Noname manuscript No.
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A review of heterogeneous data mining for brain disorders

arXiv:1508.01023v1 [cs.LG] 5 Aug 2015

Bokai Cao · Xiangnan Kong · Philip S. Yu

Abstract With rapid advances in neuroimaging techniques, the research on brain disorder identification has
become an emerging area in the data mining community. Brain disorder data poses many unique challenges
for data mining research. For example, the raw data
generated by neuroimaging experiments is in tensor representations, with typical characteristics of high dimensionality, structural complexity and nonlinear separability. Furthermore, brain connectivity networks can be
constructed from the tensor data, embedding subtle interactions between brain regions. Other clinical measures are usually available reflecting the disease status
from different perspectives. It is expected that integrating complementary information in the tensor data and
the brain network data, and incorporating other clinical
parameters will be potentially transformative for investigating disease mechanisms and for informing therapeutic interventions. Many research efforts have been
devoted to this area. They have achieved great success
in various applications, such as tensor-based modeling,
subgraph pattern mining, multi-view feature analysis.
In this paper, we review some recent data mining methods that are used for analyzing brain disorders.

Keywords Data mining · Brain diseases · Tensor
analysis · Subgraph patterns · Feature selection

B. Cao · P.S. Yu
Department of Computer Science, University of Illinois at
Chicago, Chicago, IL 60607.
E-mail: caobokai@uic.edu, psyu@cs.uic.edu
X. Kong
Department of Computer Science, Worcester Polytechnic Institute, Worcester, MA 01609.
E-mail: xkong@wpi.edu

1 Introduction
Many brain disorders are characterized by ongoing injury that is clinically silent for prolonged periods and
irreversible by the time symptoms first present. New
approaches for detection of early changes in subclinical periods will afford powerful tools for aiding clinical diagnosis, clarifying underlying mechanisms and
informing neuroprotective interventions to slow or reverse neural injury for a broad spectrum of brain disorders, including bipolar disorder, HIV infection on brain,
Alzheimer’s disease, Parkinson’s disease, etc. Early diagnosis has the potential to greatly alleviate the burden
of brain disorders and the ever increasing costs to families and society.
As the identification of brain disorders is extremely
challenging, many different diagnosis tools and methods
have been developed to obtain a large number of measurements from various examinations and laboratory
tests. Especially, recent advances in the neuroimaging
technology have provided an efficient and noninvasive
way for studying the structural and functional connectivity of the human brain, either normal or in a diseased
state [48]. This can be attributed in part to advances
in magnetic resonance imaging (MRI) capabilities [33].
Techniques such as diffusion MRI, also referred to as
diffusion tensor imaging (DTI), produce in vivo images
of the diffusion process of water molecules in biological
tissues. By leveraging the fact that the water molecule
diffusion patterns reveal microscopic details about tissue architecture, DTI can be used to perform tractography within the white matter and construct structural
connectivity networks [2, 36, 12, 38, 40]. Functional MRI
(fMRI) is a functional neuroimaging procedure that
identifies localized patterns of brain activation by detecting associated changes in the cerebral blood flow.

2

B. Cao et al.

The primary form of fMRI uses the blood oxygenation
level dependent (BOLD) response extracted from the
gray matter [3, 42, 43]. Another neuroimaging technique
is positron emission tomography (PET). Using different radioactive tracers (e.g., fluorodeoxyglucose), PET
produces a three-dimensional image of various physiological, biochemical and metabolic processes [68].
A variety of data representations can be derived
from these neuroimaging experiments, which present
many unique challenges for the data mining community.
Conventional data mining algorithms are usually developed to tackle data in one specific representation, a majority of which are particularly for vector-based data.
However, the raw neuroimaging data is in the form
of tensors, from which we can further construct brain
networks connecting regions of interest (ROIs). Both
of them are highly structured considering correlations
between adjacent voxels in the tensor data and that
between connected brain regions in the brain network
data. Moreover, it is critical to explore interactions between measurements computed from the neuroimaging
and other clinical experiments which describe subjects
in different vector spaces. In this paper, we review some
recent data mining methods for (1) mining tensor imaging data; (2) mining brain networks; (3) mining multiview feature vectors.
2 Tensor Imaging Analysis
For brain disorder identification, the raw data generated by neuroimging experiments are in tensor representations [15, 22, 68]. For example, in contrast to twodimensional X-ray images, an fMRI sample corresponds
to a four-dimensional array by recording the sequential
changes of traceable signals in each voxel1 .
Tensors are higher order arrays that generalize the
concepts of vectors (first-order tensors) and matrices
(second-order tensors), whose elements are indexed by
more than two indices. Each index expresses a mode of
variation of the data and corresponds to a coordinate
direction. In an fMRI sample, the first three modes usually encode the spatial information, while the fourth
mode encodes the temporal information. The number
of variables in each mode indicates the dimensionality
of a mode. The order of a tensor is determined by the
number of its modes. An mth-order tensor can be represented as X = (xi1 ,··· ,im ) ∈ RI1 ×···×Im , where Ii is
the dimension of X along the i-th mode.
Definition 1 (Tensor product) The tensor product
of three vectors a ∈ RI1 , b ∈ RI2 and c ∈ RI3 , denoted
1

A voxel is the smallest three-dimensional point volume
referenced in a neuroimaging of the brain.

c1
≈
X

c2
b2 + ⋯ +

b1 +
a1

cR

a2

bR
aR

Fig. 1 Tensor factorization of a third-order tensor.

by a ⊗ b ⊗ c, represents a third-order tensor with the
elements (a ⊗ b ⊗ c)i1 ,i2 ,i3 = ai1 bi2 ci3 .
Tensor product is also referred to as outer product
in some literature. An mth-order tensor is a rank-one
tensor if it can be defined as the tensor product of m
vectors.
Definition 2 (Tensor factorization) Given a thirdorder tensor X ∈ RI1 ×I2 ×I3 and an integer R, as illustrated in Figure 1, a tensor factorization of X can be
expressed as
X = X1 + X2 + · · · + XR =

