A novel node-level structure embedding and alignment representation of structural networks for brain disease analysis

Highlights

• We define an nSEA representation of brain networks to convey the richer node-level structural information.

• We develop an nSEAL framework for brain disease classification and group wise network analysis.

• We evaluate the performances of the proposed nSEAL method on a real schizophrenia dataset.

Abstract

Brain networks based on various neuroimaging technologies, such as diffusion tensor image (DTI) and functional magnetic resonance imaging (fMRI), have been widely applied to brain disease analysis. Currently, there are several node-level structural measures (e.g., local clustering coefficients and node degrees) for representing and analyzing brain networks since they usually can reflect the topological structure of brain regions. However, these measures typically describe specific types of structural information, ignoring important network properties (i.e., small structural changes) that could further improve the performance of brain network analysis. To overcome this problem, in this paper, we first define a novel node-level structure embedding and alignment (nSEA) representation to accurately characterize the node-level structural information of the brain network. Different from existing measures that characterize a specific type of structural properties with a single value, our proposed nSEA method can learn a vector representation for each node, thus contain richer structure information to capture small structural changes. Furthermore, we develop an nSEA representation based learning (nSEAL) framework for brain disease analysis. Specifically, we first perform structural embedding to calculate node vector representations for each brain network and then align vector representations of all brain networks into the common space for two group-level network analyses, including a statistical analysis and brain disease classifications. Experiment results on a real schizophrenia dataset demonstrate that our proposed method not only discover disease-related brain regions that could help to better understand the pathology of brain diseases, but also improve the classification performance of brain diseases, compared with state-of-the-art methods.

Introduction

Network analysis techniques can characterize brain structures and activities from the perspective of the complex system (Meyer-Lindenberg, 2010). Especially, with developments in noninvasive neuroimaging technologies, such as diffusion tensor image (DTI) and functional magnetic resonance imaging (fMRI), the brain networks based on the various neuroimaging data have been applied to the analysis of brain structures and functions. Existing studies have suggested that the structure of the brain network is related to cognitive states (Sharp, Scott, Leech, 2014, Wang et al., 2020), the nervous system diseases (Beaty, Benedek, Silvia, Schacter, 2016, Huang et al., 2020), and the injury of brain (Bullmore and Sporns, 2012).

In the brain network, nodes denote the brain regions, and edges correspond to the physical connections or pairwise similarity of rs-fMRI time series. To date, most researchers usually use some topological measures to characterize brain networks, and these studies mainly focus on three levels: (1) edge level, where the brain networks are described by using connections between nodes, such as connectivity strengths, subgraphs, and motifs (Zhang et al., 2018). (2) node level, where the brain networks are charactered by using the local topological structure of nodes, such as node degrees, local clustering coefficients, and betweenness (Rubinov and Sporns, 2010). (3) network level, where the brain networks are represented by using whole properties of the network, such as small-world characteristics. However, in the edge-level, it is difficult to design an efficient model for identifying brain diseases since a large number of variables (i.e., connections) (Yu et al., 2017). In addition, connections of brain network are usually considered as independent variables in most edge-level based methods, ignoring the relationships among them. Losing such relationships may decrease the performance of brain disease identification. On the other hand, in the network-level based methods, the local network properties are usually neglected, thus leading to less sensitive in capturing the details of the structural changes caused by brain diseases.

Compared to the edge-level based and network-level based methods, node-level based methods provide a proper scale of brain network representations (Gad Elkarim et al., 2012). Generally, node-level based methods characterize the structure of brain networks by integrating connectivity information (Wang et al., 2010). For example, the node degree is calculated by the number of edges linked to the node. It reflects the information of the local neighboring node, thus characterizing the local topological details of networks. Besides, using node-level based methods can directly identify disease-related brain regions, which is critical for understanding brain diseases (Shen et al., 2013).

