Graph Diffusion Kernel LMS using Random Fourier Features

2020 • In *2020 54th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, 1-5 November 2020*

Peer reviewed

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Abstract :

[en] This work introduces kernel adaptive graph filters that operate in the reproducing kernel Hilbert space. We propose a centralized graph kernel least mean squares (GKLMS) approach for identifying the nonlinear graph filters. The principles of coherence-check and random Fourier features (RFF) are used to reduce the dictionary size. Additionally, we leverage on the graph structure to derive the graph diffusion KLMS (GDKLMS). The proposed GDKLMS requires only single-hop communication during successive time instants, making it viable for real-time network-based applications. In the distributed implementation, usage of RFF avoids the requirement of a centralized pretrained dictionary in the case of coherence-check. Finally, the performance of the proposed algorithms is demonstrated in modeling a nonlinear graph filter via numerical examples. The results show that centralized and distributed implementations effectively model the nonlinear graph filters, whereas the random feature-based solutions is shown to outperform coherence-check based solutions.

Disciplines :

Electrical & electronics engineering

Gogineni, Vinay

Elias, Vitor R. M.

Alves Martins, Wallace ^{}; University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > SigCom

Werner, Stefan

External co-authors :

yes

Language :

English

Title :

Graph Diffusion Kernel LMS using Random Fourier Features

Publication date :

November 2020

Event name :

Asilomar Conference on Signals, Systems, and Computers

Event date :

from 01-11-2020 to 05-11-2020

Audience :

International

Main work title :

2020 54th Asilomar Conference on Signals, Systems, and Computers, Pacific Grove, CA, USA, 1-5 November 2020

Peer reviewed :

Peer reviewed

Focus Area :

Security, Reliability and Trust

European Projects :

H2020 - 742648 - AGNOSTIC - Actively Enhanced Cognition based Framework for Design of Complex Systems

Funders :

CE - Commission Européenne [BE]

Available on ORBilu :

