000200187 001__ 200187
000200187 005__ 20190617200720.0
000200187 0247_ $$2doi$$a10.1109/TSP.2016.2602809
000200187 022__ $$a1053-587X
000200187 02470 $$2ISI$$a000386232300007
000200187 037__ $$aARTICLE
000200187 245__ $$aLearning Laplacian Matrix in Smooth Graph Signal Representations
000200187 260__ $$bInstitute of Electrical and Electronics Engineers$$c2016$$aPiscataway
000200187 269__ $$a2016
000200187 300__ $$a14
000200187 336__ $$aJournal Articles
000200187 520__ $$aThe 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.
000200187 6531_ $$agraph learning
000200187 6531_ $$asignal processing on graphs
000200187 6531_ $$arepresentation theory
000200187 6531_ $$afactor analysis
000200187 6531_ $$aGaussian prior
000200187 700__ $$0242933$$g193962$$aDong, Xiaowen
000200187 700__ $$0244101$$g185309$$aThanou, Dorina
000200187 700__ $$g101475$$aFrossard, Pascal$$0241061
000200187 700__ $$aVandergheynst, Pierre$$g120906$$0240428
000200187 773__ $$j64$$tIEEE Transactions on Signal Processing$$k23$$q6160-6173
000200187 8564_ $$uhttp://arxiv.org/abs/1406.7842$$zURL
000200187 909C0 $$xU10851$$0252393$$pLTS4
000200187 909C0 $$pLTS2$$xU10380$$0252392
000200187 909CO $$qGLOBAL_SET$$pSTI$$particle$$ooai:infoscience.tind.io:200187
000200187 917Z8 $$x193962
000200187 917Z8 $$x101475
000200187 917Z8 $$x185309
000200187 917Z8 $$x185309
000200187 937__ $$aEPFL-ARTICLE-200187
000200187 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000200187 980__ $$aARTICLE