Semi-Supervised Learning for Graph to Signal Mapping: a Graph Signal Wiener Filter Interpretation

Benjamin Girault 1, * Paulo Gonçalves 1, * Eric Fleury 1 Arashpreet Singh Mor 1
* Corresponding author
1 DANTE - Dynamic Networks : Temporal and Structural Capture Approach
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme, IXXI - Institut Rhône-Alpin des systèmes complexes
Abstract : In this contribution, we investigate a graph to signal mapping with the objective of analysing intricate structural properties of graphs with tools borrowed from signal processing. We successfully use a graph-based semi-supervised learning approach to map nodes of a graph to signal amplitudes such that the resulting time series is smooth and the procedure efficient and scalable. Theoretical analysis of this method reveals that it essentially amounts to a linear graph-shift-invariant filter with the a priori knowledge put into the training set as input. Further analysis shows that we can interpret this filter as a Wiener filter on graphs. We finally build upon this interpretation to improve our results.
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Submitted on : Wednesday, May 14, 2014 - 10:40:57 AM
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Benjamin Girault, Paulo Gonçalves, Eric Fleury, Arashpreet Singh Mor. Semi-Supervised Learning for Graph to Signal Mapping: a Graph Signal Wiener Filter Interpretation. 2014 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), May 2014, Florence, Italy. pp.1115-1119, ⟨10.1109/ICASSP.2014.6853770⟩. ⟨hal-00942695v2⟩

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