Graph Embedding with Shifted Inner Product Similarity and Its Improved Approximation Capability
This work addresses the problem of similarity function configuration in graph embedding for machine learning practitioners, offering a more flexible approach, though it is incremental as it builds on existing inner-product methods.
The authors tackled the limitation of inner-product similarity in graph embedding by proposing a shifted variant (SIPS) that can approximate a broader class of similarities, including conditionally positive-definite ones like cosine and negative Wasserstein distance, and demonstrated its effectiveness with experiments on real-world datasets showing improved performance over existing methods.
We propose shifted inner-product similarity (SIPS), which is a novel yet very simple extension of the ordinary inner-product similarity (IPS) for neural-network based graph embedding (GE). In contrast to IPS, that is limited to approximating positive-definite (PD) similarities, SIPS goes beyond the limitation by introducing bias terms in IPS; we theoretically prove that SIPS is capable of approximating not only PD but also conditionally PD (CPD) similarities with many examples such as cosine similarity, negative Poincare distance and negative Wasserstein distance. Since SIPS with sufficiently large neural networks learns a variety of similarities, SIPS alleviates the need for configuring the similarity function of GE. Approximation error rate is also evaluated, and experiments on two real-world datasets demonstrate that graph embedding using SIPS indeed outperforms existing methods.