Block Randomized Optimization for Adaptive Hypergraph Learning

TL;DR

This paper introduces block randomized SVD and conjugate gradient methods to efficiently perform adaptive hypergraph learning for image tagging, significantly reducing computational costs while maintaining high accuracy.

Contribution

It presents novel block randomized SVD and conjugate gradient approaches integrated into hypergraph weight estimation for scalable image tagging.

Findings

High accuracy in image tagging measured by F1 score

Reduced computational requirements for hypergraph weight estimation

Effective low-rank matrix approximations via tessellation

Abstract

The high-order relations between the content in social media sharing platforms are frequently modeled by a hypergraph. Either hypergraph Laplacian matrix or the adjacency matrix is a big matrix. Randomized algorithms are used for low-rank factorizations in order to approximately decompose and eventually invert such big matrices fast. Here, block randomized Singular Value Decomposition (SVD) via subspace iteration is integrated within adaptive hypergraph weight estimation for image tagging, as a first approach. Specifically, creating low-rank submatrices along the main diagonal by tessellation permits fast matrix inversions via randomized SVD. Moreover, a second approach is proposed for solving the linear system in the optimization problem of hypergraph learning by employing the conjugate gradient method. Both proposed approaches achieve high accuracy in image tagging measured by F1 score and succeed to reduce the computational requirements of adaptive hypergraph weight estimation.