Clustering is the task to categorize a set of objects. Clustering techniques for neuroimaging applications. Alexandra Derntl and Claudia Plant*

Transcription

1 Clustering techniques for neuroimaging applications Alexandra Derntl and Claudia Plant* Clustering has been proven useful for knowledge discovery from massive data in many applications ranging from market segmentation to bioinformatics. In this study, we focus on clustering large amounts of medical image data of the human brain to identify structures of interest. Advanced Magnetic Resonance Imaging techniques enable unprecedented insights into the complex processes in the brain. However, especially for clinical studies, a huge amount of data has to be processed in order to find patterns characterizing the structure and function of the healthy brain and its alternations associated with diseases. We survey clustering methods specifically designed for neuroimaging applications such as segmentation of fiber tracks and lesions, as well as methods that can deal with multimodal imaging data. Furthermore, we will illustrate how clustering enables knowledge discovery from data by enhancing the performance of supervised techniques and discovering meaningful subgroups of subjects. The main purpose of this study is to give an introduction on how versatile clustering techniques can be applied in neuroimaging to tackle different applications where automated methods are desired John Wiley & Sons, Ltd How to cite this article: WIREs Data Mining Knowl Discov 2016, 6: doi: /widm.1174 INTRODUCTION Clustering is the task to categorize a set of objects such that similar objects are assigned to a common cluster and dissimilar objects are assigned to different clusters. Clustering is deeply rooted in human cognition as it is the basis for decision making and action. 1 Our brain constantly monitors stimuli and clusters them to form categorical decision outcomes. For example, when driving a car, we decide to turn left or right at the next intersection. Clustering is the process to map a massive amount of input data, most frequently of continuous type, to a few outcomes, most frequently of categorical type. As the ability to cluster is essential for us, researchers from data mining, machine learning, statistics, and related fields have developed a large variety of techniques for clustering data. Still, clustering is an area of highly active *Correspondence to: claudia.plant@helmholtz-muenchen.de Institute of Computational Biology, Helmholtz Zentrum München, TU München, Germany Conflict of interest: The authors have declared no conflicts of interest for this article. research as it is very challenging to come close to the clustering ability of the human brain. Nevertheless, a lot of powerful algorithms have been proposed and some of them even have been contributing to a better understanding of brain structure and function. In Neuroimaging, we have to deal with a vast amount of data that is most often complex in nature. One of the main tasks in neuroscience is image segmentation to partition the voxels into homogeneous subgroups that correspond to tissue types. Volume Points or short voxels determine a value on a regular image grid in three-dimensional space. Voxels that do not belong to any common tissue type can then be labeled as pathological structures. Similarly, grouping similar fibers returned from a process called tractography eases neuroscientists analogical work. Also, information about similar neuroimages can lead to improved diagnosis. These and many more important problems in neuroimaging turn out to be instances of clustering problems. Clustering helps to achieve a summarized view on the data because fewer groups are more easily interpreted. Besides, clustering a set of individual data points into groups can be beneficial for subsequent analysis algorithms John Wiley & Sons, Ltd Volume 6, January/February 2016

2 WIREs Data Mining and Knowledge Discovery Clustering Techniques in Neuroimaging In this study, we survey different neuroscience applications where clustering can be used in order to solve the task at hand. We will discuss applications where data provide a specific structure that makes clustering the most promising technique to solve the problem. In most applications, clustering is of course not the only option. For the task of image segmentation, there are also other common methods such as graph partitioning-based, 2 model-based, 3 and region growing-based 4 approaches, which can be applied to solve this task sufficiently. Compared to clustering, most of them need user interaction, e.g., setting a seed point or labeled training data in order to perform brain parcellation. Another advantage of clustering compared to other method is that no training data are needed. This is especially important in clinical studies where we have a limited number of patients with rare pathological conditions and want to make use of most of the data. The aim of this survey is first to provide an introduction to some neuroimaging applications for computer scientists. On the one hand, they should know how to identify a problem as an instance of clustering and be aware of available algorithms in the literature. On the other hand, new clustering algorithms designed for different purposes can be tested on their applicability to such practical problems. Second, neuroscientists should be made aware of existing computational clustering methods that can support their task at hand. Consequently, this intended audience is mirrored in the structure of the paper. Magnetic Resonance Imaging section is mostly addressed to computer scientists and the Clustering section to neuroscientists. We then describe particular applications including image segmentation, pattern discovery in medical images, and data mining of patient data that show how to select clustering methods suitable for a specific application domain. MAGNETIC RESONANCE IMAGING As the surveyed applications rely on magnetic resonance imaging (MRI) as a medical imaging technique, we briefly present its basic concepts. MRI is used in clinical environments to investigate the anatomy and physiology of the body in order to detect pathological structure or study specific functionality of the human brain. MRI scanners use magnetic fields and