We develop a method allowing us to reconstruct individual tastes of customers from a sparsely connected network of their opinions on products, services, or each other. Two distinct phase transitions occur as the density of edges in this network is increased: Above the first, macroscopic prediction of tastes becomes possible; while above the second, all unknown opinions can be uniquely reconstructed. We illustrate our ideas using a simple Gaussian model, which we study using both field-theoretical methods and numerical simulations. We point out a potential relevance of our approach to the field of bioinformatics.

• Received 6 April 2001

DOI:https://doi.org/10.1103/PhysRevLett.87.248701