My research is in the area of theory and applications of signal processing and machine learning. I work on a variety of topics including: 1) transform based signal processing with an emphasis on sparsity-constrained feature extraction and classification; 2) signal processing on graphs and networks; 3) higher-order data analysis and 4) applications in computational neuroscience.

Time-FREQUENCY ANALYSIS

In the area of time-frequency analysis, in the past decade, I focused on developing complex-valued time-frequency distributions. Conventional time-frequency distributions are real-valued. As such they are limited to quantifying only the energy distribution of signals and cannot be used to extract time-varying phase information from non-stationary signals. Extracting phase information is important in a variety of applications including the study of chaotic oscillators which are encountered in many complex systems such as the human brain. We have introduced a new class of complex-valued quadratic time-frequency distributions, namely Reduced Interference Distribution Rihaczek (RID-Rihaczek), with desirable properties such as satisfying the marginals and reducing the cross-term interference. We also defined a new phase estimation method based on RID-Rihaczek which has been shown to be more accurate compared to existing methods. This method has been implemented in neurophysiological signal processing algorithms to quantify both bivariate and multivariate phase synchrony in the human brain. More recently, we have defined a RID-Rihaczek based phase amplitude coupling measure, where the amplitude envelope and phase of the signals are extracted from this complex time-frequency distribution, to quantify the cross-frequency coupling in the brain.

Publications:

S. Aviyente and A. Y. Mutlu, “A time-frequency based approach to Phase and Phase Synchrony Estimation”, IEEE Transactions on Signal Processing, vol. 59, no. 7, pp. 3086-3098, 2011.

S. Aviyente, E. M. Bernat, W. S. Evans, and S. R. Sponheim, “A phase synchrony measure for quantifying dynamic functional integration in the brain,” Human Brain Mapping, vol. 32, no. 1, pp. 80-93, 2011.

M. Al-Khassaweneh, M. Villafane-Delgado, A. Y. Mutlu and S. Aviyente, "A measure of multivariate phase synchrony using hyperdimensional geometry." IEEE Transactions on Signal Processing 64.11 (2016): 2774-2787.

T. T. K. Munia and S. Aviyente, “Time-frequency based phase-amplitude coupling measure for neuronal oscillations,” Scientific Reports, vol. 9, no. 1, pp. 1-15, 2019.

Software:

Psychophysiology Toolbox for MATLAB

Time-Frequency Phase Amplitude Coupling Toolbox

Network SCIENCE & CommuNITY DETECTIon

In the area of network science, our group has been working on network analysis especially for dynamic and multilayer networks. We have adopted a signal processing based paradigm to the study of weighted, undirected/directed and dynamic networks. We introduced a novel framework based on low-rank subspace estimation for both tracking the changes in network structure and detecting communities in high-dimensional dynamic networks. Using principles from robust PCA and tensor representation theory, tensor based recursive subspace tracking algorithms for detecting the change points and communities using the assumption that networks with a community structure can be modeled as low-rank plus sparse tensors have been developed. This new framework for community detection for dynamic networks has been shown to be robust to outliers and sensitive to changes in community structure.

Publications

Y. Liu, J. Moser and S. Aviyente, "Network community structure detection for directional neural networks inferred from multichannel multisubject EEG data," IEEE Transactions on Biomedical Engineering, 61(7), 1919-1930.

A. G. Mahyari, D. M. Zoltowski, E. M. Bernat and S. Aviyente, “A tensor decomposition-based approach for detecting dynamic network states from EEG,” IEEE Transactions on Biomedical Engineering, vol. 64, no. 1, 2017.

A. Ozdemir, E. M. Bernat and S. Aviyente, “Recursive Tensor Subspace Tracking for Dynamic Brain Network Analysis,” IEEE Transactions on Signal and Information Processing over Networks, vol. 3, no. 4, pp. 669-682, 2017.

E. Al-Sharoa, M. Al-khassaweneh and S. Aviyente, “Tensor based temporal and multilayer community detection for studying brain dynamics during resting state fMRI,” IEEE Transactions on Biomedical Engineering, 66(3), pp. 695-709, 2019.

E. Al-Sharoa, M. Al-khassaweneh and S. Aviyente, “Detecting and Tracking Community Structure in Temporal Networks: A Low-rank + Sparse Estimation Based Evolutionary Clustering Approach,” IEEE Transactions on Signal and Information Processing over Networks, vol. 5, no. 4, pp. 723-738, 2019.

A. Karaaslanli and S. Aviyente, "Community detection in dynamic networks: Equivalence between stochastic blockmodels and evolutionary spectral clustering," IEEE Transactions on Signal and Information Processing over Networks, vol. 7, pp. 130-143, 2021.

E. Al- Sharoa and S. Aviyente, "Community Detection in Fully-Connected Multi-layer Networks through Joint Nonnegative Matrix Factorization," accepted for publication in IEEE Access, 2022.

Tensor based Learning

In the area of tensor-based learning, we have explored problems both in unsupervised and supervised learning. In the area of supervised learning, we are working on new tensor decomposition structures, i.e. multi-branch tensor train decomposition, to address the issue of storage and computational complexities. In the area of unsupervised learning, we are working on anomaly detection in spatio-temporal data.

Publications

S. E. Sofuoglu and S. Aviyente, "Graph Regularized Low-Rank Tensor-Train for Robust Principal Component Analysis, " accepted for publication in IEEE Signal Processing Letters, 2022.

S. E. Sofuoglu and S. Aviyente,"GLOSS: Tensor-Based Anomaly Detection in Spatiotemporal Urban Traffic Data," Signal Processing, 192, 2022.

S. E. Sofuoglu and S. Aviyente, “Multi-Branch Tensor Network Structure for Tensor-Train Discriminant Analysis,” IEEE Transactions on Image Processing, vol. 30, pp. 8926-8938, 2021.

A. Zare, A. Ozdemir, M. Iwen and S. Aviyente, “Extension of PCA to higher order data structures: An Introduction to Tensors, Tensor Decompositions, and Tensor PCA,” Proceedings of the IEEE, vol. 106, no. 8, 2018.