radio waves to form slice-wise image datasets of the brain by measuring the time it takes, e.g., hydrogen molecules to regain their previous nonmagnetic state. The technique is widely used in hospitals for medical diagnosis and in clinical studies, e.g., for staging of disease and follow-ups. The main advantage of MRI is that it does not expose the body to ionizing radiation compared to other imaging techniques like X-ray and therefore provides a noninvasive way to generate images from the human brain. The main purpose of MRI is the visualization of different tissue compartments and organs. It is not recommended to use it for imaging bones that contain much less hydrogen. Thus, bone tissue so far cannot easily be excited by the change of magnetic fields. Depending on the magnetic setting of the MRI scanner, different kinds of images can be generated in order to visualize different compartments. The resulting intensity values depend on the amount of, e.g., fat or liquids in the tissue. The magnetic settings define so-called MRI sequences that prescribe the details of the acquisition method including the duration to be measured such as T1- weighted, T2-weighted, FLAIR (e.g., Figure 1), and so on. 5 Sequences are selected according to the tissue types relevant for a clinical task. Specialized Modalities Besides visualizing organs and tissue compartments, two specialized modalities enhance the applicability of MRI. First, it is necessary to record areas of brain activity when subjects perform specific tasks to analyze disease or study the brain itself. Second, it is important to capture individual axonal fibers in the brain to ease the diagnoses of white matter diseases. Because of a lot of advances in the last decades on MRI imaging, it is possible to do both of these tasks. Functional MRI The goal of functional MRI (fmri) is the localization of neuronal activity in the brain that is triggered by stimuli such as, e.g., finger movement or visual inputs. Furthermore, with the help of fmri it is possible to label functional cerebral areas individually. The technique turns out to be useful in order to detect speech and memory processes in the brain as FIGURE 1 Illustration of common MRI sequences from left to right: T1-weighted, T2-weigthed, T1-Gadulinium, and FLAIR of one slice in the brain. Volume 6, January/February John Wiley & Sons, Ltd 23

3 wires.wiley.com/widm well as reorganization of the cortical areas, e.g., after a stroke. It is used in clinical studies and in medical application when it comes to procedure planning. For this purpose, application-specific areas get stimulated and therefore visualized. The biophysical foundation of fmri is the neuronal activity which is usually indicated by an increase of regional cerebral blood flow and volume, also called the blood oxygenation level dependenteffect (BOLD). The increasing cerebral blood flow and oxygen consumption inhibits the production of deoxyhemoglobin in the blood in the activated brain region. Deoxyhemoglobin is para-magnetic and influences the tissue-induced relaxation times. A big advantage of fmri is that it is possible to perform it in a standard MRI-scanner. The relatively low signal intensity in fmri of standard MRI scanners motivates a repeated signal measurement in an alternating fashion. Therefore, for each image voxel S we obtain a signal sequence S(t 1 ),..., S(t n ) for the whole brain volume which is shown in Figure 2 for a particular brain voxel. Figure 8 is showing characteristic brain activity in somatoform pain patients acquired from fmri data. 6,7 Diffusion Tensor Imaging Diffusion MRI, also referred to as diffusion tensor imaging (DTI), enables the above-mentioned tracking of axonal fibers. In clinical application, it is used in the study and treatment of neurological disorders, especially for the treatment of patients with acute stroke. It is able to visualize abnormalities in white matter fiber structure and provide more accurate models of brain connectivity than conventional MRI modalities. These features make it a preferred technique for the diagnoses of white matter diseases. The main advantage of this imaging modality is its ability to visualize anatomical connections between different regions of the brain in a noninvasive way. a b c d FIGURE 2 A simple interaction pattern where a, b, and c depict the data objects of the multivariate time series. Signal d represents a linear combination of the other given signals over time. (a) (b) (c) FIGURE 3 Illustration of several slices of DTI images (a) and corresponding diffusion tensor field (b) of the labeled area. Fibers extracted from tractography (c). The intensity of each voxel gives us the amount of water diffusion at a specific location. In contrast to conventional MRI modalities, the diffusion is captured by a tensor of values (Figure 3) instead of a scalar value at each voxel. The mobility of water is driven by thermal agitation and is highly dependent on its cellular neighborhood. Because of this property the findings, in DTI scans could indicate early pathological changes. It is possible, e.g., to diagnose alternation of the tissue after a stroke earlier than with conventional MRI measurements such as T1- or T2- weighted MRI scans. Like fmri imaging, DTI can also be performed in a standard MRI scanner. 8 CLUSTERING Before we discuss how to apply clustering methods to the analysis of data collected in neuroscience, we introduce relevant preliminaries. Unformally, a cluster is a collection of data objects that are similar or related to one another and dissimilar or unrelated to objects in another cluster. Clustering (sometimes also called cluster analysis) belongs to the unsupervised learning techniques because there are no predefined classes or labels that are provided by users along with the data points. Those methods stand in contrast with classification that belongs to the supervised learning techniques. There, possible labels for data points have to be assigned from a previously known finite set and are known for a training set. A typical way to apply clustering is to use it as a stand-alone tool to get insight into the data distribution, or as a preprocessing or intermediate step for other methods. In this section, we will introduce three different clustering notions: partitioning-based followed by hierarchy-based and finally density-based approaches. This aims to give a rough overview on the techniques that can be used in order to tackle problems that occur in computer-aided neuroscience John Wiley & Sons, Ltd Volume 6, January/February 2016

