A review of heterogeneous data mining for brain disorder identification <s> Kernel learning on graphs <s> As most ‘real-world’ data is structured, research in kernel methods has begun investigating kernels for various kinds of structured data. One of the most widely used tools for modeling structured data are graphs. An interesting and important challenge is thus to investigate kernels on instances that are represented by graphs. So far, only very specific graphs such as trees and strings have been considered. <s> BIB001 </s> A review of heterogeneous data mining for brain disorder identification <s> Kernel learning on graphs <s> A new kernel function between two labeled graphs is presented. Feature vectors are defined as the counts of label paths produced by random walks on graphs. The kernel computation finally boils down to obtaining the stationary state of a discrete-time linear system, thus is efficiently performed by solving simultaneous linear equations. Our kernel is based on an infinite dimensional feature space, so it is fundamentally different from other string or tree kernels based on dynamic programming. We will present promising empirical results in classification of chemical compounds. <s> BIB002 </s> A review of heterogeneous data mining for brain disorder identification <s> Kernel learning on graphs <s> With applications in biology, the world-wide web, and several other areas, mining of graph-structured objects has received significant interest recently. One of the major research directions in this field is concerned with predictive data mining in graph databases where each instance is represented by a graph. Some of the proposed approaches for this task rely on the excellent classification performance of support vector machines. To control the computational cost of these approaches, the underlying kernel functions are based on frequent patterns. In contrast to these approaches, we propose a kernel function based on a natural set of cyclic and tree patterns independent of their frequency, and discuss its computational aspects. To practically demonstrate the effectiveness of our approach, we use the popular NCI-HIV molecule dataset. Our experimental results show that cyclic pattern kernels can be computed quickly and offer predictive performance superior to recent graph kernels based on frequent patterns. <s> BIB003 </s> A review of heterogeneous data mining for brain disorder identification <s> Kernel learning on graphs <s> In this article, we propose a family of efficient kernels for large graphs with discrete node labels. Key to our method is a rapid feature extraction scheme based on the Weisfeiler-Lehman test of isomorphism on graphs. It maps the original graph to a sequence of graphs, whose node attributes capture topological and label information. A family of kernels can be defined based on this Weisfeiler-Lehman sequence of graphs, including a highly efficient kernel comparing subtree-like patterns. Its runtime scales only linearly in the number of edges of the graphs and the length of the Weisfeiler-Lehman graph sequence. In our experimental evaluation, our kernels outperform state-of-the-art graph kernels on several graph classification benchmark data sets in terms of accuracy and runtime. Our kernels open the door to large-scale applications of graph kernels in various disciplines such as computational biology and social network analysis. <s> BIB004 </s> A review of heterogeneous data mining for brain disorder identification <s> Kernel learning on graphs <s> In this paper, a high-dimensional pattern classification framework, based on functional associations between brain regions during resting-state, is proposed to accurately identify MCI individuals from subjects who experience normal aging. The proposed technique employs multi-spectrum networks to characterize the complex yet subtle blood oxygenation level dependent (BOLD) signal changes caused by pathological attacks. The utilization of multi-spectrum networks in identifying MCI individuals is motivated by the inherent frequency-specific properties of BOLD spectrum. It is believed that frequency specific information extracted from different spectra may delineate the complex yet subtle variations of BOLD signals more effectively. In the proposed technique, regional mean time series of each region-of-interest (ROI) is band-pass filtered ( Hz) before it is decomposed into five frequency sub-bands. Five connectivity networks are constructed, one from each frequency sub-band. Clustering coefficient of each ROI in relation to the other ROIs are extracted as features for classification. Classification accuracy was evaluated via leave-one-out cross-validation to ensure generalization of performance. The classification accuracy obtained by this approach is 86.5%, which is an increase of at least 18.9% from the conventional full-spectrum methods. A cross-validation estimation of the generalization performance shows an area of 0.863 under the receiver operating characteristic (ROC) curve, indicating good diagnostic power. It was also found that, based on the selected features, portions of the prefrontal cortex, orbitofrontal cortex, temporal lobe, and parietal lobe regions provided the most discriminant information for classification, in line with results reported in previous studies. Analysis on individual frequency sub-bands demonstrated that different sub-bands contribute differently to classification, providing extra evidence regarding frequency-specific distribution of BOLD signals. Our MCI classification framework, which allows accurate early detection of functional brain abnormalities, makes an important positive contribution to the treatment management of potential AD patients. <s> BIB005 </s> A review of heterogeneous data mining for brain disorder identification <s> Kernel learning on graphs <s> Rapid advances in neuroimaging techniques have provided an efficient and noninvasive way for exploring the structural and functional connectivity of the human brain. Quantitative measurement of abnormality of brain connectivity in patients with neurodegenerative diseases, such as mild cognitive impairment (MCI) and Alzheimer's disease (AD), have also been widely reported, especially at a group level. Recently, machine learning techniques have been applied to the study of AD and MCI, i.e., to identify the individuals with AD/MCI from the healthy controls (HCs). However, most existing methods focus on using only a single property of a connectivity network, although multiple network properties, such as local connectivity and global topological properties, can potentially be used. In this paper, by employing multikernel based approach, we propose a novel connectivity based framework to integrate multiple properties of connectivity network for improving the classification performance. Specifically, two different types of kernels (i.e., vector-based kernel and graph kernel) are used to quantify two different yet complementary properties of the network, i.e., local connectivity and global topological properties. Then, multikernel learning (MKL) technique is adopted to fuse these heterogeneous kernels for neuroimaging classification. We test the performance of our proposed method on two different data sets. First, we test it on the functional connectivity networks of 12 MCI and 25 HC subjects. The results show that our method achieves significant performance improvement over those using only one type of network property. Specifically, our method achieves a classification accuracy of 91.9%, which is 10.8% better than those by single network-property-based methods. Then, we test our method for gender classification on a large set of functional connectivity networks with 133 infants scanned at birth, 1 year, and 2 years, also demonstrating very promising results. <s> BIB006
In the setting of supervised learning on graphs, the target is to train a classifier using a given set of graph data D ¼ fðG i ; y i Þg n i¼1 , so that we can predict the labelŷ 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 cannot 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 BIB005   . 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 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 multikernel SVM, Wee et al. integrate information from DTI and fMRI and achieve accurate early detection of brain abnormalities  . 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  . 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 BIB004 . For example, product graph kernel is based on the idea of counting the number of walks in product graphs BIB001 ; marginalized graph kernel works by comparing the label sequences generated by synchronized random walks of labeled graphs BIB002 ; and cyclic pattern kernels for graphs count pairs of matching cyclic/tree patterns in two graphs BIB003 . 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 BIB006 . 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, Weisfeiler-Lehman subtree kernel BIB004 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.