Deep network embedding with adversarial regularization
Methods and systems for embedding a network in a latent space include generating a representation of an input network graph in the latent space using an autoencoder model and generating a representation of a set of noise samples in the latent space using a generator model. A discriminator model discriminates between the representation of the input network graph and the representation of the set of noise samples. The autoencoder model, the generator model, and the discriminator model are jointly trained by minimizing a joint loss function that includes parameters for each model. A final representation of the input network graph is generated using the trained autoencoder model.
1. A method for embedding a network in a latent space, comprising:
generating a representation of an input network graph in the latent space using an autoencoder model;
generating a representation of a set of noise samples in the latent space using a generator model;
discriminating between the representation of the input network graph and the representation of the set of noise samples using a discriminator model;
jointly training the autoencoder model, the generator model, and the discriminator model, using a processor device, by minimizing a joint loss function that includes parameters for each model, wherein the joint loss function is defined as:
joint (ϕ,ψ,θ, w )= AE (ϕ,ψ; x )+λ 1 LE (ϕ; x )+λ 2 W ( ϕ ( x ), θ ( z ))
where ϕ and ω are parameters of the autoencoder model, θ is a parameter of the generator model, w is a parameter of the discriminator model, AE is a loss function for the autoencoder, LE is a locality-preserving loss function, W is the dual of the Earth Mover distance measure between ϕ ( x ) and θ ( z ), ϕ ( x ) is a distribution of the representations from the autoencoder model and, θ ( z ) is a distribution of the representations from the generator model, λ 1 is a parameter that sets the relative strength between the locality-preserving constraint and the auto-encoder constraint, and λ 2 is a parameter that sets the relative strength of minimizing the distributions between ϕ ( x ) and θ ( z ); and
generating a final representation of the input network graph using the trained autoencoder model.
2. The method of claim 1 , further comprising sampling random walks of the network graph.
3. The method of claim 2 , wherein generating the representation of the input network graph uses the sampled random walks as input to the autoencoder model.
4. The method of claim 1 , further comprising generating a reconstructed network graph using the autoencoder model and the representation of the input network graph.
5. The method of claim 4 , further comprising computing an autoencoder loss and a locality-preserving loss based on the input network graph and the reconstruction of the input network graph.
6. The method of claim 5 , further comprising training the autoencoder model using the autoencoder loss and the locality-preserving loss.
7. The method of claim 1 , wherein a parameter for the discriminator model is clipped to a maximum and minimum value.
8. The method of claim 1 , further comprising inferring missing edges from the final representation of the input graph to provide a connection suggestion in a social network.
9. A system for embedding a network in a latent space, comprising:
an auto-encoder configured to generate a representation of an input network graph in the latent space using an autoencoder model and to generate a final representation of the input network graph after the autoencoder model has been trained;
a generator configured to generate a representation of a set of noise samples in the latent space using a generator model;
a discriminator configured to discriminate between the representation of the input network graph and the representation of the set of noise samples using a discriminator model; and
a training module comprising a processor configured to jointly train the autoencoder model, the generator model, and the discriminator model by minimizing a joint loss function that includes parameters for each model, wherein the joint loss function is defined as:
joint (ϕ,ψ,θ, w )= AE (ϕ,ψ; x )+λ 1 LE (ϕ; x )+λ 2 W ( ϕ ( x ), θ ( z ))
where ϕ and ψ are parameters of the autoencoder model, θ is a parameter of the generator model, w is a parameter of the discriminator model, AE is a loss function for the autoencoder, LE is a locality-preserving loss function, W is the dual of the Earth Mover distance measure between ϕ ( x ) and θ ( z ), ϕ ( x ) is a distribution of the representations from the autoencoder model and, θ ( z ) is a distribution of the representations from the generator model, λ 1 is a parameter that sets the relative strength between the locality-preserving constraint and the auto-encoder constraint, and λ 2 is a parameter that sets the relative strength of minimizing the distributions between ϕ ( x ) and θ ( z ).
10. The system of claim 9 , further comprising a random walk module configured to sample random walks of the network graph.
11. The system of claim 10 , wherein the autoencoder uses the sampled random walks as input to the autoencoder model.
12. The system of claim 9 , wherein the autoencoder is further configured to generate a reconstructed network graph using the autoencoder model and the representation of the input network graph.
13. The system of claim 12 , wherein the training module is further configured to compute an autoencoder loss and a locality-preserving loss based on the input network graph and the reconstruction of the input network graph.
14. The system of claim 13 , wherein the training module is further configured to train the autoencoder model using the autoencoder loss and the locality-preserving loss.
15. The system of claim 9 , wherein a parameter for the discriminator model is clipped to a maximum and minimum value.
16. The system of claim 9 , further comprising a link inference module configured to infer missing edges from the final representation of the input graph to provide a connection suggestion in a social network.