4 WIREs Data Mining and Knowledge Discovery Clustering Techniques in Neuroimaging Partitioning-Based Methods One of the most popular partitioning-based clustering algorithms is k-means because it partitions n observations into k clusters. The term was first introduced in Ref 9, but the principle of the method traces back to Ref 10. The k in k-means stands for the number of clusters. Besides k, the algorithm requires a metric distance function on a vector space. Usually, k-means starts with an arbitrary partitioning of the objects, i.e., data points represented by vectors into k clusters. After this initialization, the algorithm iteratively performs the following two steps until convergence: first the so-called centroids get updated, which means that for each cluster, the mean vector of its assigned objects is computed. Second, all data points are reassigned their (now) closest centroid. The algorithm converges as soon as no object changes its cluster assignment during two subsequent iterations. The objective of k-means is given by a well-defined cost function J: JS ð i,k,μ i Þ= Xk i =1 X x j 2S i k x j μ i k 2 ð1þ where (S 1,, S k ) is a partitioning of S, the data set of vectors, and μ i are the k vectors representing the centroids of the k clusters. The algorithm minimizes the sum of squared distances of the objects x j to their assigned centroids. This optimization goal coincides well with our definition of the clustering problem provided in the beginning where the objects assigned to a common cluster should be as similar as possible. The second aspect of the definition that objects in different clusters should differ as much as possible is implicitly addressed at the same time. However, finding a global minimum of the objective function is NP-hard even in the two-dimensional case. 11 The objective function is nonlinear and nonconvex, which implies that no efficient algorithm can be provided to detect the global minimum exactly. Generally, k- means converges to a local minimum of the objective function in an acceptable time frame. In many cases, the result is close to optimal and k-means is thus among the most frequently used clustering algorithms. In practice, it is useful to try different random initializations by restarting the iterative procedure and keeping the best result to overcome limitation of finding local optima only. There are many algorithms following and extending the k-means paradigm. Perhaps most notably, the expectation maximization (EM) algorithm 12 estimates the parameters for each component of a Gaussian mixture model (e.g., Figure 4(a) and (b)). Like k-means, the EM algorithm consists of two major steps that are carried out until the likelihood converges. Instead of calculating only centroids, the algorithm deals with parameters Θ =(μ i, Σ i ) i 2 {i k} where μ again represents the means (or centroids) and Σ the covariance matrix of a Gaussian distribution representing a cluster. In the first step, the probability for a data point belonging to a Gaussian component is calculated based on a fixed setting of Θ. This step is called the E-step for expectation. In the second (maximization) step, the M-step, new values for Θ are calculated to maximize the likelihood of the probabilities obtained in the E-step. Intuitively, a new centroid μ i is found by taking a weighted average of all data points proportionally to their probability of belonging to cluster i. The EM algorithm is a more statistically grounded method than similar fuzzy clustering approaches like fuzzy c- means, 13 because it can be shown that the likelihood increases in each iteration. Another category of iterative partitioning-based clustering methods, called k-medoids, is obtained by requiring that objects representing the clusters are taken from the set of data points. Centroids in k- means may instead lie in the vector space but not in the data set itself. As a consequence, also nonmetric data can be clustered. This principle underlies, e.g., the algorithms Clustering Large Applications Based (a) (b) (c) FIGURE 4 Illustration of (a) three clusters generated from different gaussian distribution, (b) Gaussian mixture model fitted with the EM algorithm on the given data points, and (c) dendrogram as output of a hierachical clustering. Volume 6, January/February John Wiley & Sons, Ltd 25

5 wires.wiley.com/widm on Randomized Search (CLARANS) 14 or Partitioning around Medoids (PAM). 15 A shortcoming of most partitioning-based methods is that parameters like the number of clusters k have to be set in advance. To address these particular problems with local optima and the parameterization, hierarchy-based and density-based clustering can be employed. 16 Hierarchical-Based Methods A fundamental algorithm for hierarchical clustering is the so-called Single Link 17 approach. This algorithm generates a dendrogram, i.e., a tree diagram of hierarchically organized clusters (Figure 4(c)). Initially, all objects are represented as a singleton cluster instance. The most similar pairs of clusters are fused in order to compose a cluster at the next higher level, which is performed in an iterative fashion. Variety is introduced by the manner of how to merge the object distances to clusters (e.g., by taking the minimal distance of all pairwise distance comparisons or the average/maximal distance). Apart from the distance function, no parameters have to be taken into account. There is no objective function to be minimized and the result is determined by the data. The runtime of Single Link is quadratic in terms of the number of objects N, which means that it is a polynomial time algorithm. A so-called chaining effect can occur where distinct clusters are fused via a chain of outliers, particularly when taking the minimal distance merging. By resorting to the average or maximal distance merging, this particular effect can be avoided. 