The node-level measurements have been widely applied to group-level brain network analysis. For example, Hadley et al. (2016) utilized measurements of functional segregation and integration to analysis 32 unmedicated patients with schizophrenia and 32 matched healthy controls, and found reduced clustering and increased global efficiency in the schizophrenia. Liao et al. (2010) observed smaller degree of connectivity in patients of mesial temporal lobe epilepsy. Moreover, node-level measurements have been applied to identify brain diseases. For example, the local clustering coefficient has been used for mild cognitive impairment classification in several studies (Jie, Zhang, Gao, Wang, Wee, Shen, 2014, Wee, Yap, Zhang, Denny, Browndyke, Potter, Welsh-Bohmer, Wang, Shen, 2012). However, there are two disadvantages in existing studies. Firstly, these node-level measurements are often calculated based on the graph theory that characterizes node structure information with a single type of properties, and thus the measurement of each node is usually represented as a single value. As a result, the important information, such as small changes of the network, cannot be accurately characterized. These two brain networks in Fig. 1 have small structural differences. Obviously, the traditional node-level measurement (i.e., node degree) can not reflect the real structural differences of these networks. Secondly, most node measurements are usually calculated based on the local structure of nodes, ignoring the larger scale of network structure. However, existing studies found that larger scales of network structure can increase the interpretability of the hierarchy of the brain, which may help identify disease-related biomarkers and further improve the diagnosis performance of brain diseases (Tomson, Schreiner, Narayan, Rosser, Enrique, Silva, Allen, Bookheimer, Bearden, 2015, Wang, Huang, Liu, Zhang, 2019). Therefore, designing an appropriate node-level representation to characterize structure information of brain networks is still a critical and challenging task.

Recently, network embedding methods have been applied to information networks, such as social networks (Zhang et al., 2017) and language networks (Chen and Sun, 2017). These embedding methods can be categorized into two broad categories: Factorization based methods and Random Walk based methods. Briefly, the former category deals with a matrix about the connection information (e.g. the connection matrix or the Laplace matrix), and factorize this matrix to obtain the vector-based representation of nodes (Tang et al., 2015). The latter category deals with node sequences generated by using fixed-length random walks in the network. The vector-based representations are obtained by maximizing the probability of observing the last node and the next node (Perozzi et al., 2014). These methods can preserve higher-order proximity between nodes, and achieve meaningful results in the task of link predictions and node classifications. However, these methods are typically designed to the single network. Hence, it cannot be directly used in the group-level analysis due to that node vectors representations from different networks are not in the common space (Faruqui and Dyer, 2014). A feasible method to solve this problem is to learn the representation of whole networks, but classification performance of this method is not ideal since local structural changes from disease-related regions are masked when learning the global network representation (Haroon, Miller, Sanacora, 2017, Huang et al., 2019).

To overcome these problems, in this paper, we define a novel node-level structure embedding and alignment (nSEA) representation of brain networks. The main idea of our method is to map node-level structure information into a vector representation with the common space. Specifically, we first perform the skip-gram model (Levy and Goldberg, 2014) to obtain node vector representations that contain richer structure information of nodes. Then, we align the vector representations of all brain networks into the common space by optimizing the orthogonal Procrustes problem (Heusser et al., 2017). Furthermore, we develop an nSEA representation based learning (nSEAL) framework for two group-level brain network analyses, including a statistic analysis and classifications. The statistic analysis is performed on node distance vectors generated by the vector representation of each node. In the classification, we compute the pairwise distance between brain networks by jointing node vector representations and node degree vectors, and then use the k nearest neighbor (KNN) classifier to identify the label of each network. Experiment results on a real schizophrenia dataset demonstrate that our proposed method can not only outperform several state-of-the-art approaches in the brain disease diagnosis, but also discover disease-related regions for improving the understanding of schizophrenia pathology.

The contributions of our proposed method can be summarized into the following three folds: (1) we define an nSEA representation of brain networks to convey the richer node-level structural information than traditional node measurements. (2) We develop an nSEAL framework for brain disease classifications and a statistic analysis. (3) We evaluate the performances of the proposed nSEAL method on a real schizophrenia dataset.

The rest of the paper is organized as follows. In Section 2, we describe the materials used in this study and present our proposed method and learning framework. Then, we introduce experiments and results in Section 3. In Section 4, we give the discussions for the experiments and results. Finally, we conclude this paper in Section 5.