Network Coordinate Systems (NCS) are promising techniques to predict unknown network distances from a limited number of measurements. Most NCS algorithms are based on metric space embedding and suffer from the inability to represent distance asymmetries and Triangle Inequality Violations (TIVs). To overcome these drawbacks, we formulate the problem of network distance prediction as guessing the missing elements of a distance matrix and solve it by matrix factorization. A distinct feature of our approach, called Decentralized Matrix Factorization (DMF), is that it is fully decentralized. The factorization of the incomplete distance matrix is collaboratively and iteratively done at all nodes with each node retrieving only a small number of distance measurements. There are no special nodes such as landmarks nor a central node where the distance measurements are collected and stored. We compare DMF with two popular NCS algorithms: Vivaldi and IDES. The former is based on metric space embedding, while the latter is also based on matrix factorization but uses landmarks. Experimental results show that DMF achieves competitive accuracy with the double advantage of having no landmarks and of being able to represent distance asymmetries and TIVs.