On the heterogeneous web information spaces, users have been suffering from efficiently searching for relevant information. This paper proposes a mediator agent system to estimate the semantics of unknown web spaces by learning the fragments gathered during the users' focused crawling. This process is organized as the following three tasks; (i) gathering semantic information about web spaces from personal agents while focused crawling in unknown spaces, (ii) reorganizing the information by using ontology alignment algorithm, and (iii) providing relevant semantic information to personal agents right before focused crawling. It makes the personal agent possible to recognize the corresponding user's behaviors in semantically heterogeneous spaces and predict his searching contexts. For the experiments, we implemented comparison-shopping system with heterogeneous web spaces. As a result, our proposed method efficiently supported the users, and then, network traffic was also reduced.