16,18 In the next section, we are going to introduce a clustering approach related to Single Link which forms the basis of density-based cluster analysis. Density-Based Methods To augment the capabilities of hierarchical clustering schemes, information about the density of spatial regions (i.e., the number of neighboring points in a spatial neighborhood, not to be confused with probability densities) may be taken into account to differentiate core cluster points from noise. One of the most cited algorithms in densitybased clustering is called Density-Based Spatial Clustering of Applications with Noise (DBSCAN) proposed by Ester et al. 19 DBSCAN assumes that clusters represent areas of high object density which are separated by areas of lower object density. Based on this assumption, each data point is either categorized as core, border, or noise, as Figure 5 visualizes. " Core obj. Noise obj. Density-connected objects MinPts = 3 FIGURE 5 Illustration of the types of points DBSCAN determines. In this example, a core object has to have at least MinPts = 3 objects in its ε-neighborhood. To perform this distinction, a distance measure d, a maximal cluster distance ε to define neighborhoods, and a minimal number of ε-adjacent points (MinPts) is required. A data point x i is a core object if and only if at least MinPts points are in its ε-neighborhood with respect to d. It is a border point if it is not core but has at least one core point in its ε-neighborhood. Otherwise, it is considered a noise object. If one object x i is in the ε-neighborhood of a core-object x j, then x i is said to be directly density reachable from x j. The relation density connectivity is then defined as the symmetric, transitive closure of direct density reachability. A density-based (ε, MinPts)-cluster is consequently defined as a maximal set of density-connected objects. It can be proved that a(ε, MinPts)-cluster can be detected by collecting all density reachable objects starting from an arbitrary core object which is implemented in DBSCAN. More specifically, a graph of core objects linked by their ε-neighborhood is built. Border objects are connected to the core object they are most connected to and noise objects are ignored. Each cluster then corresponds to a strongly connected component of the graph. In contrast to k-means, DBSCAN results in a disconnected partitioning of the objects into clusters. It is furthermore nonhierarchical. Even the number of clusters k does not have to be parametrized in advance and the approach is more robust against noise objects and the shape of the cluster. By contrast, k-means is only able to detect Gaussian-like, in other words, convex clusters. The number of clusters found by DBSCAN depends on the parameters MinPts and ε. There are settings where the algorithm is hard to parameterize correctly. For instance, this is the case if different object densities appear in various regions of the data space or if a cluster structure turns out be hierarchical. In order to deal with these issues, the approach Ordering Points to Identify the Clustering Structure (OPTICS) by Ankerst et al. 20 amends DBSCAN in order to act in a hierarchical manner. It combines ideas from density-based and hierarchical John Wiley & Sons, Ltd Volume 6, January/February 2016

6 WIREs Data Mining and Knowledge Discovery Clustering Techniques in Neuroimaging approaches. The purpose of OPTICS is to estimate the clusters even if ε is changing during a single iteration among all data points. OPTICS results in a reachability plot where a hierarchical cluster structure gets visualized with a linear order of the data points. If the parameter MinPts is set to 1, OPTICS converges to SingleLink. However, OPTICS can avoid chaining effect previously mentioned by setting MinPts to larger values. 16,18 APPLICATION IN NEUROSCIENCE In this section, we discuss applications of clustering in neuroscience by using the image output of an MRI-scanner. We will first describe how clustering can be applied to image segmentation for fiber tracking and lesion detection. Then, we will go on with techniques to discover knowledge in fmri images. Finally, we will discuss data-mining applications in studies like Alzheimer s disease (AD) in order to find similar subgroups of patients or enhancing the performance of supervised techniques. Image Segmentation Image segmentation is the task of partitioning an image into mutually exclusive regions. Delineating structures of interest can be considered as one of the most important processes in medical research studies. Even after years of intensive research, segmentation remains still a challenging task. This is indebted due to varying image contents with different intensity values, image noise, non-uniform object-of-interest, and other factors. Many algorithms and techniques for image segmentation are available but there is still a need to develop efficient, fast techniques for medical image segmentation ranging from fiber tracking to lesion detection. Fiber Tracking Fiber Tracking is a useful tool, e.g., for procedure planning when it comes to the surgical extraction of tumor tissue close to important neural pathways. This applies especially to tumors close to the speech, visual and motor cortex. The fibers usually get rendered before the actual procedure to estimate in advance how to enter the tumor area in the least invasive manner. 21 This is performed by first preprocessing the image including registration and motion compensation. Usually, a large number of individual fibers get extracted but the main task is to identify meaningful groups of fibers from the Diffusion- Weighted Images (DWIs). In practice, excess fiber tracks get filtered out by an expert using visual dissection. To do so, they mark a specific region of interest (ROI) in order to detect the fibers passing through this target region by incorporating their domain knowledge. This turns out to be timeconsuming and also biased, especially for different patients. This fact constitutes the main motivation for using clustering algorithms to tackle the problem of grouping individual fiber tracks more efficiently and more accurately. A very important prerequisite for any clustering algorithm is the right choice of an effective similarity measure over the set of fibers. Because of the occurrence of partial volume effects and noise, the fibers calculated by tractography include incomplete fibers or outliers that have to be eliminated. Fiber clustering is useful in order to focus more on the relevant clusters or in the case of fiber tracking, on bundles instead of individual outliers such as incomplete fibers or noise. Density-based cluster approaches therefore could be used to robustly extract meaningful fibers as mentioned in Density-Based Methods section. They are more robust against outliers and the shape of the clusters. Two recently developed methods make use of these attributes. 