Laplacian matrix learning for smooth graph signal representation
The construction of a meaningful graph plays a crucial role in the emerging field of signal processing on graphs. In this paper, we address the problem of learning graph Laplacians, which is similar to learning graph topologies, such that the input data form graph signals with smooth variations on t...
| Main Authors: | , , , |
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| Format: | Conference item |
| Language: | English |
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IEEE
2015
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| _version_ | 1826311575226548224 |
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| author | Dong, X Thanou, D Frossard, P Vandergheynst, P |
| author_facet | Dong, X Thanou, D Frossard, P Vandergheynst, P |
| author_sort | Dong, X |
| collection | OXFORD |
| description | The construction of a meaningful graph plays a crucial role in the emerging field of signal processing on graphs. In this paper, we address the problem of learning graph Laplacians, which is similar to learning graph topologies, such that the input data form graph signals with smooth variations on the resulting topology. We adopt a factor analysis model for the graph signals and impose a Gaussian probabilistic prior on the latent variables that control these graph signals. We show that the Gaussian prior leads to an efficient representation that favours the smoothness property of the graph signals, and propose an algorithm for learning graphs that enforce such property. Experiments demonstrate that the proposed framework can efficiently infer meaningful graph topologies from only the signal observations. |
| first_indexed | 2024-03-07T08:13:17Z |
| format | Conference item |
| id | oxford-uuid:e0377fc4-8540-4346-93e4-7696d426407a |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:13:17Z |
| publishDate | 2015 |
| publisher | IEEE |
| record_format | dspace |
| spelling | oxford-uuid:e0377fc4-8540-4346-93e4-7696d426407a2023-12-04T08:26:27ZLaplacian matrix learning for smooth graph signal representationConference itemhttp://purl.org/coar/resource_type/c_5794uuid:e0377fc4-8540-4346-93e4-7696d426407aEnglishSymplectic ElementsIEEE2015Dong, XThanou, DFrossard, PVandergheynst, PThe construction of a meaningful graph plays a crucial role in the emerging field of signal processing on graphs. In this paper, we address the problem of learning graph Laplacians, which is similar to learning graph topologies, such that the input data form graph signals with smooth variations on the resulting topology. We adopt a factor analysis model for the graph signals and impose a Gaussian probabilistic prior on the latent variables that control these graph signals. We show that the Gaussian prior leads to an efficient representation that favours the smoothness property of the graph signals, and propose an algorithm for learning graphs that enforce such property. Experiments demonstrate that the proposed framework can efficiently infer meaningful graph topologies from only the signal observations. |
| spellingShingle | Dong, X Thanou, D Frossard, P Vandergheynst, P Laplacian matrix learning for smooth graph signal representation |
| title | Laplacian matrix learning for smooth graph signal representation |
| title_full | Laplacian matrix learning for smooth graph signal representation |
| title_fullStr | Laplacian matrix learning for smooth graph signal representation |
| title_full_unstemmed | Laplacian matrix learning for smooth graph signal representation |
| title_short | Laplacian matrix learning for smooth graph signal representation |
| title_sort | laplacian matrix learning for smooth graph signal representation |
| work_keys_str_mv | AT dongx laplacianmatrixlearningforsmoothgraphsignalrepresentation AT thanoud laplacianmatrixlearningforsmoothgraphsignalrepresentation AT frossardp laplacianmatrixlearningforsmoothgraphsignalrepresentation AT vandergheynstp laplacianmatrixlearningforsmoothgraphsignalrepresentation |