R
X

ar ⊗ br ⊗ cr

(1)

r=1

One of the major difficulties brought by the tensor data is the curse of dimensionality. The total number of voxels contained in a multi-mode tensor, say,
X = (xi1 ,··· ,im ) ∈ RI1 ×···×Im is I1 × · · · × Im which is
exponential to the number of modes. If we unfold the
tensor into a vector, the number of features will be extremely high [69]. This makes traditional data mining
methods prone to overfitting, especially with a small
sample size. Both computational scalability and theoretical guarantee of the traditional models are compromised by such high dimensionality [22].
On the other hand, complex structural information
is embedded in the tensor data. For example, in the neuroimaging data, values of adjacent voxels are usually
correlated with each other [33]. Such spatial relationships among different voxels in a tensor image can be
very important in neuroimaging applications. Conventional tensor-based approaches focus on reshaping the
tensor data into matrices/vectors and thus the original
spatial relationships are lost. The integration of structural information is expected to improve the accuracy
and interpretability of tensor models.

2.1 Classification
Suppose we have a set of tensor data D = {(Xi , yi )}ni=1
for classification problem, where Xi ∈ RI1 ×···×Im is the
neuroimaging data represented as an mth-order tensor
and yi ∈ {−1, +1} is the corresponding binary class label of Xi . For example, if the i-th subject has Alzheimer’s

A review of heterogeneous data mining for brain disorders

disease, the subject is associated with a positive label,
i.e., yi = +1. Otherwise, if the subject is in the control
group, the subject is associated with a negative label,
i.e., yi = −1.
Supervised tensor learning can be formulated as the
optimization problem of support tensor machines (STMs)
[55] which is a generalization of the standard support
vector machines (SVMs) from vector data to tensor
data. The objective of such learning algorithms is to
learn a hyperplane by which the samples with different
labels are divided as wide as possible. However, tensor data may not be linearly separable in the input
space. To achieve a better performance on finding the
most discriminative biomarkers or identifying infected
subjects from the control group, in many neuroimaging
applications, nonlinear transformation of the original
tensor data should be considered. He et al. study the
problem of supervised tensor learning with nonlinear
kernels which can preserve the structure of tensor data
[22]. The proposed kernel is an extension of kernels in
the vector space to the tensor space which can take the
multidimensional structure complexity into account.

2.2 Regression
Slightly different from classifying disease status (discrete label), another family of problems use tensor neuroimages to predict cognitive outcome (continuous label). The problems can be formulated in a regression
setup by treating clinical outcome as the real label, i.e.,
yi ∈ R, and treating tensor neuroimages as the input.
However, most classical regression methods take vectors as input features. Simply reshaping a tensor into a
vector is clearly an unsatisfactory solution.
Zhou et al. exploit the tensor structure in imaging
data and integrate tensor decomposition within a statistical regression paradigm to model multidimensional arrays [69]. By imposing a low rank approximation to the
extremely high dimensional complex imaging data, the
curse of dimensionality is greatly alleviated, thereby allowing development of a fast estimation algorithm and
regularization. Numerical analysis demonstrates its potential applications in identifying regions of interest in
brains that are relevant to a particular clinical response.

2.3 Network Discovery
Modern imaging techniques have allowed us to study
the human brain as a complex system by modeling it
as a network [1]. For example, the fMRI scans consist of
activations of thousands of voxels over time embedding
a complex interaction of signals and noise [19], which

3

naturally presents the problem of eliciting the underlying network from brain activities in the spatio-temporal
tensor data. A brain connectivity network, also called a
connectome [52], consists of nodes (gray matter regions)
and edges (white matter tracts in structural networks
or correlations between two BOLD time series in functional networks).
Although the anatomical atlases in the brain have
been extensively studied for decades, task/subject specific networks have still not been completely explored
with consideration of functional or structural connectivity information. An anatomically parcellated region
may contain subregions that are characterized by dramatically different functional or structural connectivity
patterns, thereby significantly limiting the utility of the
constructed networks. There are usually trade-offs between reducing noise and preserving utility in brain parcellation [33]. Thus investigating how to directly construct brain networks from tensor imaging data and
understanding how they develop, deteriorate and vary
across individuals will benefit disease diagnosis [15].
Davidson et al. pose the problem of network discovery from fMRI data which involves simplifying spatiotemporal data into regions of the brain (nodes) and relationships between those regions (edges) [15]. Here the
nodes represent collections of voxels that are known to
behave cohesively over time; the edges can indicate a
number of properties between nodes such as facilitation/inhibition (increases/decreases activity) or probabilistic (synchronized activity) relationships; the weight
associated with each edge encodes the strength of the
relationship.
A tensor can be decomposed into several factors.
However, unconstrained tensor decomposition results
of the fMRI data may not be good for node discovery
because each factor is typically not a spatially contiguous region nor does it necessarily match an anatomical region. That is to say, many spatially adjacent voxels in the same structure are not active in the same
factor which is anatomically impossible. Therefore, to
achieve the purpose of discovering nodes while preserving anatomical adjacency, known anatomical regions in
the brain are used as masks and constraints are added
to enforce that the discovered factors should closely
match these masks [15].
Overall, current research on tensor imaging analysis
presents two directions: (1) supervised: for a particular
brain disorder, a classifier can be trained by modeling
the relationship between a set of neuroimages and their
associated labels (disease status or clinical response);
(2) unsupervised: regardless of brain disorders, a brain
network can be discovered from a given neuroimage.

4

3 Brain Network Analysis
We have briefly introduced that brain networks can be
constructed from neuroimaging data where nodes correspond to brain regions, e.g., insula, hippocampus, thalamus, and links correspond to the functional/structural
connectivity between brain regions. The linkage structure in brain networks can encode tremendous information about the mental health of human subjects. For example, in brain networks derived from functional magnetic resonance imaging (fMRI), functional connections
can encode the correlations between the functional activities of brain regions. While structural links in diffusion tensor imaging (DTI) brain networks can capture
the number of neural fibers connecting different brain
regions. The complex structures and the lack of vector
representations for the brain network data raise major
challenges for data mining.
Next, we will discuss different approaches on how
to conduct further analysis for constructed brain networks, which are also referred to as graphs hereafter.
Definition 3 (Binary graph) A binary graph is represented as G = (V, E), where V = {v1 , · · · , vnv } is the
set of vertices, E ⊆ V × V is the set of deterministic
edges.