22,23 Those methods use an adapted DBSCAN approach to track fibers. In Ref 23, the authors designed an adapted dynamic time warping (DTW) in order to define fiber similarity to capture local similarity among fibers belonging to a common bundle but having different start and end points. Two years after, that Ref 22 provides a technique called Warped Longest Common Subsequence technique (WLCS) to measure the similarity among fibers. According to these evaluation results, WLCS is more accurate and more robust to noise and local time shifting within fibers than other similarity measures (Figure 6). Both methods provide a lower bounding technique in order to deal with the time complexity of fiber similarity to speed up computation. The reason why both methods chose a densitybased clustering approach is that those techniques are able to deal better with noisy fibers. Those may be caused by limitations of imaging or by the previously applied tractography of the fibers. The big advantage of density-based methods hereby is that noisy fibers can be easily excluded from any cluster that turns out to be beneficial for further processing. In contrast to density-based approaches, other clustering notions can be applied, e.g., spectral clustering 24 or hierachical clustering 25 to perform fiber tracking. Lesion Detection Pathological structures such as brain lesions appearing in multiple sclerosis (MS), 26 Glioma 27 and Volume 6, January/February John Wiley & Sons, Ltd 27

7 wires.wiley.com/widm Ground truth Level 1 Level 2 Level 3 Level 4 Level 5 Level 6 Level 7 Level 8 FIGURE 6 Illustration of fibers, on the very left the ground truth fibers are shown and the different levels of the fiber tracking using the approach of Mai et al. 22 The very last level has similar fiber bundles found according to the ground truth annotation. Stroke 28 can lead to severe neurological damage. One important characteristic of such lesions is that they most often appear hyper-intense, i.e., bright in FLAIR (Figure 7), or T1 Gadolinium MR images and hypo-intense, i.e., dark in T1- or T2-weighted images. The brain consists of three main tissue types: white matter (WM), gray matter (GM), and cerebrospinal fluid (CSF). Those tissues can be identified in T1-weighted images or similar MRI modalities (i.e. sequences). For the clustering task, it is beneficial to rely on a combination of different images from different modalities, since there is no universal modality which covers all required image attributes. In clinical practice, it is common that radiologists combine different MR images for their diagnosis in order to get a better overview of the physical condition of the brain. Some algorithms apply clustering in a sense that they try to detect the healthy tissue compartments such as WM, GM, and CSF to perform image segmentation tasks, in order to find lesions. Knowledge about the distribution of healthy tissue compartments is often important in order to distinguish them from the pathological ones. Depending on the lesion type, pathological voxels may form a proper cluster themselves 28 or just appear as uniform outliers. 26 For detecting the parameters of the intensity distributions of WM, GM, CSF, most methods employ so-called tissue atlases that represent an average segmentation among a certain amount of patients which is then converted into a probabilistic map for the different tissue types. Certain preprocessing steps are required. One important step is the coregistration where the images get aligned spatially. This usually constitutes of an affine registration since the input modalities all belong to the same patient. The next step is the so called bias-field correction which is performed in order to remove spatially varying low-frequencies FIGURE 7 Illustration of an extensive stroke lesion in MRI FLAIR brain scan labeled in blue which appear hyper-intense. which could disturb the segmentation results. The final step is skull-stripping which is the computationally extraction of the brain voxels in order to remove the skull as well as eyes and other nonbrain structures that could have a bad influence on the segmentation result. The advantage of unsupervised methods compared to supervised approaches is that no training set or ground truth is needed to perform the segmentation task. This makes the algorithms more flexible when working with different modalities. However, sometimes some parameters have to be configured in advance. 26 Supervised notions turn out to reliably achieve a reasonable high accuracy. 29 Sometimes supervised methods are enhanced by unsupervised techniques to achieve even higher accuracy if sufficient labeled training data is available. 30 Most of the methods still need postprocessing steps because they do not consider global spatial information except for the tissue atlases. 26,28 Therefore, false positives need to be eliminated. In the last years, brain lesion segmentation challenges are conducted to evaluate automated segmentation notions against each other among different research groups on the same datasets. 31 This is beneficial as most segmentation studies are evaluated independently of each other. They are conducted on different datasets with different ground truth labels where the results cannot be easily repeated. In the next section, we are going to discuss pattern discovery in images acquired by fmri John Wiley & Sons, Ltd Volume 6, January/February 2016

