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research article

Learning Laplacian Matrix in Smooth Graph Signal Representations

Dong, Xiaowen  
•
Thanou, Dorina  
•
Frossard, Pascal  
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2016
IEEE Transactions on Signal Processing

The construction of a meaningful graph plays a crucial role in the success of many graph-based representations and algorithms for handling structured data, especially in the emerging field of graph signal processing. However, a meaningful graph is not always readily available from the data, nor easy to define depending on the application domain. In particular, it is often desirable in graph signal processing applications that a graph is chosen such that the data admit certain regularity or smoothness on the graph. In this paper, we address the problem of learning graph Laplacians, which is equivalent to learning graph topologies, such that the input data form graph signals with smooth variations on the resulting topology. To this end, we adopt a factor analysis model for the graph signals and impose a Gaussian probabilistic prior on the latent variables that control these signals. We show that the Gaussian prior leads to an efficient representation that favors the smoothness property of the graph signals. We then propose an algorithm for learning graphs that enforce such property and is based on minimizing the variations of the signals on the learned graph. Experiments on both synthetic and real world data demonstrate that the proposed graph learning framework can lead to efficiently inferring meaningful graph topologies from signal observations under the smoothness prior.

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Type
research article
DOI
10.1109/TSP.2016.2602809
Web of Science ID

WOS:000386232300007

ArXiv ID

1406.7842

Author(s)
Dong, Xiaowen  
Thanou, Dorina  
Frossard, Pascal  
Vandergheynst, Pierre  
Date Issued

2016

Publisher

Institute of Electrical and Electronics Engineers

Published in
IEEE Transactions on Signal Processing
Volume

64

Issue

23

Start page

6160

End page

6173

Subjects

graph learning

•

signal processing on graphs

•

representation theory

•

factor analysis

•

Gaussian prior

Editorial or Peer reviewed

REVIEWED

Written at

EPFL

EPFL units
LTS4  
LTS2  
Available on Infoscience
July 10, 2014
Use this identifier to reference this record
https://infoscience.epfl.ch/handle/20.500.14299/105002
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