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Graph Signal Prediction using Graph and Temporal Smoothing

Farmahini Farahani, Navid | 2024

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 57585 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Babaiezadeh, Massoud
  7. Abstract:
  8. The problem of linear prediction is one of the traditional issues in signal processing. With the genesis of graph signal processing, the prediction of signals defined on graphs has been recently addressed. Some existing methods provide approaches for predicting samples of a graph signal based on a known adjacency matrix among nodes. On the other hand, some studies have used graph smoothing technique, which ensures that the estimated signals remain smooth on the graph. Furthermore, graph neural networks have been proposed recently, and some research has considered methods for predicting graph signals using a graph neural network, which is possible by using extracted features from the training data. Another case in predicting graph signals is the prediction of multilayer graph signals, which refers to connecting the layers of an existing graph for more accurate prediction of future samples of the graph signal. In this context, no mathematical methods have been found to predict multilayer graph signals, and only methods using graph neural networks have been proposed. In this research, we propose four convex optimization functions for predicting graph sig- nals, with two related to single-layer graph signal prediction and the other two focused on multilayer graph signal prediction. In the first method for predicting single-layer graph signals, concepts of graph and temporal smoothing are utilized to ensure that the predicted signal remains smooth in both spatial and temporal dimensions. The second method, which is an upgraded version of the first one, refers to splitting a graph signal into two signals, one with high frequency and the other with low frequency; this method predicts them simultaneously. For the first method of multilayer graph signal prediction we propose layer smoothing using coefficients calculated by a transformer, where the corresponding cost function can ensure the predicted signal is smooth across the layers. Finally, the second method for this problem involves converting a two-layer graph signal into a single-layer signal for the prediction process, so in this case, the process of graph signal linear prediction is similar to that of single-layer graph prediction.
  9. Keywords:
  10. Linear Prediction ; Graph Signal Processing ; Graph Fourier Transform ; Graph Learning ; Multi-Layer Graphs ; Multilayer Graph Linear Prediction ; Spatio-Temporal Smoothing ; Graph Linear Prediction

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