RGCLI: Robust Graph that Considers Labeled Instances for Semi-Supervised Learning

Graph-based semi-supervised learning (SSL) provides a powerful framework for the modeling of manifold structures in high-dimensional spaces. Additionally, graph representation is effective for the propagation of the few initial labels existing in training data. Graph-based SSL requires robust graphs as input for an accurate data mining task, such as classification. In contrast to most graph construction methods, which ignore the labeled instances available in SSL scenarios, a previous study proposed a graph-construction method, named GBILI, to exploit the informativeness conveyed by such instances available in a semi-supervised classification domain. Here, we have improved the method proposing an optimized algorithm referred to as Robust Graph that Considers Labeled Instances (RGCLI) for the generation of more robust graphs. The contributions of this paper are threefold: i) reduction of GBILI time complexity from quadratic to O(nklogn). This enhancement allows addressing large datasets; ii) demonstration of RGCLI mathematical properties, proving the constructed graph is an optimal graph to model the smoothness assumption of SSL; and iii) evaluation of the efficacy of the proposed approach in a comprehensive semi-supervised classification scenario with several datasets, including an image segmentation task, which needs a large graph to represent the image. Such experiments show the use of labeled vertices in the graph construction process improves the graph topology, hence, the learning task in which it will be employed.