SparseGraphX: exponentially regularized optimal sparse graph for enhanced label propagation

Abstract

Graph-based semi-supervised learning’s inherent ability to exploit the underlying structure of data distribution for supplementing label propagation has gained momentum over recent years. However, its effectiveness highly relies on the graph's structure quality and deteriorates when dealing with high dimensional, noisy, unevenly distributed data thus, necessitating adaptivity with sparsity in graph construction. To achieve this, an Exponentially Regularized Optimal Sparse Graph (EROSG) is introduced that inculcates these characteristics by exploring local connectivity ensuring efficient label propagation with reduced complexity. Accordingly, EROSG constructs the affinity matrix using a novel distance metric to widen the sample-wise interclass deviation and strengthen the local connectivity. The resulting affinity matrix is then optimized by Lagrangian multipliers with non-negative and SoftMax constraints to yield the adaptive sparse graph facilitating label propagation. Extensive analysis of EROSG on diverse datasets demonstrates consistent and superior accuracy of over 93% with a minimum availability of 5–10% of labeled data which is lacking in its competitors. Also, EROSG’s parameter-free nature lessens realization complexity emphasizing the need of the hour.

Graphical abstract