To construct a WiFi positioning system, dedicated individuals usually gather radio scans with ground truth data. This laborious operation limits the widespread use of WiFi-based locating system. Off-the-shelf smartphones have the capability to scan radio signals from WiFi Access Points (APs). In this paper we propose a scheme to construct a map of WiFi AP positions autonomously without ground truth information. From radio scans, we extract dissimilarities between pairs of WiFi APs, then analyze the dissimilarities to produce a geometric configuration of WiFi APs based on a multidimensional scaling technique. To validate our scheme, we conducted experiments on five floors of an office building that has an area of 50 m by 35 m in each floor. WiFi APs were located within a 10m error range, and floors of APs are recognized without error.