8 WIREs Data Mining and Knowledge Discovery Clustering Techniques in Neuroimaging Pattern Discovery in fmri and DTI Images Pattern discovery in fmri can be seen as addressing the problem of clustering fmri time series in groups of voxels with similar activation. fmri data are high-dimensional in nature as each voxel corresponds to a number of signals in the time domain. Clustering approaches are applied in order to visualize the structure of interest that is often composed of many voxels of a specific brain region. In such cases, brain parcellations are applied to divide the brain into nonoverlapping areas. There are three typical ways for finding those areas in the literature. One way would be to define a ROI that may lead to other regions being ignored. Therefore, those methods heavily rely on the choice of ROI. Other methods for brain parcellation use brain atlases, which give a certain labeling of specific brain structure. However, atlases are often inconsistent among each other. A further disadvantage possibly leading to unreliable results is atlases that do not fit the given data well. Therefore, data-driven parcellation aims to overcome these previously mentioned drawbacks. They do not rely on any previously defined brain structures. The most popular parcellation techniques are, e.g., mixture models, 32,33 variants of k-means, or hierarchical clustering. 37,38 Parcellations can be calculated from so called dictionary learning techniques such as various notions of independent component analysis (ICA) and principal component analysis (PCA). Approaches based on linear mixing approaches usually need other probabilistic models to calculate brain parcellations than clustering. However, Refs 39 and 40 used clustering in order to improve the reliability of ICA approaches. One example of k-means based clustering was conducted by Plant et al. 35,36 They clustered interaction patterns to find characteristic patterns in patients suffering from somatoform pain disorder which differs from healthy controls (Figure 8). The discovery of functional homogeneous regions in the brain is a difficult task. However, datadriven methods based on clustering offer promising alternative to atlas and ROI-based approaches for clinical studies. 42 Another method to visualize fmri and DTI images is based on graph-theoretic approaches. These approaches visualize the interactions between the brain regions in fmri and DTI to display anatomical patterns in the brain. Those graph structures are acquired by different computational models. In order to compare brain graphs, e.g., of healthy controls against patient with schizophrenia usually the coherent cluster structures in the graph gets visualized. Cluster structures are depicted by clique-like Patient-cluster Contol-cluster FIGURE 8 Illustration of activated brain regions in healthy controls compared to patients with somatoform pain. arrangement in the graph. An extensive review on the topic of brain graphs has been published by Ref 43. In the next section, we are going to discuss data-mining techniques particularly designed for population studies. Data Mining in Research Studies Data-mining approaches provide techniques to extract knowledge from millions of data points with regard to reduce it to a limited number of patterns. These are used to obtain a sufficiently high accuracy in predicting or diagnosing, i.e., neurological diseases from different cases such as AD, Schizophrenia, Parkinson s, and Autism. The main target in those medical applications is the reliability of the methods in terms of accuracy and statistical significance of the output, particularly for making meaningful predictions. Enhancing the Performance of Supervised Techniques A useful application for combining and enhancing supervised techniques with clustering in order to achieve high accuracy was proposed in Refs In Ref 46, a patient-specific prediction of AD at an early stage such as mild cognitive impairment (MCI) was proposed. This is indicated by atrophical alternation in the cortical as well as subcortical areas of the brain which can reliably be detected in MRI scans. The authors proposed a data-mining framework that consists of three coherent steps to predict the conversion from MCI to AD. It starts with a feature selection process based on information gain (IG) in order to select the most discriminative brain regions when predicting AD from MCI patients. Those particular areas are then used as an input for DBSCAN to formulate clusters of the most similar brain voxels. In the third and final step, the output of DBSCAN serves as an input for three different Volume 6, January/February John Wiley & Sons, Ltd 29

9 wires.wiley.com/widm supervised techniques (Figure 9). At the validation stage of the framework, the discriminatory power of the learned patterns is evaluated using a disconnected test set. Claudia et al. 46 were able to predict the conversion from MCI to AD over healthy controls, AD and MCI patients with high accuracy. In the set of MCI patients, there some subjects converted from this specific stage to AD after some follow-ups in the upcoming years. Their data served as a ground truth of the presented framework. Another AD-related study conducted by Martin et al., 44 which uses density-based clustering with DBSCAN after the feature selection process with IG to improve the performance of classification on white-matter degeneration among AD patients in DTI images. These authors were able to show that the high accuracy of the results of their proposed framework was invariant to images acquired from different MRI scanners. Hui et al. 47 conducted a similar study. They also enhanced supervised techniques but on restingstate fmri images of patients. They performed this by training a classifier based on a fuzzy C-means (Clustering section) to identify schizophrenic patients among healthy controls. Similar studies were conducted by Focke et al. 45 for patients with various kinds of degenerative diseases such as idiopathic Parkinson syndrome, multiple systems atrophy, and progressive supranuclear palsy. They first used a MCI e.g., With SVM Healthy elderly FIGURE 9 Illustration of SVM in order to distinguish between healthy and MCI patients. clustering notion implemented in SPM 48 to cluster voxels belonging to specific main brain tissues. The output of the quantified tissue types was used as an input for a classifier where they were able to identify some of the diseases. For instance, controls with PSP could be separated from IPS patients using MRI scans with a decent or even high accuracy. This is just a small portion of the studies which were conducted to identify different neurodegenerative diseases from MRI scans of patients that combine unsupervised and supervised techniques. Discovering Subgroups of Subjects Discovering subgroups among patients is important in clinical studies. Clustering is typically used in combination with statistical analysis to identify subtypes of particular neurogenerative diseases. Examples include Parkinson, 49 Autism, 50 Schizophrenia, 51 and Alzheimer s disease. 