6 research outputs found
Weighted Spectral Embedding of Graphs
We present a novel spectral embedding of graphs that incorporates weights
assigned to the nodes, quantifying their relative importance. This spectral
embedding is based on the first eigenvectors of some properly normalized
version of the Laplacian. We prove that these eigenvectors correspond to the
configurations of lowest energy of an equivalent physical system, either
mechanical or electrical, in which the weight of each node can be interpreted
as its mass or its capacitance, respectively. Experiments on a real dataset
illustrate the impact of weighting on the embedding
Weighted Spectral Embedding of Graphs
International audienceWe present a novel spectral embedding of graphs that incorporates weights assigned to the nodes, quantifying their relative importance. This spectral embedding is based on the first eigenvectors of some properly normalized version of the Laplacian. We prove that these eigenvectors correspond to the configurations of lowest energy of an equivalent physical system, either mechanical or electrical, in which the weight of each node can be interpreted as its mass or its capacitance, respectively. Experiments on a real dataset illustrate the impact of weighting on the embedding
Invariant embedding for graph classification
Design of a graph embedding invariant by node permutation for a graph classification task.International audienceLearning on graphs requires a graph feature representation able to discriminate among different graphs while being amenable to fast computation. The graph isomorphism problem tells us that no fast representation of graphs is known if we require the representation to be both invariant to nodes permutation and able to discriminate two non-isomorphic graphs. Most graph representations explored so far require to be invariant. We explore new graph representations by relaxing this constraint. We present a generic embedding of graphs relying on spectral graph theory called Invariant Graph Embedding (IGE). We show that for a large family of graphs, our embedding is still invariant. To evaluate the quality and utility of our IGE, we apply them to the graph classification problem and show that IGE reaches the state-of-the-art on benchmark datasets