Node Embeddings and Exact Low-Rank Representations of Complex Networks
Sudhanshu Chanpuriya,Cameron Musco,Konstantinos Sotiropoulos,Charalampos Tsourakakis
In this work we show that the results of Seshadhri et al. are intimately connected to the model they use rather than the low-dimensional structure of complex networks. Specifically, we prove that a minor relaxation of their model can generate sparse graphs with high triangle density. Surprisingly, we show that this same model leads to exact low-dimensional factorizations of many real-world networks. We give a simple algorithm based on logistic principal component analysis (LPCA) that succeeds in finding such exact embeddings. Finally, we perform a large number of experiments that verify the ability of very low-dimensional embeddings to capture local structure in real-world networks.
