An Ad-hoc graph node vector embedding algorithm for general knowledge graphs using Kinetica-Graph

TL;DR

This paper introduces a novel node embedding algorithm for knowledge graphs that combines multiple structural and label-based indicators into a unified vector space, optimized via stochastic gradient descent.

Contribution

The proposed method uniquely integrates local and remote graph features with a recursive spectral bisection approach for improved node similarity representation.

Findings

Effective embedding of nodes capturing local and global graph features

Reduced embedding error through stochastic gradient descent optimization

Demonstrated applicability on general knowledge graphs

Abstract

This paper discusses how to generate general graph node embeddings from knowledge graph representations. The embedded space is composed of a number of sub-features to mimic both local affinity and remote structural relevance. These sub-feature dimensions are defined by several indicators that we speculate to catch nodal similarities, such as hop-based topological patterns, the number of overlapping labels, the transitional probabilities (markov-chain probabilities), and the cluster indices computed by our recursive spectral bisection (RSB) algorithm. These measures are flattened over the one dimensional vector space into their respective sub-component ranges such that the entire set of vector similarity functions could be used for finding similar nodes. The error is defined by the sum of pairwise square differences across a randomly selected sample of graph nodes between the assumed embeddings and the ground truth estimates as our novel loss function. The ground truth is estimated to be a combination of pairwise Jaccard similarity and the number of overlapping labels. Finally, we demonstrate a multi-variate stochastic gradient descent (SGD) algorithm to compute the weighing factors among sub-vector spaces to minimize the average error using a random sampling logic.