3.1 Kernel Learning on Graphs
In the setting of supervised learning on graphs, the target is to train a classifier using a given set of graph data
D = {(Gi , yi )}ni=1 , so that we can predict the label ŷ
for a test graph G. With applications to brain networks,
it is desirable to identify the disease status for a subject based on his/her uncovered brain network. Recent
development of brain network analysis has made characterization of brain disorders at a whole-brain connectivity level possible, thus providing a new direction for
brain disease classification.
Due to the complex structures and the lack of vector
representations, graph data can not be directly used as
the input for most data mining algorithms. A straightforward solution that has been extensively explored is
to first derive features from brain networks and then
construct a kernel on the feature vectors.
Wee et al. use brain connectivity networks for disease diagnosis on mild cognitive impairment (MCI),
which is an early phase of Alzheimer’s disease (AD)
and usually regarded as a good target for early diagnosis and therapeutic interventions [61, 62, 63]. In the
step of feature extraction, weighted local clustering coefficients of each ROI in relation to the remaining ROIs
are extracted from all the constructed brain networks to

B. Cao et al.

quantify the prevalence of clustered connectivity around
the ROIs. To select the most discriminative features for
classification, statistical t-test is performed and features
with p-values smaller than a predefined threshold are
selected to construct a kernel matrix. Through the employment of the multi-kernel SVM, Wee et al. integrate
information from DTI and fMRI and achieve accurate
early detection of brain abnormalities [63].
However, such strategy simply treats a graph as a
collection of nodes/links, and then extracts local measures (e.g., clustering coefficient) for each node or performs statistical analysis on each link, thereby blinding the connectivity structures of brain networks. Motivated by the fact that some data in real-world applications are naturally represented by means of graphs,
while compressing and converting them to vectorial representations would definitely lose structural information, kernel methods for graphs have been extensively
studied for a decade [5].
A graph kernel maps the graph data from the original graph space to the feature space and further measures the similarity between two graphs by comparing
their topological structures [49]. For example, product
graph kernel is based on the idea of counting the number of walks in product graphs [18]; marginalized graph
kernel works by comparing the label sequences generated by synchronized random walks of labeled graphs
[30]; cyclic pattern kernels for graphs count pairs of
matching cyclic/tree patterns in two graphs [23].
To identify individuals with AD/MCI from healthy
controls, instead of using only a single property of brain
networks, Jie et al. integrate multiple properties of fMRI
brain networks to improve the disease diagnosis performance [27]. Two different yet complementary network
properties, i.e., local connectivity and global topological properties are quantified by computing two different
types of kernels, i.e., a vector-based kernel and a graph
kernel. As a local network property, weighted clustering coefficients are extracted to compute a vector-based
kernel. As a topology-based graph kernel, WeisfeilerLehman subtree kernel [49] is used to measure the topological similarity between paired fMRI brain networks.
It is shown that this type of graph kernel can effectively capture the topological information from fMRI
brain networks. The multi-kernel SVM is employed to
fuse these two heterogeneous kernels for distinguishing
individuals with MCI from healthy controls.
3.2 Subgraph Pattern Mining
In brain network analysis, the ideal patterns we want
to mine from the data should take care of both local
and global graph topological information. Graph kernel

A review of heterogeneous data mining for brain disorders

+ Alzheimer's disease

+ Alzheimer's disease

5

+ Alzheimer's disease
0.5

0.8

0.016

0.064

0.004

0.144

0.036

0.576

0.016

0.144

0.2

0.3
0.8

0.6

0.9

0.8

0.9

0.6

0.2
0.6
0.3

0.5
0.5

- Normal

- Normal

0.8

- Normal

0.6

0.9

Fig. 3 An example of fMRI brain networks (left) and all posA discriminative subgraph pattern

sible instantiations of linkage structures between red nodes
(right) [10].

Fig. 2 An example of discriminative subgraph patterns in

brain networks.

methods seem promising, which however are not interpretable. Subgraph patterns are more suitable for brain
networks, which can simultaneously model the network
connectivity patterns around the nodes and capture the
changes in local area [33].
Definition 4 (Subgraph) Let G0 = (V 0 , E 0 ) and G =
(V, E) be two binary graphs. G0 is a subgraph of G
(denoted as G0 ⊆ G) iff V 0 ⊆ V and E 0 ⊆ E. If G0 is a
subgraph of G, then G is supergraph of G0 .
A subgraph pattern, in a brain network, represents a
collection of brain regions and their connections. For example, as shown in Figure 2, three brain regions should
work collaboratively for normal people and the absence
of any connection between them can result in Alzheimer’s
disease in different degree. Therefore, it is valuable to
understand which connections collectively play a significant role in disease mechanism by finding discriminative
subgraph patterns in brain networks.
Mining subgraph patterns from graph data has been
extensively studied by many researchers [29, 13, 56, 66].
In general, a variety of filtering criteria are proposed.
A typical evaluation criterion is frequency, which aims
at searching for frequently appearing subgraph features
in a graph dataset satisfying a prespecified threshold.
Most of the frequent subgraph mining approaches are
unsupervised. For example, Yan and Han develop a
depth-first search algorithm: gSpan [67]. This algorithm
builds a lexicographic order among graphs, and maps
each graph to an unique minimum DFS code as its
canonical label. Based on this lexicographic order, gSpan
adopts the depth-first search strategy to mine frequent
connected subgraphs efficiently. Many other approaches
for frequent subgraph mining have also been proposed,
e.g., AGM [26], FSG [34], MoFa [4], FFSM [24], and
Gaston [41].

