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Geotagging personal data such as photos and videos are continuously becoming easier and more popular. Nevertheless, browsing such data on general purpose maps can be difficult, due to the frequent zoom and pan operations as well as visual components unnecessary for the task. This paper presents Placegram, a compact diagrammatic map visualization for personal geotagged data browsing based on cognitive map theories. An evaluation using real-life data sets shows that the speed of finding and pointing to places from the participants' own data increased by a factor of 2.1-2.9, and the number of interesting places discovered from others' data within a time limit increased by 48.8 percent in Placegram compared to a general purpose map. Placegram was even slightly faster than a simple text list, while at the same time, preserving the geographic senses of direction and location. Subjective ratings and comments from participants support these results, indicating that Placegram is significantly preferred over both a general map and a text list.