52 The investigation of Erro et al. 49 focuses on newly diagnosed untreated patients with Parkinson s disease. The clustering was conducted on demographical, motor- and nonmotorical data sets. The data was clustered by k-means in combination with the Gower method in order to deal with mixed data such as continuous and categorical data. Indeed, four distinct groups of patients have been found using this method. Similarly, Hrdlicka et al. 50 aimed to find subtypes of patients with autism. This was achieved by a hierarchical clustering on MRI scans. Categorical data, e.g., frequency of epilepsy, types of EEG, and genetic data was used for subsequent statistical analysis of the clusters. Lee et al. 51 proposed a method for paternal age-related schizophrenia (PARS), which is a subgroup of schizophrenia. They used a k-means clustering notion to generate hypotheses about differences between PARS and other types of schizophrenia. Using this approach, they could identify that PARS cases differ from other patients with schizophrenia. In particular, discrepancies between verbal and performance intelligence occurred more frequently in clusters of PARS subjects. Pasquini et al. 52 investigated similarities between healthy elderly people, elderly patients with AD or MCI, and healthy young people. The authors used data from resting-state fmri brain scans of younger and older healthy persons and patients diagnosed with MCI and AD dementia. They used explicit measures of intrinsic brain activity with different hierarchical clustering methods. The authors found that, independently of the applied techniques and involved areas, healthy older subjects intrinsic brain activity was consistently more similar to AD patients than to younger controls John Wiley & Sons, Ltd Volume 6, January/February 2016

10 WIREs Data Mining and Knowledge Discovery Clustering Techniques in Neuroimaging Furthermore, clustering can be used to differentiate not only among subtypes of one particular disease but also to differentiate different disorders. For instance, Du et al. 53 tried to investigate biomarkers from resting-state fmri to distinguish between common psychiatric disorders such as schizophrenia, bipolar disorder, and schizoaffective disorder. Also techniques to find relationships between them were explored. The authors found specific brain regions that turn out to be useful to distinguish types of mental disorders. Their method involved a combination of different techniques such as support vector machines (SVM), hierarchical clustering, and an approach called t-distributed stochastic neighbor embedding (t-sne) projection. 54 To sum up, successful results from different studies justify that clustering provides a powerful methodology to find subgroups of subjects for various neurological diseases and should be considered for future studies. Validation of Clustering Algorithms In previous sections, we talked about different ways to obtain knowledge from data by using various clustering approaches. One of the main questions when we perform clustering in medicine is how to verify or validate clustering results. Expert knowledge and interdisciplinary work play an important role to validate the result of medical research studies. To avoid certain bias of one particular expert rater, it is common to combine different expert labels. For instance, Landman et al. 55 proposed a tool called simultaneous truth and performance level estimation (STAPLE) to robustly fuse expert labels and calculate its reliability. In image segmentation, the Dice coefficient 56 or Hausdorff distance 57 are commonly used to measure the amount of coverage between expert label and segmentation. The Rand index 58 or derivates of it 59 are used to compare the clustering outcome. Some applications do not require any external evaluation criteria like the Rand index. This is the case when clustering is intended to provide a summarized view on the data for interpretation of expert raters (e.g., Discovering Subgroups of Subjects section). However, validation of clustering remains an active topic in data mining research. 60 The results of these efforts will improve validation in the neuroscience context as well. CONCLUSION AND FUTURE WORK Starting from pioneering works in the early seventies of the last century, 61 magnetic resonance imagining is opening up novel opportunities to study brain structure and function with an ever increasing accuracy. Because the early variants of the algorithm K- means dating back to the fifties of the last century, 62 a large variety of advanced clustering methods have been proposed. A search for the keyword clustering in the leading computer science bibliography yields almost 25,000 hits in August 2015 with many more to come. The approaches summarized in this survey demonstrate the potential for synergies between both research areas which is far from being fully exploited. We identify six challenges for interdisciplinary research that are highly rewarding to be tackled in the upcoming years: 1. deeper integration of clustering into the workflow of knowledge discovery from neuroimaging data; 2. clustering of heterogeneous modalities; 3. integrating domain knowledge and further data sources; 4. transferring the discovered patterns to novel studies; 5. exploiting the opportunities of modern hardware; and 6. bridging the gap between research and clinical practice. Clustering usually is only a single step in a complex data analysis workflow starting from preprocessing techniques like coregistration and de-noising until the interpretation of the findings by neuroscientists. Each method of the workflow and also every clustering technique are based on specific assumptions or require parametrization. It is essential to investigate the interplay and dependencies of clustering with the other steps in the analysis workflow. In future work, clustering should be more tightly integrated into the overall workflow. For example, for the identification of fiber bundles from DTI images it would be desirable to integrate fiber clustering and fiber tracking. Both steps can profit much from another. Even a rough clustering of fiber bundles is useful to distinguish between signal and noise in fiber tracking. The approximate characteristics like length and shape of the fibers greatly facilitate their clustering. In an iterative algorithm, the major clusters corresponding to the fiber bundles and the characteristics of each single fiber could emerge simultaneously. Most existing approaches apply clustering on a single imaging modality only. In many studies, multiple modalities like fmri, DTI, PET, and structural Volume 6, January/February John Wiley & Sons, Ltd 31

