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WiFi positioning systems require radio maps in the form of either RF fingerprints or positions of WiFi access points (APs). In particular, knowledge of the AP positions is essential to enable a locating mechanism as well as to understand the nature of underlying WiFi networks, such as density, connectivity, interference characteristics, and so on. In this paper, we propose an approach called Serendipity, which locates WiFi APs in an unsupervised manner using radio scans collected by ordinary smartphone users. From the radio scans, we extract dissimilarities between all pairs of WiFi APs and estimate relative positions of APs by analyzing the dissimilarities based on a multidimensional scaling technique. We then find the absolute positions with additional radio scans whose positions are known. The discovered positions of WiFi APs are used for the positioning of smartphones or the management of the WiFi networks. To validate the proposed approach, we conducted experiments on several indoor locations.