since 11 November 2020

Scopus citations^{®}

12

Scopus citations^{®}

without self-citations

without self-citations

3

- D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega, and P. Vandergheynst, "The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains, " IEEE Signal Process. Mag., vol. 30, pp. 83-98, May 2013.
- A. Sandryhaila and J. M. F. Moura, "Discrete signal processing on graphs, " IEEE Trans. Signal Process., vol. 61, pp. 1644-1656, Apr. 2013.
- A. Ortega, P. Frossard, J. Kova?cevíc, J. M. F. Moura, and P. Vandergheynst, "Graph signal processing: Overview, challenges, and applications, " Proc. IEEE, vol. 106, pp. 808-828, May 2018.
- E. Ceci and S. Barbarossa, "Graph signal processing in the presence of topology uncertainties, " in IEEE Trans. Signal Process., 2020.
- I. Jablonski, "Graph signal processing in applications to sensor networks, smart grids, and smart cities, " IEEE Sensors J., vol. 17, pp. 7659-7666, Dec. 2017.
- A. Gavili and X. Zhang, "On the shift operator, graph frequency, and optimal filtering in graph signal processing, " IEEE Trans. Signal Process., vol. 65, pp. 6303-6318, Dec. 2017.
- J. Mei and J. M. F. Moura, "Signal processing on graphs: Causal modeling of unstructured data, " IEEE Trans. Signal Process., vol. 65, pp. 2077-2092, Apr. 2017.
- A. Loukas, A. Simonetto, and G. Leus, "Distributed autoregressive moving average graph filters, " IEEE Signal Process. Lett., vol. 22, pp. 1931-1935, Nov. 2015.
- E. Isufi, A. Loukas, N. Perraudin and G. Leus, "Forecasting time series with VARMA recursions on graphs, " in IEEE Trans. Signal Process., vol. 67, no. 18, pp. 4870-4885, Sep. 2019.
- A. Sandryhaila and J. M. F. Moura, "Discrete signal processing on graphs: Graph filters, " in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2013, pp. 6163-6166.
- R. Nassif, C. Richard, J. Chen, and A. H. Sayed, "A graph diffusion LMS strategy for adaptive graph signal processing, " in Conf. Rec. Asilomar Conf. Signals Syst. Comput., pp. 1973-1976, Oct. 2017.
- R. Nassif, C. Richard, J. Chen, and A. H. Sayed, "Distributed diffusion adaptation over graph signals, " in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2018, pp. 4129-4133.
- P. Di Lorenzo, P. Banelli, S. Barbarossa, and S. Sardellitti, "Distributed adaptive learning of graph signals, " IEEE Trans. Signal Process., vol. 65, pp. 4193-4208, Aug. 2017.
- F. Hua, R. Nassif, C. Richard, H. Wang and A. H. Sayed, "Online distributed learning over graphs with multitask graph-filter models, " in IEEE Trans. Signal Inf. Process. Netw., vol. 6, pp. 63-77, Jan. 2020.
- M. J. M. Spelta and W. A. Martins, "Normalized LMS algorithm and data-selective strategies for adaptive graph signal estimation, " in Signal Process., vol. 167, 107326, Feb. 2020.
- A. Venkitaraman, S. Chatterjee and P. Händel, "Predicting graph signals using kernel regression where the input signal is agnostic to a graph, " in IEEE Trans. Signal Inf. Process. Netw., vol. 5, no. 4, pp. 698-710, Dec. 2019.
- J. F. Walker, N. Jenkins and N. Jenkins Wind Energy Technology. Wiley, June 1997.
- W. Liu, J. C. Príncipe, and S. Haykin, Kernel Adaptive Filtering. Wiley, Feb. 2010.
- W. Gao, J. Chen, C. Richard, and J. Huang, "Diffusion adaptation over networks with kernel least-mean-square, " in Proc. IEEE Int. Workshop Comput. Adv. Multisens. Adapt. Process., 2015, pp. 217-220.
- A. J. Smola and R. Kondor, "Kernels and regularization on graphs, " in Learning Theory and Kernel Machines. Lecture Notes in Computer Science, vol. 2777, pp. 144-158, Springer, 2003.
- S. Theodoridis, K. Slavakis, and I. Yamada, "Adaptive learning in a world of projections, " IEEE Signal Process. Mag., vol. 28, pp. 97-123, Jan. 2011.
- D. Romero, M. Ma, and G. B. Giannakis, "Kernel-based reconstruction of graph signals, " IEEE Trans. Signal Process., vol. 65, pp. 764-778, Feb. 2017.
- Y. Shen, G. Leus, and G. B. Giannakis, "Online graph-adaptive learning with scalability and privacy, " IEEE Trans. Signal Process., vol. 67, pp. 2471-2483, May 2019.
- P. Bouboulis, S. Chouvardas, and S. Theodoridis, "Online distributed learning over networks in RKH spaces using random Fourier features, " IEEE Trans. Signal Process., vol. 66, no. 7, pp. 1920-1932, 2018.
- B.-S. Shin, M. Yukawa, R. L. G. Cavalcante, and A. Dekorsy, "Distributed adaptive learning with multiple kernels in diffusion networks, " IEEE Trans. Signal Process., vol. 66, pp. 5505-5519, Nov. 2018.
- S. Wang, L. Dang, B. Chen, S. Duan, L. Wang, and C. K. Tse, "Random Fourier filters under maximum correntropy criterion, " IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 65, pp. 3390-3403, Oct. 2018.
- K. Chen, S. Werner, A. Kuh, and Y.-F. Huang, "Nonlinear adaptive filtering with kernel set-membership approach, " IEEE Trans. Signal Process., pp. 1-1, 2020.
- C. Richard, J. Bermudez, and P. Honeine, "Online prediction of time series data with kernels, " IEEE Trans. Signal Process., vol. 57, pp. 1058-1067, Mar. 2009.
- A. Rahimi and B. Recht, "Random features for large-scale kernel machines, " in Proc. Adv. Neural Inf. Process. Syst., pp. 1177-1184, 2007.
- A. H. Sayed, S. Tu, J. Chen, X. Zhao, and Z. J. Towfic, "Diffusion strategies for adaptation and learning over networks: An examination of distributed strategies and network behavior, " IEEE Signal Process. Mag., vol. 30, pp. 155-171, May 2013.
- A. H. Sayed, "Adaptive networks, " Proc. IEEE, vol. 102, pp. 460-497, Apr. 2014.
- A. H. Sayed, "Adaptation, learning, and optimization over networks, " in Foundations and Trends® in Mach. Learn., vol. 7, pp. 311-801, 2014.
- M. O. Franz and B. Schölkopf, "A unifying view of Wiener and Volterra theory and polynomial kernel regression, " Neural Comput., vol. 18, pp. 3097-3118, Dec. 2006.
- A. Singh, N. Ahuja, and P. Moulin, "Online learning with kernels: Overcoming the growing sum problem, " in Proc. IEEE Int. Workshop Mach. Learn. Signal Process., 2012, pp. 1-6.
- P. Bouboulis, S. Pougkakiotis, and S. Theodoridis, "Efficient KLMS and KRLS algorithms: A random Fourier feature perspective, " in Proc. IEEE Stat. Signal Process. Workshop, 2016, pp. 1-5.
- S. Chouvardas and M. Draief, "A diffusion kernel LMS algorithm for nonlinear adaptive networks, " in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process., 2016, pp. 4164-4168.