Research

Background on Graphs and Multiplex and Attributed Networks

Brain Network. Each node represents a brain region.

Many real-world systems, such as social networks, transportation systems, and biological networks, are often represented as complex networks/graphs.
Agents are represented as the nodes of the graph, and the relationships between them are encoded by the edges of the graph.
An important aspect of network analysis is the discovery of communities—groups of nodes that are more densely connected to each other than to the rest of the network.

Traditional network models that employ simple graphs usually fail to capture the multiple types of interactions that can exist between agents.
Many complex systems are better represented by multiplex networks rather than single-layer networks.
A multiplex network is a particular type of multilayer network where all layers share the same set of nodes but may have very different topologies.

Social Multiplex Network, same group of people in different social media platforms (layers).

Projects

Community Detection in Multiplex Networks

We introduced a new community detection method for multiplex networks, focusing on detecting both common and unique communities across different network layers, called Multiplex Orthogonal Nonnegative Matrix Tri-Factorization (MX-ONMTF)

Purple, pink, and green are common communities across all or different subset of layers.

Existing multiplex community detection approaches Identify a community partition that best fits all given layers or communities that are shared by either some or all the layers.
Propose a framework, MX-ONMTF [1] for detecting communities common across layers as well as private communities, communities that are unique to each layer.

[1] M. Ortiz-Bouza and S. Aviyente, “Community Detection in Multiplex Networks based on Orthogonal Nonnegative Matrix Tri-factorization,” IEEE Access, vol. 12, pp. 6423–6436, 2024.

Application to Social Networks: Lazega Law Firm Multiplex Network

The Lazega Law Firm Multiplex Network captures interactions among 71 lawyers across advice, friendship, and co-work layers. MX-ONMTF identifies one common community (in red) and five private ones. The red group includes lawyers who exchange work advice, maintain friendships, and collaborate on projects.

Application to Brain Networks: Electroencephalogram (EEG) Data

We applied MX-ONMTF to EEG-derived functional connectomes and identify common and individual brain communities, revealing variability and consistency in brain regions during cognitive tasks and emphasizing community detection's role in understanding individual brain differences [2].

[2] B. Osterkamp, M. Ortiz-Bouza, and S. Aviyente. “Variability of Functional Connectomes Through Community Structure,” 2023 IEEE International Conference on Acoustics, Speech, and Signal Processing Workshops (ICASSPW), 2023.

[3] H. Yang, M. Ortiz-Bouza, T. Vu, F. Laport, V. Calhoun, S. Aviyente, and T. Adali, “Subgroup Identification Through Multiplex Community Structure within Functional Connectivity Networks” 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2024.

Application to Brain Networks: fMRI Data

We applied MX-ONMTF to resting-state fMRI data where the nodes represent patients, and the layers are different brain regions' functional connectivity networks [3]. Results from applying MX-ONMTF to 464 psychotic patients show that the identified subgroups (communities) exhibit significant group differences on multiple meaningful functional networks as well as in their clinical scores.

2. Learning Optimal Graph Filters for Clustering of Attributed Graphs

This research focuses on developing a graph signal processing-based (GSP) method for clustering attributed graphs, where nodes are not only connected but also have attributes (signals).

The proposed method, GraFiCA [4], introduces a two-step optimization process where:

Clustering is performed based on node attributes and graph connectivity.
Graph filter parameters (Finite Impulse Response (FIR) and Autoregressive Moving Average (ARMA) filters) are optimized to enhance cluster separability by learning from the graph structure and attributes simultaneously.
GraFiCA was evaluated on several real-world networks, including citation and social networks, showing superior performance compared to state-of-the-art methods.

The optimal learned filter for Sinanet is an all-pass filter, as the original node attributes carry most of the class information. Filtering the attributes may not improve the accuracy of clustering, as seen in the second row of this figure, where the attributes before and after filtering are very similar. On the contrary, for Cora, the clusters become better separated after filtering and the optimal learned filter is low-pass.

The filter parameters are optimized for the clustering task.
GraFiCA does not constrain the filters to be low-pass.
Results indicate that the structure of the learned filters is determined directly by the data.

[4] M. Ortiz-Bouza and S. Aviyente, “Learning Optimal Graph Filters for Clustering of Attributed Graphs” arXiv preprint, 2024.

3. Discriminative Community Detection for Multiplex Networks

This project addresses the challenge of detecting communities that distinguish between two groups of multiplex networks, such as different experimental conditions in brain networks, and healthy and diseased patient groups. We propose two novel methods based on spectral clustering:

Multiplex Discriminative Spectral Clustering (MX-DSC) [5]: This method identifies discriminative subgraph structures that differentiate between groups.
Multiplex Discriminative and Consensus Spectral Clustering (MX-DCSC) [5]: This approach simultaneously detects both discriminative communities between groups and consensus communities within a group.

Application to Brain Networks: EEG Data (Error vs. Correct Response)

We applied MX-DSC to functional connectivity networks (FCNs) derived from EEG data from a cognitive control error processing study. The FCNs, modeled as multiplex networks with layers representing subjects, captured brain activity during error and correct responses (two groups).

Key Findings:

The method detected discriminative communities between the error and correct response networks.
A discriminative community for error responses was identified around fronto-central regions of the brain (FCz, FC1, FC2, Cz, C1). This result aligns with prior research showing that these regions are more active during error trials than correct ones.
The parietal-occipital region was identified as a shared community for both response types, which is activated due to visual stimuli.

Handwritten Digits (UCI Dataset)

We applied MX-DSC to the UCI Handwritten Digits dataset, focusing on distinguishing between digits 1 and 7, which are often misclassified due to similar patterns. The multiplex networks were built from six feature sets, with each layer representing a different feature and each node representing an image.

Key Findings:

The method successfully identified discriminative subgraphs (group of images) where the digits 1 and 7 were clearly written and distinct, while non-discriminative subgraphs contained noisier, less defined samples.
By applying spectral clustering to the discriminative subgraph samples, a Normalized Mutual Information (NMI) of 0.7037 was achieved, indicating strong clustering performance. In contrast, the non-discriminative samples had a lower NMI of 0.3091, reflecting poorer separation.

[5] M. Ortiz-Bouza and S. Aviyente, “Discriminative Community Detection for Multiplex Networks” 2024 IEEE International Workshop on Machine Learning for Signal Processing (MLSP), 2024.

4. Learning Graph Filters for Hub Node Identification

Top-K hubs detected by GraFHub when applied to an fMRI data from the Human Connectome Project (HCP). The size and the color of the nodes correspond to the number of times across 56 subjects a particular node has been detected as a hub and the brain network (Yeo’s parcellation networks) to which the node belongs, respectively.

Introduce a framework, GraFHub [6], to identify brain network hubs by integrating structural and functional data.
Uses Graph Signal Processing (GSP) to model brain activity signals on the structural connectivity graph.

Identifies hub nodes as those with high activity and sparse connections, assuming that:
- Hub nodes have high-frequency activity relative to their neighbors.
- Non-hub nodes exhibit smooth, low-frequency activity.
Learns optimal graph filters to separate hub nodes from non-hubs, enhancing detection accuracy.

Key Findings:

GraFHub effectively identifies hubs in the default mode network (DMN) and other key brain regions.
Offers a more comprehensive understanding of brain hubs, supporting advanced insights into brain organization and function.

[6] M. Ortiz-Bouza, D. Vu, A. Karaaslanli, and S. Aviyente, “Learning Graph Filters for Structure-Function Coupling based Hub Node Identification” IEEE Transactions on Signal and Information Processing over Networks, vol. 11, pp. 980-993, 2025.

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