dynamic network data exploration through semi-supervised functional embedding
The paper presents a framework for semi-supervised nonlinear embedding methods useful for exploratory analysis and visualization of spatio-temporal network data. The method provides a functional embedding based on a neural network optimizing the graph-based cost function. It exploits an online stochastic gradient descent which, avoiding the costly matrix computations and the out-of-sample problem, makes it naturally applicable for large-scale dynamic spatio-temporal problems. The semi-supervised schemes are introduced to guide the method with precisely defined locations, pairwise distances or norms of the selected data samples in the embedded space. The method is useful for exploring the complex fully dynamic networks with a variable number of geo-referenced nodes and evolving edges. The approach is illustrated with a case study devoted to the real-time embedding of the geo-referenced data on instant messaging on the internet.
functional embedding complex systems manifold learning social networks