Moreover, the problem of supervised subgraph mining has been studied in recent work which examines
how to improve the efficiency of searching the discriminative subgraph patterns for graph classification. Yan
et al. introduce two concepts structural leap search and
frequency-descending mining, and propose LEAP [66]
which is one of the first work in discriminative subgraph mining. Thoma et al. propose CORK which can
yield a near-optimal solution using greedy feature selection [56]. Ranu and Singh propose a scalable approach,
called GraphSig, that is capable of mining discriminative subgraphs with a low frequency threshold [46].
Jin et al. propose COM which takes into account the
co-occurences of subgraph patterns, thereby facilitating the mining process [28]. Jin et al. further propose
an evolutionary computation method, called GAIA, to
mine discriminative subgraph patterns using a randomized searching strategy [29]. Zhu et al. design a diversified discrimination score based on the log ratio which
can reduce the overlap between selected features by considering the embedding overlaps in the graphs [70].
Conventional graph mining approaches are best suited
for binary edges, where the structure of graph objects is
deterministic, and the binary edges represent the presence of linkages between the nodes [33]. In fMRI brain
network data however, there are inherently weighted
edges in the graph linkage structure, as shown in Figure 3 (left). A straightforward solution is to threshold
weighted networks to yield binary networks. However,
such simplification will result in great loss of information. Ideal data mining methods for brain network analysis should be able to overcome these methodological
problems by generalizing the network edges to positive
and negative weighted cases, e.g., probabilistic weights
in fMRI brain networks, integral weights in DTI brain
networks.
Definition 5 (Weighted graph) A weighted graph is
e = (V, E, p), where V = {v1 , · · · , vn }
represented as G
v

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B. Cao et al.

is the set of vertices, E ⊆ V × V is the set of nondeterministic edges. p : E → (0, 1] is a function that assigns
a probability of existence to each edge in E.
fMRI brain networks can be modeled as weighted
graphs where each edge e ∈ E is associated with a
probability p(e) indicating the likelihood of whether
this edge should exist or not [32, 10]. It is assumed that
p(e) of different edges in a weighted graph are independent from each other. Therefore, by enumerating the
possible existence of all edges in a weighted graph, we
can obtain a set of binary graphs. For example, in Fig. 3
(right), consider the three red nodes and links between
them as a weighted graph. There are 23 = 8 binary
graphs that can be implied with different probabilities.
e the probability of G
e containFor a weighted graph G,
ing a subgraph feature G0 is defined as the probability
e contains subgraph
that a binary graph G implied by G
0
G . Kong et al. propose a discriminative subgraph feature selection method based on dynamic programming
to compute the probability distribution of the discrimination scores for each subgraph pattern within a set of
weighted graphs [32].
For brain network analysis, usually we only have a
small number of graph instances [32]. In these applications, the graph view alone is not sufficient for mining
important subgraphs. Fortunately, the side information
is available along with the graph data for brain disorder identification. For example, in neurological studies,
hundreds of clinical, immunologic, serologic and cognitive measures may be available for each subject, apart
from brain networks. These measures compose multiple side views which contain a tremendous amount of
supplemental information for diagnostic purposes. It is
desirable to extract valuable information from a plurality of side views to guide the process of subgraph
mining in brain networks.
Figure 4(a) illustrates the process of selecting subgraph patterns in conventional graph classification approaches. Obviously, the valuable information embedded in side views is not fully leveraged in feature selection process. To tackle this problem, Cao et al. introduce an effective algorithm for discriminative subgraph selection using multiple side views [9], as illustrated in Figure 4(b). Side information consistency is
first validated via statistical hypothesis testing which
suggests that the similarity of side view features between instances with the same label should have higher
probability to be larger than that with different labels.
Based on such observations, it is assumed that the similarity/distance between instances in the space of subgraph features should be consistent with that in the
space of a side view. That is to say, if two instances
are similar in the space of a side view, they should also

Side Views

Mine
Brain Networks

Subgraph Patterns

Graph Classiﬁcation

(a) Treating side views and subgraph patterns separately.
Side Views

Guide
Mine
Brain Networks

Subgraph Patterns

Graph Classiﬁcation

(b) Using side views as guidance for the process of selecting
subgraph patterns.
Fig. 4 Two strategies of leveraging side views in feature se-

lection process for graph classification.

be close to each other in the space of subgraph features. Therefore the target is to minimize the distance
between subgraph features of each pair of similar instances in each side view [9]. In contrast to existing
subgraph mining approaches that focus on the graph
view alone, the proposed method can explore multiple
vector-based side views to find an optimal set of subgraph features for graph classification.
For graph classification, brain network analysis approaches can generally be put into three groups: (1)
extracting some local measures (e.g., clustering coefficient) to train a standard vector-based classifier; (2) directly adopting graph kernels for classification; (3) finding discriminative subgraph patterns. Different types of
methods model the connectivity embedded in brain networks in different ways.

4 Multi-view Feature Analysis
Medical science witnesses everyday measurements from
a series of medical examinations documented for each
subject, including clinical, imaging, immunologic, serologic and cognitive measures [7], as shown in Figure 5.
Each group of measures characterize the health state
of a subject from different aspects. This type of data is
named as multi-view data, and each group of measures
form a distinct view quantifying subjects in one specific
feature space. Therefore, it is critical to combine them
to improve the learning performance, while simply concatenating features from all views and transforming a
multi-view data into a single-view data, as the method
(a) shown in Figure 6, would fail to leverage the underlying correlations between different views.

A review of heterogeneous data mining for brain disorders

MRI sequence A

Cognitive measures
View 1

View 2

View 6

HIV/
seronegative

View 3

View 5

View 4

MRI sequence B

Serologic measures

Immunologic
measures

Clinical measures

Fig. 5 An example of multi-view learning in medical studies

[6].

