Learning Laplacian Matrix in Smooth Graph Signal Representations

By Xiaowen Dong, Dorina Thanou, Pascal Frossard, Pierre Vandergheynst. 2014

705 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

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Citations in the corpus

Fully Decentralized Joint Learning of Personalized Models and Collaboration Graphs (2019, background): “…form allows to regularize weights and degrees in a ﬂexible way (which encompasses some recent work from the graph signal processing community (Dong et al., 2016; Kalofolias, 2016; Berger et al., 2018)), while the separable structure is key to the de-sign of an eﬃcient decentralized…”
Graph Learning Based on Total Variation Minimization (2018, methodology): “Following [19], we search for a local minimum of (8) by alternately performing the (individually convex) minimizations with respect to w and X, which amounts to the following iterations (summarized in Algorithm 1, n is the iteration index): 1.”
Connecting the Dots: Identifying Network Structure via Graph Signal Processing (2018, methodology): “Examples include the Laplacianbased factor analysis model [9] in (26), and common graph constructions using the Gaussian kernel to define edge weights Wij := exp ( −‖x̄i−x̄j‖2 σ2 ) are recovered for g(W) = σ2 ∑ i,jWij(log(Wij)− 1).”
Learning Graphs From Data: A Signal Representation Perspective (2018, methodology): “The problem is solved via alternating minimization in [39], in which the step of solving for L bears similarity to the optimization in [27].”
Graph Learning From Data Under Laplacian and Structural Constraints (2016, methodology): “For both of the GLS methods [42] [43] addressing the problems in (13) and (14), α1 is selected from {0}∪{0.”
Graph Learning: A Survey (2021, methodology): “[55] adopted a factor analysis model for graph”
Network Topology Inference from Spectral Templates (2016, methodology): “to infer the underlying graph topology; see also [1], [8]–[12].”
Iterative Deep Graph Learning for Graph Neural Networks: Better and Robust Node Embeddings (2020, background): “In the field of graph signal processing, researchers have explored various ways of learning graphs from data [10, 12, 50, 25, 3, 1], with certain structural constraints (e.”