  We propose a network-filtering method, the Triangulated Maximally Filtered
Graph (TMFG), that provides an approximate solution to the Weighted Maximal
Planar Graph problem. The underlying idea of TMFG consists in building a
triangulation that maximizes a score function associated with the amount of
information retained by the network. TMFG uses as weights any arbitrary
similarity measure to arrange data into a meaningful network structure that can
be used for clustering, community detection and modeling. The method is fast,
adaptable and scalable to very large datasets, it allows online updating and
learning as new data can be inserted and deleted with combinations of local and
non-local moves. TMFG permits readjustments of the network in consequence of
changes in the strength of the similarity measure. The method is based on local
topological moves and can therefore take advantage of parallel and GPUs
computing. We discuss how this network-filtering method can be used intuitively
and efficiently for big data studies and its significance from an
information-theoretic perspective.