4.1 Multi-view Learning
Suppose we have a multi-view classification task with
n labeled
m different views:
n instances represented
ofrom
n
(1)
(2)
(m)
(v)
D=
xi , xi , · · · , xi , yi
, where xi ∈ RIv ,
i=1
Iv is the dimensionality of the v-th view, and yi ∈
{−1, +1} is the class label of the i-th instance.
Representative methods for multi-view learning can
be categorized into three groups: co-training, multiple
kernel learning, and subspace learning [65]. Generally,
the co-training style algorithm is a classic approach
for semi-supervised learning, which trains in alternation to maximize the mutual agreement on different
views. Multiple kernel learning algorithms combine kernels that naturally correspond to different views, either
linearly [35] or nonlinearly [58, 14] to improve learning performance. Subspace learning algorithms learn a
latent subspace, from which multiple views are generated. Multiple kernel learning and subspace learning are
generalized as co-regularization style algorithms [53],
where the disagreement between the functions of different views is taken as a part of the objective function to
be minimized. Overall, by exploring the consistency and
complementary properties of different views, multi-view
learning is more effective than single-view learning.
In the multi-view setting for brain disorders, or for
medical studies in general, a critical problem is that
there may be limited subjects available (i.e., a small n)
yet introducing a large number of measurements (i.e.,
Pm
a large i=1 Ii ). Within the multi-view data, not all

7

features in different views are relevant to the learning
task, and some irrelevant features may introduce unexpected noise. The irrelevant information can even be
exaggerated after view combinations thereby degrading performance. Therefore, it is necessary to take care
of feature selection in the learning process. Feature selection results can also be used by researchers to find
biomarkers for brain diseases. Such biomarkers are clinically imperative for detecting injury to the brain in the
earliest stage before it is irreversible. Valid biomarkers
can be used to aid diagnosis, monitor disease progression and evaluate effects of intervention [32].
Conventional feature selection approaches can be divided into three main directions: filter, wrapper, and
embedded methods [20]. Filter methods compute a discrimination score of each feature independently of the
other features based on the correlation between the
feature and the label, e.g., information gain, Gini index, Relief [44, 47]. Wrapper methods measure the usefulness of feature subsets according to their predictive
power, optimizing the subsequent induction procedure
that uses the respective subset for classification [21, 45,
50, 37, 6]. Embedded methods perform feature selection
in the process of model training based on sparsity regularization [17, 16, 59, 60]. For example, Miranda et al.
add a regularization term that penalizes the size of the
selected feature subset to the standard cost function of
SVM, thereby optimizing the new objective function to
conduct feature selection [39]. Essentially, the process
of feature selection and learning algorithm interact in
embedded methods which means the learning part and
the feature selection part can not be separated, while
wrapper methods utilize the learning algorithm as a
black box.
However, directly applying these feature selection
approaches to each separate view would fail to leverage multi-view correlations. By taking into account the
latent interactions among views and the redundancy
triggered by multiple views, it is desirable to combine
multi-view data in a principled manner and perform
feature selection to obtain consensus and discriminative low dimensional feature representations.
4.2 Modeling View Correlations
Recent years have witnessed many research efforts devoted to the integration of feature selection and multiview learning. Tang et al. study multi-view feature selection in the unsupervised setting by constraining that
similar data instances from each view should have similar pseudo-class labels [54]. Considering brain disorder
identification, different neuroimaging features may capture different but complementary characteristics of the

8

data. For example, the voxel-based tensor features convey the global information, while the ROI-based Automated Anatomical Labeling (AAL) [57] features summarize the local information from multiple representative brain regions. Incorporating these data and additional non-imaging data sources can potentially improve the prediction. For Alzheimer’s disease (AD) classification, Ye et al. propose a kernel-based method for
integrating heterogeneous data, including tensor and
AAL features from MRI images, demographic information and genetic information [68]. The kernel framework
is further extended for selecting features (biomarkers)
from heterogeneous data sources that play more significant roles than others in AD diagnosis.
Huang et al. propose a sparse composite linear discriminant analysis model for identification of diseaserelated brain regions of AD from multiple data sources
[25]. Two sets of parameters are learned: one represents
the common information shared by all the data sources
about a feature, and the other represents the specific
information only captured by a particular data source
about the feature. Experiments are conducted on the
PET and MRI data which measure structural and functional aspects, respectively, of the same AD pathology.
However, the proposed approach requires the input as
the same set of variables from multiple data sources.
Xiang et al. investigate multi-source incomplete data
for AD and introduce a unified feature learning model
to handle block-wise missing data which achieves simultaneous feature-level and source-level selection [64].
For modeling view correlations, in general, a coefficient is assigned for each view, either at the view-level
or feature-level. For example, in multiple kernel learning, a kernel is constructed from each view and a set of
kernel coefficients are learned to obtain an optimal combined kernel matrix. These approaches, however, fail to
explicitly consider correlations between features.
4.3 Modeling Feature Correlations
One of the key issues for multi-view classification is to
choose an appropriate tool to model features and their
correlations hidden in multiple views, since this directly
determines how information will be used. In contrast
to modeling on views, another direction for modeling
multi-view data is to directly consider the correlations
between features from multiple views. Since taking the
tensor product of their respective feature spaces corresponds to the interaction of features from multiple
views, the concept of tensor serves as a backbone for
incorporating multi-view features into a consensus representation by means of tensor product, where the complex multiple relationships among views are embedded

B. Cao et al.

Modeling

Feature selection
Method (a)

View 1

Method (b)

View 2
View 3

Method (c)

Fig. 6 Schematic view of the key differences among three

strategies of multi-view feature selection [6].

within the tensor structures. By mining structural information contained in the tensor, knowledge of multiview features can be extracted and used to establish a
predictive model.
Smalter et al. formulate the problem of feature selection in the tensor product space as an integer quadratic
programming problem [51]. However, this method is
computationally intractable on many views, since it directly selects features in the tensor product space resulting in the curse of dimensionality, as the method (b)
shown in Figure 6. Cao et al. propose to use a tensorbased approach to model features and their correlations
hidden in the original multi-view data [6]. The operation of tensor product can be used to bring m-view
feature vectors of each instance together, leading to
a tensorial representation for common structure across
multiple views, and allowing us to adequately diffuse relationships and encode information among multi-view
features. In this manner, the multi-view classification
task is essentially transformed from an independent domain of each view to a consensus domain as a tensor
classification problem.
Qm
(v)
By using Xi to denote v=1 ⊗xi , the dataset of
labeled multi-view instances can be represented as D =
{(Xi , yi )}ni=1 . Note that each multi-view instance Xi
is an mth-order tensor that lies in the tensor product
space RI1 ×···×Im . Based on the definitions of inner product and tensor norm, multi-view classification can be
formulated as a global convex optimization problem in
the framework of supervised tensor learning [55]. This
model is named as multi-view SVM [6], and it can be
solved with the use of optimization techniques developed for SVM.
Furthermore, a dual method for multi-view feature
selection is proposed in [6] that leverages the relationship between original multi-view features and reconstructed tensor product features to facilitate the im-

