Graph construction based on labeled instances for semi-supervised learning

Semi-Supervised Learning (SSL) techniques have become very relevant since they require a small set of labeled data. In this context, graph-based algorithms have gained prominence in the area due to their capacity to exploiting, besides information about data points, the relationships among them. Moreover, data represented in graphs allow the use of collective inference (vertices can affect each other), propagation of labels (autocorrelation among neighbors) and use of neighborhood characteristics of a vertex. An important step in graph-based SSL methods is the conversion of tabular data into a weighted graph. The graph construction has a key role in the quality of the classification in graph-based methods. This paper explores a method for graph construction that uses available labeled data. We provide extensive experiments showing the proposed method has many advantages: good classification accuracy, quadratic time complexity, no sensitivity to the parameter k > 10, sparse graph formation with average degree around 2 and hub formation from the labeled points, which facilitates the propagation of labels