11 wires.wiley.com/widm MRI are available for each subject. We are currently just beginning to integrate information from different images. For lesion detection, it is already common practice to integrate structural MRI images taken with different contrasts 26,28 (see Lesion Detection section). First approaches even integrate different modalities (see Discovering Subgroups of Subjects section). Integrating multiple imaging modalities is very challenging as they rely on different basic physical principles and therefore capture images of completely different semantics. Typically, the resolution and the signal-to-noise ratio also differ. We need flexible approaches simultaneously extracting information relevant for clustering for each image and combining the information in different images. Probably, it is necessary to consider beyond the images also domain knowledge, e.g., anatomical atlases or the feedback of neuroscience experts. For integrating side information into clustering, supervised and semisupervised techniques have been proposed (e.g., Refs 63 66). Most of these approaches (e.g. Ref 66) consider besides the data information in the form of instance-level constraints. The algorithm aims at assigning each pair of objects with a must-link constraint to a common cluster and each pair of objects with a cannot-link constraint to different clusters. Instance-level constraints are useful to model user feedback. Some pairs of objects are shown to the user together with the request to give must-link or cannotlink feedback. Because the user can only give feedback on a limited number of pairs, active learning approaches aim at determining those points for which feedback is most urgently needed. 67 The pairs identified by active learning approaches are usually close to the cluster borders. Constraints have not only been studied on the instance level but also on the cluster level. 63 The user can indicate if a cluster should be split or two clusters should be merged. Other approaches (e.g. Ref 64) consider supervision in the form of labels that are available the data objects. This type of supervision is more appropriate than constraints to integrate the information of an anatomical brain atlas into clustering. We expect much benefits from applying and extending semisupervised clustering algorithms in the context of neuroimaging applications. In this study, we focused on neuroimaging data. Current neuroscience studies however are not restricted to collect image data. Usually, a wide range of data sources of heterogeneous data types are collected to characterize a single subject: neuropsychological testing, demographic data, biomarkers, and genetic information. As an ultimate goal, we want to integrate all the available information. Clustering of heterogeneous data has recently attracted considerable attention Some approaches focus on clustering data of numerical and categorical type, addressing the problem from a Bayesian 68 or an information-theoretic perspective. 69,70 These approaches are applicable to demographic data usually consisting of a mix of numerical and categorical variables. In graph mining, a wide range of techniques for the analysis of heterogeneous information networks, i.e., graphs with several types of nodes and edges have been proposed (e.g., Ref 71). Other approaches consider attributed graphs where additional numerical or categorical attributes are available for the nodes (e.g., Ref 72). As neuroimaging data are frequently modeled as a graph with nodes representing brain regions and edges representing interactions, 73 the extension of such approaches to support neuroscience questions is very promising. We expect many interesting contributions on the topic of clustering heterogeneous neuroscience data in the coming years. We just started integrating information and it is a long way toward exploiting all available information. A central limitation shared by most neuroimaging studies is that the number of subjects is limited, often in order of magnitude of several tens and rarely several hundreds. For each subject, lots of information are available and with clustering we aim at discovering complex patterns within the images and within the group of subjects. To enhance the validity of the results, we should consider transfer learning approaches in future work (see Ref 74) for a survey. Approaches to transfer clustering consider besides the data of the current study also the information learned in previous studies on different collectives. The data available in current neuroimaging studies are massive in volume. The clustering algorithms discussed in this study and our ideas for novel techniques introduced in this section require support by the computing power of modern hardware. Some recent approaches provide solutions for massively parallel clustering on graphic processing units (e.g., Ref 75) on multicore machines (e.g., Ref 76), and distributed environments (e.g., Ref 77). In future work, we need to develop adaptive clustering approaches considering the memory hierarchy of the device and exploiting parallelism at different levels. Highperformance clustering approaches will also contribute toward bridging the gap between research and clinical practice. Today, clustering is mainly applied to analyze the data of research studies. A runtime of minutes or hours, even days is acceptable because it takes a very long time to recruit subjects and acquire John Wiley & Sons, Ltd Volume 6, January/February 2016