自適應網路基於擴散策略的圖訊號處理演算法

Adaptive Network Diffusion-based Strategy Algorithms in Graph Signal Processing

陳冠文(Kuan-Wen Chen)

指導教授 ： 貝蘇章

國立臺灣大學/電機資訊學院/電信工程學研究所/碩士(2022年)

https://doi.org/10.6342/NTU202201024

摘要

隨著無線或有線網路的發展，自適應網路吸引到了相當的關注，透過收集空間上相鄰節點的資訊，經過不斷的適應以及學習，我們可以有效率地去進行訊號的估計。本論文中將會介紹一些圖訊號處理的演算法，分別是基於圖傅立葉轉換、基於增量及基於擴散的演算法，並分析其性能表現，之後針對基於擴散的演算法去進行改善，透過三種不同的方法可以使演算法達到更好的表現。第一種方法為自適應組合權重，當我們再利用相鄰節點的資料時，愈相似的節點愈可以幫助我們學習，因此透過自適應組合權重，我們可以合理地進行權重的分配，第二種方法為可變步長，讓演算法隨著迭代的進行，選擇不同步長，來調整其收斂速度及穩態誤差，第三種方法為控制變數，在學習階段時，不一定所有相鄰的節點都有幫助，因此使用控制變數，來決定是否向相鄰節點進行學習。

關鍵字

圖訊號處理 ； 擴散 ； 自適應組合權重 ； 可變步長 ； 控制變數

並列摘要

With the development of the wireless or wired networks, adaptive networks have drawn a lot of attention. By collecting the information of the adjacent nodes, and through continuous adaptive learnings, we can efficiently estimate signals. In this paper, we introduce some algorithms which are GFT-based, incremental-based and diffusion-based respectively in graph signal processing and analyze their performance. Then, we focus on improving the performance of the diffusion-based algorithm. The first method is adaptive combination weight. When we utilize the information of the adjacent nodes, the similar nodes can help to learn. Therefore, through adaptive combination weight, we can reasonably assign the weights. The second method is variable step size. With the iteration of the algorithm, we can choose different step size and adjust its convergence speed and steady state error. The third method is control variable. In the learning stage, not all adjacent nodes are helpful. Thus, we determine whether to learn from adjacent nodes by control variable.

並列關鍵字

Graph Signal Processing ； diffusion ； adaptive combination weight ； variable step size ； control variable

參考文獻

[1] P. Di Lorenzo, P. Banelli, E. Isufi, S. Barbarossa and G. Leus, "Adaptive Graph Signal Processing: Algorithms and Optimal Sampling Strategies," in IEEE Transactions on Signal Processing, vol. 66, no. 13, pp. 3584-3598, 1 July1, 2018, doi: 10.1109/TSP.2018.2835384.

[2] M. J. Ahmadi, R. Arablouei and R. Abdolee, "Efficient Estimation of Graph Signals With Adaptive Sampling," in IEEE Transactions on Signal Processing, vol. 68, pp. 3808-3823, 2020, doi: 10.1109/TSP.2020.3002607.

[3] C. G. Lopes and A. H. Sayed, "Distributed Adaptive Incremental Strategies: Formulation and Performance Analysis," 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings, 2006, pp. III-III, doi: 10.1109/ICASSP.2006.1660721.

[4] C. G. Lopes and A. H. Sayed, "Incremental Adaptive Strategies Over Distributed Networks," in IEEE Transactions on Signal Processing, vol. 55, no. 8, pp. 4064-4077, Aug. 2007, doi: 10.1109/TSP.2007.896034.

[5] C. G. Lopes and A. H. Sayed, "Diffusion Least-Mean Squares Over Adaptive Networks: Formulation and Performance Analysis," in IEEE Transactions on Signal Processing, vol. 56, no. 7, pp. 3122-3136, July 2008, doi: 10.1109/TSP.2008.917383.