GRAPH LEARNING FROM SEQUENTIAL DATA

Graphs provide a powerful framework to represent high-dimensional but structured data, and to make inferences about relationships between subsets of the data. In this work we consider graph signals that evolve dynamically according to a heat diffusion process and are subject to persistent perturbations. We develop an online algorithm that is able to learn the underlying graph structure from observations of the signal evolution. The algorithm is adaptive in nature and in particular able to respond to changes in the graph structure and the perturbation statistics.

[1]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[2]  Fan Chung,et al.  The heat kernel as the pagerank of a graph , 2007, Proceedings of the National Academy of Sciences.

[3]  R. Tibshirani,et al.  Sparse inverse covariance estimation with the graphical lasso. , 2008, Biostatistics.

[4]  Michael R. Lyu,et al.  Mining social networks using heat diffusion processes for marketing candidates selection , 2008, CIKM '08.

[5]  Ali H. Sayed,et al.  Adaptive Filters , 2008 .

[6]  Joshua B. Tenenbaum,et al.  Discovering Structure by Learning Sparse Graphs , 2010 .

[7]  Robert Shorten,et al.  Hurwitz Stability of Metzler Matrices , 2010, IEEE Transactions on Automatic Control.

[8]  Pascal Frossard,et al.  The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains , 2012, IEEE Signal Processing Magazine.

[9]  Alfred O. Hero,et al.  Dynamic Stochastic Blockmodels for Time-Evolving Social Networks , 2014, IEEE Journal of Selected Topics in Signal Processing.

[10]  Daniele Durante,et al.  Locally Adaptive Dynamic Networks , 2015, 1505.05668.

[11]  Vassilis Kalofolias,et al.  How to Learn a Graph from Smooth Signals , 2016, AISTATS.

[12]  Antonio Ortega,et al.  Generalized Laplacian precision matrix estimation for graph signal processing , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[13]  Pascal Frossard,et al.  Learning Laplacian Matrix in Smooth Graph Signal Representations , 2014, IEEE Transactions on Signal Processing.

[14]  José M. F. Moura,et al.  Signal Processing on Graphs: Causal Modeling of Unstructured Data , 2015, IEEE Transactions on Signal Processing.

[15]  Pascal Frossard,et al.  Learning Heat Diffusion Graphs , 2016, IEEE Transactions on Signal and Information Processing over Networks.

[16]  Baltasar Beferull-Lozano,et al.  Online topology estimation for vector autoregressive processes in data networks , 2017, 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP).