As the Internet has become a communication infrastructure, inter-domain routing instabilities have become prone to serious problems. Some studies have proposed methods that infer instabilities and their locations by clustering BGP update messages collected at multiple observation points and are based on post-processing using public messages. However, to realize real-time processing, which is vital for network operations, single point observation is a feasible option with costs and today's competitive environments in mind. Therefore, we propose an inference method including a new clustering algorithm that is suitable for messages collected at a single observation point. We also describe the empirical results used to validate our method. Keywords-component; BGP; routing instability; analysis of the Internet; network operation