A Quest for Structure: Jointly Learning the Graph Structure and Semi-Supervised Classification

Semi-supervised learning (SSL) is effectively used for numerous classification problems, thanks to its ability to make use of abundant unlabeled data. The main assumption of various SSL algorithms is that the nearby points on the data manifold are likely to share a label. Graph-based SSL constructs a graph from point-cloud data as an approximation to the underlying manifold, followed by label inference. It is no surprise that the quality of the constructed graph in capturing the essential structure of the data is critical to the accuracy of the subsequent inference step [6]. How should one construct a graph from the input point-cloud data for graph-based SSL? In this work we introduce a new, parallel graph learning framework (called PG-learn) for the graph construction step of SSL. Our solution has two main ingredients: (1) a gradient-based optimization of the edge weights (more specifically, different kernel bandwidths in each dimension) based on a validation loss function, and (2) a parallel hyperparameter search algorithm with an adaptive resource allocation scheme. In essence, (1) allows us to search around a (random) initial hyperparameter configuration for a better one with lower validation loss. Since the search space of hyperparameters is huge for high-dimensional problems, (2) empowers our gradient-based search to go through as many different initial configurations as possible, where runs for relatively unpromising starting configurations are terminated early to allocate the time for others. As such, PG-learn is a carefully-designed hybrid of random and adaptive search. Through experiments on multi-class classification problems, we show that PG-learn significantly outperforms a variety of existing graph construction schemes in accuracy (per fixed time budget for hyperparameter tuning), and scales more effectively to high dimensional problems.