Efficient global network learning from local reconstructions

Discovering complex interactions is an important issue in numerous fields ranging from social sciences to systems biology. Over the past few decades, many network learning methods have exhibited competitive results on various types of data. A commonly reached conclusion is that some learning approaches are more advisable than others depending on the dataset type or the complexity of the underlying network. Another frequently encountered issue relates to the ever increasing number of variables that need to be simultaneously dealt with, especially when only a small number of observations is available. The ScaleNet, a novel reconstruction method which can embed different types of network discovery approaches within a spectral framework for large graphical model was introduced recently. The approach identifies sets of connected variables based on the magnitude and sign of the eigenvector elements of a normalized graph Laplacian matrix, and it learns in parallel multiple relevant sub-graphs of a large network. However, the number of eigenvectors to be used and the size of the sub-graphs are to be fixed by an expensive procedure of cross-validation. In this contribution, we propose heuristics to find both optimal number of eigenvectors and the number of nodes in the sub-networks. We illustrate by the results on standard large-scale data sets and on a real human gut graph reconstruction that the proposed approaches save computational time, i.e. are efficient, and reach the state-of-the-art performance.