Learning Product Graphs from Spectral Templates

Graph Learning (GL) is at the core of inference and analysis of connections in data mining and machine learning (ML). By observing a dataset of graph signals, and considering specific assumptions, Graph Signal Processing (GSP) tools can provide practical constraints in the GL approach. One applicable constraint can infer a graph with desired frequency signatures, i.e., spectral templates. However, a severe computational burden is a challenging barrier, especially for inference from high-dimensional graph signals. To address this issue and in the case of the underlying graph having graph product structure, we propose learning product (high dimensional) graphs from product spectral templates with significantly reduced complexity rather than learning them directly from high-dimensional graph signals, which, to the best of our knowledge, has not been addressed in the related areas. In contrast to the rare current approaches, our approach can learn all types of product graphs (with more than two graphs) without knowing the type of graph products and has fewer parameters. Experimental results on both the synthetic and real-world data, i.e., brain signal analysis and multi-view object images, illustrate explainable and meaningful factor graphs supported by expert-related research, as well as outperforming the rare current restricted approaches.Comment: 10 figures, 12 pages, Submitted to IEEE Transactions on Signal and Information Processing over Networks on 10-Oct-202

Estimation of a Causal Directed Acyclic Graph Process using Non-Gaussianity

Numerous approaches have been proposed to discover causal dependencies in machine learning and data mining; among them, the state-of-the-art VAR-LiNGAM (short for Vector Auto-Regressive Linear Non-Gaussian Acyclic Model) is a desirable approach to reveal both the instantaneous and time-lagged relationships. However, all the obtained VAR matrices need to be analyzed to infer the final causal graph, leading to a rise in the number of parameters. To address this issue, we propose the CGP-LiNGAM (short for Causal Graph Process-LiNGAM), which has significantly fewer model parameters and deals with only one causal graph for interpreting the causal relations by exploiting Graph Signal Processing (GSP)

ProductGraphSleepNet: Sleep Staging using Product Spatio-Temporal Graph Learning with Attentive Temporal Aggregation

The classification of sleep stages plays a crucial role in understanding and diagnosing sleep pathophysiology. Sleep stage scoring relies heavily on visual inspection by an expert that is time consuming and subjective procedure. Recently, deep learning neural network approaches have been leveraged to develop a generalized automated sleep staging and account for shifts in distributions that may be caused by inherent inter/intra-subject variability, heterogeneity across datasets, and different recording environments. However, these networks ignore the connections among brain regions, and disregard the sequential connections between temporally adjacent sleep epochs. To address these issues, this work proposes an adaptive product graph learning-based graph convolutional network, named ProductGraphSleepNet, for learning joint spatio-temporal graphs along with a bidirectional gated recurrent unit and a modified graph attention network to capture the attentive dynamics of sleep stage transitions. Evaluation on two public databases: the Montreal Archive of Sleep Studies (MASS) SS3; and the SleepEDF, which contain full night polysomnography recordings of 62 and 20 healthy subjects, respectively, demonstrates performance comparable to the state-of-the-art (Accuracy: 0.867;0.838, F1-score: 0.818;0.774 and Kappa: 0.802;0.775, on each database respectively). More importantly, the proposed network makes it possible for clinicians to comprehend and interpret the learned connectivity graphs for sleep stages.Comment: 9 pages, 6 figure