Meiby Ortiz-Bouza

Meiby Ortiz-Bouza, Selin Aviyente

Networks are commonly used to model complex systems. The different entities in the system are represented by nodes of the network and their interactions by edges. In most real life systems, the different entities may interact in different ways necessitating the use of multiplex networks where multiple links are used to model the interactions. One of the major tools for inferring network topology is community detection. Although there are numerous works on community detection in single-layer networks, existing community detection methods for multiplex networks mostly learn a common community structure across layers and do not take the heterogeneity across layers into account. In this paper, we introduce a new multiplex community detection method that identifies communities that are common across layers as well as those that are unique to each layer. The proposed method, Multiplex Orthogonal Nonnegative Matrix Tri-Factorization, represents the adjacency matrix of each layer as the sum of two low-rank matrix factorizations corresponding to the common and private communities, respectively. Unlike most of the existing methods, which require the number of communities to be pre-determined, the proposed method also introduces a two stage method to determine the number of common and private communities. The proposed algorithm is evaluated on synthetic and real multiplex networks, as well as for multiview clustering applications, and compared to state-of-the-art techniques.

Meiby Ortiz-Bouza, Selin Aviyente

Many real-world systems can be represented as graphs where the different entities in the system are presented by nodes and their interactions by edges. An important task in studying large datasets with graphical structure is graph clustering. While there has been a lot of work on graph clustering using the connectivity between the nodes, many real-world networks also have node attributes. Clustering attributed graphs requires joint modeling of graph structure and node attributes. Recent work has focused on combining these two complementary sources of information through graph convolutional networks and graph filtering. However, these methods are mostly limited to lowpass filtering and do not explicitly learn the filter parameters for the clustering task. In this paper, we introduce a graph signal processing based approach, where we learn the parameters of Finite Impulse Response (FIR) and Autoregressive Moving Average (ARMA) graph filters optimized for clustering. The proposed approach is formulated as a two-step iterative optimization problem, focusing on learning interpretable graph filters that are optimal for the given data and that maximize the separation between different clusters. The proposed approach is evaluated on attributed networks and compared to the state-of-the-art methods.

Meiby Ortiz-Bouza, Selin Aviyente

Multiplex networks have emerged as a promising approach for modeling complex systems, where each layer represents a different mode of interaction among entities of the same type. A core task in analyzing these networks is to identify the community structure for a better understanding of the overall functioning of the network. While different methods have been proposed to detect the community structure of multiplex networks, the majority deal with extracting the consensus community structure across layers. In this paper, we address the community detection problem across two closely related multiplex networks. For example in neuroimaging studies, it is common to have multiple multiplex brain networks where each layer corresponds to an individual and each group to different experimental conditions. In this setting, one may be interested in both learning the community structure representing each experimental condition and the discriminative community structure between two groups. In this paper, we introduce two discriminative community detection algorithms based on spectral clustering. The first approach aims to identify the discriminative subgraph structure between the groups, while the second one learns the discriminative and the consensus community structures, simultaneously. The proposed approaches are evaluated on both simulated and real world multiplex networks.

Meiby Ortiz-Bouza, Duc Vu, Abdullah Karaaslanli et al.

Over the past two decades, tools from network science have been leveraged to characterize the organization of both structural and functional networks of the brain. One such measure of network organization is hub node identification. Hubs are specialized nodes within a network that link distinct brain units corresponding to specialized functional processes. Conventional methods for identifying hub nodes utilize different types of centrality measures and participation coefficient to profile various aspects of nodal importance. These methods solely rely on the functional connectivity networks constructed from functional magnetic resonance imaging (fMRI), ignoring the structure-function coupling in the brain. In this paper, we introduce a graph signal processing (GSP) based hub detection framework that utilizes both the structural connectivity and the functional activation to identify hub nodes. The proposed framework models functional activity as graph signals on the structural connectivity. Hub nodes are then detected based on the premise that hub nodes are sparse, have higher level of activity compared to their neighbors, and the non-hub nodes' activity can be modeled as the output of a graph-based filter. Based on these assumptions, an optimization framework, GraFHub, is formulated to learn the coefficients of the optimal polynomial graph filter and detect the hub nodes. The proposed framework is evaluated on both simulated data and resting state fMRI (rs-fMRI) data from Human Connectome Project (HCP).