Network equipment, such as routers, switches, and RADIUS servers, generate various log messages induced by network events such as hardware failures and protocol flaps. In large production networks, analyzing the log messages is crucial for diagnosing network anomalies; however, it has become challenging due to the following two reasons. First, the log messages are composed of unstructured text messages generated in accordance with vendor-specific rules. Second, network events that induce the log messages span several geographical locations, network layers, protocols, and services. We developed a method to tackle these obstacles consisting of two techniques: statistical template extraction (STE) and log tensor factorization (LTF). The former leverages a statistical clustering technique to automatically extract primary templates from unstructured log messages. The latter builds a statistical model that collects spatial-temporal patterns of log messages. Such spatial-temporal patterns provide useful insights into understanding the impact and patterns of hidden network events. We evaluate our techniques using a massive amount of network log messages collected from a large operating network and confirm that our model fits the data well. We also investigate several case studies that validate the usefulness of our method.