In recent years, users of ambient intelligence environments have been overwhelmed by the huge numbers of social media available. Consequentially, users have trouble finding social media suited to their needs. To help users in ambient environment get relevant media tailored to their interests, we propose a new method which adapts the Katz measure, a path-ensemble based proximity measure, for the use in social tagging services. We model the ternary relations among user, resource and tag as a weighted, undirected tripartite graph. We then apply the Katz measure to this graph, and exploit it to provide personalized recommendation for individual users within ambient intelligence environments. The experimental evaluations show that the proposed method improves the recommendation performance compared to existing algorithms.