Representation Learning with Weighted Inner Product for Universal Approximation of General Similarities
This work addresses the challenge of similarity model selection in graph embedding for machine learning practitioners, offering a universal approximation method that is incremental in its approach.
The authors tackled the problem of approximating arbitrary general similarities in neural network-based graph embedding by proposing weighted inner product similarity (WIPS), which optimizes weights in the inner product to handle various kernel types without model selection, resulting in high-quality node representations and accurate similarity approximations in experiments.
We propose $\textit{weighted inner product similarity}$ (WIPS) for neural network-based graph embedding. In addition to the parameters of neural networks, we optimize the weights of the inner product by allowing positive and negative values. Despite its simplicity, WIPS can approximate arbitrary general similarities including positive definite, conditionally positive definite, and indefinite kernels. WIPS is free from similarity model selection, since it can learn any similarity models such as cosine similarity, negative Poincaré distance and negative Wasserstein distance. Our experiments show that the proposed method can learn high-quality distributed representations of nodes from real datasets, leading to an accurate approximation of similarities as well as high performance in inductive tasks.