Metric projection for dynamic multiplex networks

Evolving multiplex networks are a powerful model for representing the dynamics along time of different phenomena, such as social networks, power grids, biological pathways. However, exploring the structure of the multiplex network time series is still an open problem. Here we propose a two-steps strategy to tackle this problem based on the concept of distance (metric) between networks. Given a multiplex graph, first a network of networks is built for each time steps, and then a real valued time series is obtained by the sequence of (simple) networks by evaluating the distance from the first element of the series. The effectiveness of this approach in detecting the occurring changes along the original time series is shown on a synthetic example first, and then on the Gulf dataset of political events

An introduction to spectral distances in networks (extended version)

Many functions have been recently defined to assess the similarity among networks as tools for quantitative comparison. They stem from very different frameworks - and they are tuned for dealing with different situations. Here we show an overview of the spectral distances, highlighting their behavior in some basic cases of static and dynamic synthetic and real networks

A unifying view for performance measures in multi-class prediction

In the last few years, many different performance measures have been introduced to overcome the weakness of the most natural metric, the Accuracy. Among them, Matthews Correlation Coefficient has recently gained popularity among researchers not only in machine learning but also in several application fields such as bioinformatics. Nonetheless, further novel functions are being proposed in literature. We show that Confusion Entropy, a recently introduced classifier performance measure for multi-class problems, has a strong (monotone) relation with the multi-class generalization of a classical metric, the Matthews Correlation Coefficient. Computational evidence in support of the claim is provided, together with an outline of the theoretical explanation

Sparse Predictive Structure of Deconvolved Functional Brain Networks

The functional and structural representation of the brain as a complex network is marked by the fact that the comparison of noisy and intrinsically correlated high-dimensional structures between experimental conditions or groups shuns typical mass univariate methods. Furthermore most network estimation methods cannot distinguish between real and spurious correlation arising from the convolution due to nodes' interaction, which thus introduces additional noise in the data. We propose a machine learning pipeline aimed at identifying multivariate differences between brain networks associated to different experimental conditions. The pipeline (1) leverages the deconvolved individual contribution of each edge and (2) maps the task into a sparse classification problem in order to construct the associated "sparse deconvolved predictive network", i.e., a graph with the same nodes of those compared but whose edge weights are defined by their relevance for out of sample predictions in classification. We present an application of the proposed method by decoding the covert attention direction (left or right) based on the single-trial functional connectivity matrix extracted from high-frequency magnetoencephalography (MEG) data. Our results demonstrate how network deconvolution matched with sparse classification methods outperforms typical approaches for MEG decoding