Two approaches to low-parametric SimRank computation

TL;DR

This paper introduces two low-parametric methods for approximating SimRank matrices, focusing on reducing memory usage while maintaining accuracy in similarity estimation between graph nodes.

Contribution

It proposes two novel low-parametric embedding approaches for SimRank computation, utilizing non-symmetric and symmetric forms with efficient algorithms that avoid dense matrices.

Findings

Algorithms achieve good approximation accuracy in real datasets.

Both methods effectively preserve the most similar elements per node.

Approaches significantly reduce memory consumption compared to traditional methods.

Abstract

In this work, we discuss low-parametric approaches for approximating SimRank matrices, which estimate the similarity between pairs of nodes in a graph. Although SimRank matrices and their computation require a significant amount of memory, common approaches mostly address the problem of algorithmic complexity. We propose two major formats for the economical embedding of target data. The first approach adopts a non-symmetric form that can be computed using a specialized alternating optimization algorithm. The second is based on a symmetric representation and Newton-type iterations. We propose numerical implementations for both methodologies that avoid working with dense matrices and maintain low memory consumption. Furthermore, we study both types of embeddings numerically using real data from publicly available datasets. The results show that our algorithms yield a good approximation of the SimRank matrices, both in terms of the error norm (particularly the Chebyshev norm) and in preserving the average number of the most similar elements for each given node.