200187
20190822050914.0
1053-587X
10.1109/TSP.2016.2602809
doi
000386232300007
ISI
arXiv
1406.7842
ARTICLE
Learning Laplacian Matrix in Smooth Graph Signal Representations
Piscataway
2016
Institute of Electrical and Electronics Engineers
2016
14
Journal Articles
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.
graph learning
signal processing on graphs
representation theory
factor analysis
Gaussian prior
Dong, Xiaowen
193962
242933
Thanou, Dorina
185309
244101
Frossard, Pascal
101475
241061
Vandergheynst, Pierre
120906
240428
6160-6173
23
IEEE Transactions on Signal Processing
64
LTS4
252393
U10851
LTS2
252392
U10380
oai:infoscience.tind.io:200187
article
STI
GLOBAL_SET
193962
101475
185309
185309
EPFL-ARTICLE-200187
EPFL
PUBLISHED
REVIEWED
ARTICLE