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

4 Oct 2018Akifumi OkunoGeewook KimHidetoshi Shimodaira

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... (read more)

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