A review of heterogeneous data mining for brain disorders

9

plementation of feature selection, as the method (c) in
Figure 6. It is a wrapper model which selects useful
features in conjunction with the classifier and simultaneously exploits the correlations among multiple views.
Following the idea of SVM-based recursive feature elimination [21], multi-view feature selection is consistently
formulated and implemented in the framework of multiview SVM. This idea can extend to include lower order
feature interactions and to employ a variety of loss functions for classification or regression [11].

5 Future Work

Fig. 7 A bioinformatics heterogeneous information network

schema.

The human brain is one of the most complicated biological structures in the known universe. While it is
very challenging to understand how it works, especially
when disorders and diseases occur, dozens of leading
technology firms, academic institutions, scientists, and
other key contributors to the field of neuroscience have
devoted themselves to this area and made significant
improvements in various dimensions2 . Data mining on
brain disorder identification has become an emerging
area and a promising research direction.
This paper provides an overview of data mining approaches with applications to brain disorder identification which have attracted increasing attention in both
data mining and neuroscience communities in recent
years. A taxonomy is built based upon data representations, i.e., tensor imaging data, brain network data
and multi-view data, following which the relationships
between different data mining algorithms and different
neuroimaging applications are summarized. We briefly
present some potential topics of interest in the future.
Bridging heterogeneous data representations.
As introduced in this paper, we can usually derive data
from neuroimaging experiments in three representations,
including raw tensor imaging data, brain network data
and multi-view vector-based data. It is critical to study
how to train a model on a mixture of data representations, although it is very challenging to combine data
that are represented in tensor space, vector space and
graph space, respectively. There is a straightforward
idea of defining different kernels on different feature
spaces and combing them through multi-kernel algorithms. However it is usually hard to interpret the results. The concept of side view has been introduced to
facilitate the process of mining brain networks, which
may also be used to guide supervised tensor learning.
It is even more interesting if we can learn on tensors
and graphs simultaneously.
2

http://www.whitehouse.gov/BRAIN

Integrating multiple neuroimaging modalities.
There are a variety of neuroimaging techniques available characterizing subjects from different perspectives
and providing complementary information. For example, DTI contains local microstructural characteristics
of water diffusion; structural MRI can be used to delineate brain atrophy; fMRI records BOLD response related to neural activity; PET measures metabolic patterns [63]. Based on such multimodality representation,
it is desirable to find useful patterns with rich semantics. For example, it is important to know which connectivity between brain regions is significant in the sense
of both structure and functionality. On the other hand,
by leveraging the complementary information embedded in the multimodality representation, better performance on disease diagnosis can be expected.
Mining bioinformatics information networks.
Bioinformatics network is a rich source of heterogeneous
information involving disease mechanisms, as shown in
Figure 7. The problems of gene-disease association and
drug-target binding prediction have been studied in the
setting of heterogeneous information networks [8, 31].
For example, in gene-disease association prediction, different gene sequences can lead to certain diseases. Researchers would like to predict the association relationships between genes and diseases. Understanding the
correlations between brain disorders and other diseases
and the causality between certain genes and brain diseases can be transformative for yielding new insights
concerning risk and protective relationships, for clarifying disease mechanisms, for aiding diagnostics and
clinical monitoring, for biomarker discovery, for identification of new treatment targets and for evaluating
effects of intervention.

10

References
1. O. Ajilore, L. Zhan, J. GadElkarim, A. Zhang, J. D.
Feusner, S. Yang, P. M. Thompson, A. Kumar, and
A. Leow. Constructing the resting state structural connectome. Frontiers in neuroinformatics, 7, 2013.
2. P. J. Basser and C. Pierpaoli. Microstructural and physiological features of tissues elucidated by quantitativediffusion-tensor MRI. Journal of Magnetic Resonance, Series B, 111(3):209–219, 1996.
3. B. Biswal, F. Zerrin Yetkin, V. M. Haughton, and J. S.
Hyde. Functional connectivity in the motor cortex of
resting human brain using echo-planar MRI. Magnetic
resonance in medicine, 34(4):537–541, 1995.
4. C. Borgelt and M. R. Berthold. Mining molecular fragments: Finding relevant substructures of molecules. In
ICDM, pages 51–58. IEEE, 2002.
5. F. Camastra and A. Petrosino. Kernel methods for
graphs: A comprehensive approach. In Knowledge-Based
Intelligent Information and Engineering Systems, pages
662–669. Springer, 2008.
6. B. Cao, L. He, X. Kong, P. S. Yu, Z. Hao, and A. B.
Ragin. Tensor-based multi-view feature selection with
applications to brain diseases. In ICDM, pages 40–49.
IEEE, 2014.
7. B. Cao, X. Kong, C. Kettering, P. S. Yu, and A. B. Ragin.
Determinants of HIV-induced brain changes in three different periods of the early clinical course: A data mining
analysis. NeuroImage: Clinical, 2015.
8. B. Cao, X. Kong, and P. S. Yu. Collective prediction
of multiple types of links in heterogeneous information
networks. In ICDM, pages 50–59. IEEE, 2014.
9. B. Cao, X. Kong, J. Zhang, P. S. Yu, and A. B. Ragin.
Mining brain networks using multiple side views for neurological disorder identification.
10. B. Cao, L. Zhan, X. Kong, P. S. Yu, N. Vizueta, L. L.
Altshuler, and A. D. Leow. Identification of discriminative subgraph patterns in fMRI brain networks in bipolar affective disorder. In Brain Informatics and Health.
Springer, 2015.
11. B. Cao, H. Zhou, and P. S. Yu. Multi-view machines.
arXiv, 2015.
12. T. L. Chenevert, J. A. Brunberg, and J. Pipe. Anisotropic
diffusion in human white matter: demonstration with mr
techniques in vivo. Radiology, 177(2):401–405, 1990.
13. H. Cheng, D. Lo, Y. Zhou, X. Wang, and X. Yan. Identifying bug signatures using discriminative graph mining.
In ISSTA, pages 141–152. ACM, 2009.
14. C. Cortes, M. Mohri, and A. Rostamizadeh. Learning
non-linear combinations of kernels. In NIPS, pages 396–
404, 2009.
15. I. Davidson, S. Gilpin, O. Carmichael, and P. Walker.
Network discovery via constrained tensor analysis of
fMRI data. In KDD, pages 194–202. ACM, 2013.
16. Z. Fang and Z. M. Zhang. Discriminative feature selection
for multi-view cross-domain learning. In CIKM, pages
1321–1330. ACM, 2013.
17. Y. Feng, J. Xiao, Y. Zhuang, and X. Liu. Adaptive unsupervised multi-view feature selection for visual concept
recognition. In ACCV, pages 343–357, 2012.
18. T. Gärtner, P. Flach, and S. Wrobel. On graph kernels:
Hardness results and efficient alternatives. In Learning
Theory and Kernel Machines, pages 129–143. Springer,
2003.
19. C. R. Genovese, N. A. Lazar, and T. Nichols. Thresholding of statistical maps in functional neuroimaging using
the false discovery rate. Neuroimage, 15(4):870–878, 2002.

