Abdullah Karaaslanli

Mohammad Eini, Abdullah Karaaslanli, Vassilis Kalantzis et al.

Several graph data mining, signal processing, and machine learning downstream tasks rely on information related to the eigenvectors of the associated adjacency or Laplacian matrix. Classical eigendecomposition methods are powerful when the matrix remains static but cannot be applied to problems where the matrix entries are updated or the number of rows and columns increases frequently. Such scenarios occur routinely in graph analytics when the graph is changing dynamically and either edges and/or nodes are being added and removed. This paper puts forth a new algorithmic framework to update the eigenvectors associated with the leading eigenvalues of an initial adjacency or Laplacian matrix as the graph evolves dynamically. The proposed algorithm is based on Rayleigh-Ritz projections, in which the original eigenvalue problem is projected onto a restricted subspace which ideally encapsulates the invariant subspace associated with the sought eigenvectors. Following ideas from eigenvector perturbation analysis, we present a new methodology to build the projection subspace. The proposed framework features lower computational and memory complexity with respect to competitive alternatives while empirical results show strong qualitative performance, both in terms of eigenvector approximation and accuracy of downstream learning tasks of central node identification and node clustering.

Abdullah Karaaslanli, Bisakh Banerjee, Tapabrata Maiti et al.

Real-world data is often represented through the relationships between data samples, forming a graph structure. In many applications, it is necessary to learn this graph structure from the observed data. Current graph learning research has primarily focused on unsigned graphs, which consist only of positive edges. However, many biological and social systems are better described by signed graphs that account for both positive and negative interactions, capturing similarity and dissimilarity between samples. In this paper, we develop a method for learning signed graphs from a set of smooth signed graph signals. Specifically, we employ the net Laplacian as a graph shift operator (GSO) to define smooth signed graph signals as the outputs of a low-pass signed graph filter defined by the net Laplacian. The signed graph is then learned by formulating a non-convex optimization problem where the total variation of the observed signals is minimized with respect to the net Laplacian. The proposed problem is solved using alternating direction method of multipliers (ADMM) and a fast algorithm reducing the per-ADMM iteration complexity from quadratic to linear in the number of nodes is introduced. Furthermore, theoretical proofs of convergence for the algorithm and a bound on the estimation error of the learned net Laplacian as a function of sample size, number of nodes, and graph topology are provided. Finally, the proposed method is evaluated on simulated data and gene regulatory network inference problem and compared to existing signed graph learning methods.

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).

Abdullah Karaaslanli, Selin Aviyente

Graph topology inference, i.e., learning graphs from a given set of nodal observations, is a significant task in many application domains. Existing approaches are mostly limited to learning a single graph assuming that the observed data is homogeneous. This is problematic because many modern datasets are heterogeneous or mixed and involve multiple related graphs, i.e., multiview graphs. Recent work proposing to learn multiview graphs ensures the similarity of learned view graphs through pairwise regularization, where each pair of views is encouraged to have similar structures. However, this approach cannot infer the shared structure across views. In this work, we propose an alternative method based on consensus regularization, where views are ensured to be similar through a learned consensus graph representing the common structure of the views. In particular, we propose an optimization problem, where graph data is assumed to be smooth over the multiview graph and the topology of the individual views and that of the consensus graph are learned, simultaneously. Our optimization problem is designed to be general in the sense that different regularization functions can be used depending on what the shared structure across views is. Moreover, we propose two regularization functions that extend fused and group graphical lasso to consensus based regularization. Proposed multiview graph learning is evaluated on simulated data and shown to have better performance than existing methods. It is also employed to infer the functional brain connectivity networks of multiple subjects from their electroencephalogram (EEG) recordings. The proposed method reveals the structure shared by subjects as well as the characteristics unique to each subject.