and transcriptomic molecular subtype composition.

These studies have offered new insights into the characterization of tumor
heterogeneity on both microscopic, i.e., histology and molecular, and
macroscopic, i.e., imaging levels, consequently providing a more comprehensive
understanding of the tumor aggressiveness and patient prognosis, and
ultimately, the development of personalized treatments.

## 4\. Conclusion

Taken together, these novel clustering algorithms tailored for high resolution
yet highly variable neuroimaging datasets have demonstrated a broad utility in
disease subtyping across many neurological and psychiatric conditions.
Simultaneously, cautions need to be taken in order not to overclaim the
biological importance of subtypes, since all clustering methods find patterns
in data, even if such patterns don’t have a meaningful underlying biological
correlate [3]. External validations are necessary. For instance, evidence of
post-hoc evaluations, e.g., a difference in clinical variables or genetic
architectures, can support the biological relevance of identified
neuroimaging-based subtypes [77]. Moreover, good practices such as split-
sample analysis, permutation tests [7], and comparison to the guideline of
semi-simulated experiments [76] discern the robustness of the subtypes. As
dataset sizes and imaging resolution improve over time, unique computational
challenges are expected to appear, along with unique opportunities to further
refine our methodologies to decipher the diversity of brain diseases.

## Acknowledgments

This work was supported, in part, by NIH grants R01NS042645, U01AG068057,
R01MH112070 and RF1AG054409.

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