B. Cao et al.
20. I. Guyon and A. Elisseeff. An introduction to variable
and feature selection. The Journal of Machine Learning
Research, 3:1157–1182, 2003.
21. I. Guyon, J. Weston, S. Barnhill, and V. Vapnik. Gene selection for cancer classification using support vector machines. Machine learning, 46(1-3):389–422, 2002.
22. L. He, X. Kong, P. S. Yu, A. B. Ragin, Z. Hao, and
X. Yang. DuSK: A dual structure-preserving kernel for
supervised tensor learning with applications to neuroimages. In SDM. SIAM, 2014.
23. T. Horváth, T. Gärtner, and S. Wrobel. Cyclic pattern
kernels for predictive graph mining. In KDD, pages 158–
167. ACM, 2004.
24. J. Huan, W. Wang, and J. Prins. Efficient mining of
frequent subgraphs in the presence of isomorphism. In
ICDM, pages 549–552. IEEE, 2003.
25. S. Huang, J. Li, J. Ye, T. Wu, K. Chen, A. Fleisher,
and E. Reiman. Identifying Alzheimer’s disease-related
brain regions from multi-modality neuroimaging data using sparse composite linear discrimination analysis. In
NIPS, pages 1431–1439, 2011.
26. A. Inokuchi, T. Washio, and H. Motoda. An aprioribased algorithm for mining frequent substructures from
graph data. In Principles of Data Mining and Knowledge
Discovery, pages 13–23. Springer, 2000.
27. B. Jie, D. Zhang, W. Gao, Q. Wang, C. Wee, and D. Shen.
Integration of network topological and connectivity properties for neuroimaging classification. Biomedical Engineering, 61(2):576, 2014.
28. N. Jin, C. Young, and W. Wang. Graph classification
based on pattern co-occurrence. In CIKM, pages 573–
582. ACM, 2009.
29. N. Jin, C. Young, and W. Wang. GAIA: graph classification using evolutionary computation. In SIGMOD, pages
879–890. ACM, 2010.
30. H. Kashima, K. Tsuda, and A. Inokuchi. Marginalized
kernels between labeled graphs. In ICML, volume 3, pages
321–328, 2003.
31. X. Kong, B. Cao, and P. S. Yu. Multi-label classification
by mining label and instance correlations from heterogeneous information networks. In KDD, pages 614–622.
ACM, 2013.
32. X. Kong, A. B. Ragin, X. Wang, and P. S. Yu. Discriminative feature selection for uncertain graph classification.
In SDM, pages 82–93. SIAM, 2013.
33. X. Kong and P. S. Yu. Brain network analysis: a data
mining perspective. ACM SIGKDD Explorations Newsletter, 15(2):30–38, 2014.
34. M. Kuramochi and G. Karypis. Frequent subgraph discovery. In ICDM, pages 313–320. IEEE, 2001.
35. G. R. Lanckriet, N. Cristianini, P. Bartlett, L. E. Ghaoui,
and M. I. Jordan. Learning the kernel matrix with
semidefinite programming. The Journal of Machine Learning Research, 5:27–72, 2004.
36. D. Le Bihan, E. Breton, D. Lallemand, P. Grenier, E. Cabanis, and M. Laval-Jeantet. Mr imaging of intravoxel incoherent motions: application to diffusion and perfusion
in neurologic disorders. Radiology, 161(2):401–407, 1986.
37. S. Maldonado and R. Weber. A wrapper method for feature selection using support vector machines. Information
Sciences, 179(13):2208–2217, 2009.
38. M. J. McKeown, S. Makeig, G. G. Brown, T.-P. Jung,
S. S. Kindermann, A. J. Bell, and T. J. Sejnowski. Analysis of fMRI data by blind separation into independent
spatial components. Human Brain Mapping, 6:160–188,
1998.

