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We propose shifted inner-product similarity (SIPS), which is a novel yet verysimple extension of the ordinary inner-product similarity (IPS) forneural-network based graph embedding (GE). In contrast to IPS, that is limitedto approximating positive-definite (PD) similarities, SIPS goes beyond thelimitation by introducing bias terms in IPS; we theoretically prove that SIPSis capable of approximating not only PD but also conditionally PD (CPD)similarities with many examples such as cosine similarity, negative Poincaredistance and negative Wasserstein distance. Since SIPS with sufficiently largeneural networks learns a variety of similarities, SIPS alleviates the need forconfiguring the similarity function of GE. Approximation error rate is alsoevaluated, and experiments on two real-world datasets demonstrate that graphembedding using SIPS indeed outperforms existing methods.

Graph Embedding with Shifted Inner Product Similarity and Its Improved Approximation Capability