A review of heterogeneous data mining for brain disorders
39. J. Miranda, R. Montoya, and R. Weber. Linear penalization support vector machines for feature selection. In
Pattern Recognition and Machine Intelligence, pages 188–
192. Springer, 2005.
40. M. E. Moseley, Y. Cohen, J. Kucharczyk, J. Mintorovitch,
H. Asgari, M. Wendland, J. Tsuruda, and D. Norman.
Diffusion-weighted mr imaging of anisotropic water diffusion in cat central nervous system. Radiology, 176(2):439–
445, 1990.
41. S. Nijssen and J. N. Kok. A quickstart in frequent structure mining can make a difference. In KDD, pages 647–
652. ACM, 2004.
42. S. Ogawa, T. Lee, A. Kay, and D. Tank. Brain magnetic
resonance imaging with contrast dependent on blood oxygenation. Proceedings of the National Academy of Sciences,
87(24):9868–9872, 1990.
43. S. Ogawa, T.-M. Lee, A. S. Nayak, and P. Glynn.
Oxygenation-sensitive contrast in magnetic resonance
image of rodent brain at high magnetic fields. Magnetic
resonance in medicine, 14(1):68–78, 1990.
44. H. Peng, F. Long, and C. Ding. Feature selection based
on mutual information criteria of max-dependency, maxrelevance, and min-redundancy. Pattern Analysis and Machine Intelligence, 27(8):1226–1238, 2005.
45. A. Rakotomamonjy.
Variable selection using SVMbased criteria. The Journal of Machine Learning Research,
3:1357–1370, 2003.
46. S. Ranu and A. K. Singh. Graphsig: A scalable approach
to mining significant subgraphs in large graph databases.
In ICDE, pages 844–855. IEEE, 2009.
47. M. Robnik-Šikonja and I. Kononenko. Theoretical and
empirical analysis of relieff and rrelieff. Machine learning,
53(1-2):23–69, 2003.
48. M. Rubinov and O. Sporns. Complex network measures
of brain connectivity: uses and interpretations. Neuroimage, 52(3):1059–1069, 2010.
49. N. Shervashidze, P. Schweitzer, E. J. Van Leeuwen,
K. Mehlhorn, and K. M. Borgwardt. Weisfeiler-lehman
graph kernels. The Journal of Machine Learning Research,
12:2539–2561, 2011.
50. M.-D. Shieh and C.-C. Yang. Multiclass SVM-RFE for
product form feature selection. Expert Systems with Applications, 35(1):531–541, 2008.
51. A. Smalter, J. Huan, and G. Lushington. Feature selection in the tensor product feature space. In ICDM, pages
1004–1009, 2009.
52. O. Sporns, G. Tononi, and R. Kötter. The human connectome: a structural description of the human brain. PLoS
computational biology, 1(4):e42, 2005.
53. S. Sun. A survey of multi-view machine learning. Neural
Computing and Applications, 23(7-8):2031–2038, 2013.
54. J. Tang, X. Hu, H. Gao, and H. Liu. Unsupervised feature
selection for multi-view data in social media. In SDM,
pages 270–278. SIAM, 2013.
55. D. Tao, X. Li, X. Wu, W. Hu, and S. J. Maybank. Supervised tensor learning. Knowledge and Information Systems,
13(1):1–42, 2007.
56. M. Thoma, H. Cheng, A. Gretton, J. Han, H.-P. Kriegel,
A. J. Smola, L. Song, S. Y. Philip, X. Yan, and K. M.
Borgwardt. Near-optimal supervised feature selection
among frequent subgraphs. In SDM, pages 1076–1087.
SIAM, 2009.
57. N. Tzourio-Mazoyer, B. Landeau, D. Papathanassiou,
F. Crivello, O. Etard, N. Delcroix, B. Mazoyer, and
M. Joliot. Automated anatomical labeling of activations in SPM using a macroscopic anatomical parcellation of the MNI MRI single-subject brain. Neuroimage,
15(1):273–289, 2002.

11
58. M. Varma and B. R. Babu. More generality in efficient
multiple kernel learning. In ICML, pages 1065–1072,
2009.
59. H. Wang, F. Nie, and H. Huang. Multi-view clustering
and feature learning via structured sparsity. In ICML,
pages 352–360, 2013.
60. H. Wang, F. Nie, H. Huang, and C. Ding. Heterogeneous
visual features fusion via sparse multimodal machine. In
CVPR, pages 3097–3102, 2013.
61. C.-Y. Wee, P.-T. Yap, K. Denny, J. N. Browndyke,
G. G. Potter, K. A. Welsh-Bohmer, L. Wang, and
D. Shen. Resting-state multi-spectrum functional connectivity networks for identification of mci patients. PloS
one, 7(5):e37828, 2012.
62. C.-Y. Wee, P.-T. Yap, W. Li, K. Denny, J. N. Browndyke,
G. G. Potter, K. A. Welsh-Bohmer, L. Wang, and
D. Shen. Enriched white matter connectivity networks
for accurate identification of mci patients. Neuroimage,
54(3):1812–1822, 2011.
63. C.-Y. Wee, P.-T. Yap, D. Zhang, K. Denny, J. N.
Browndyke, G. G. Potter, K. A. Welsh-Bohmer, L. Wang,
and D. Shen. Identification of mci individuals using structural and functional connectivity networks. Neuroimage,
59(3):2045–2056, 2012.
64. S. Xiang, L. Yuan, W. Fan, Y. Wang, P. M. Thompson,
and J. Ye. Multi-source learning with block-wise missing
data for Alzheimer’s disease prediction. In KDD, pages
185–193. ACM, 2013.
65. C. Xu, D. Tao, and C. Xu. A survey on multi-view learning. arXiv, 2013.
66. X. Yan, H. Cheng, J. Han, and P. S. Yu. Mining significant graph patterns by leap search. In SIGMOD, pages
433–444. ACM, 2008.
67. X. Yan and J. Han. gspan: Graph-based substructure
pattern mining. In ICDM, pages 721–724. IEEE, 2002.
68. J. Ye, K. Chen, T. Wu, J. Li, Z. Zhao, R. Patel, M. Bae,
R. Janardan, H. Liu, G. Alexander, et al. Heterogeneous
data fusion for Alzheimer’s disease study. In KDD, pages
1025–1033. ACM, 2008.
69. H. Zhou, L. Li, and H. Zhu. Tensor regression with applications in neuroimaging data analysis. Journal of the
American Statistical Association, 108(502):540–552, 2013.
70. Y. Zhu, J. X. Yu, H. Cheng, and L. Qin. Graph classification: a diversified discriminative feature selection approach. In CIKM, pages 205–214. ACM, 2012.

