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The popularity of embedded positioning technologies in mobile devices and the development of mobile communication technology have paved the way for powerful location-based services (LBSs). To make LBSs useful and user- friendly, heavy use is made of context information, including patterns in user location data which are extracted by data mining methods. However, there is a potential conflict of interest: the data mining methods want as precise data as possible, while the users want to protect their privacy by not disclosing their exact movements. This paper aims to resolve this conflict by proposing a general framework that allows user location data to be anonymized, thus preserving privacy, while still allowing interesting patterns to be discovered. The framework allows users to specify individual desired levels of privacy that the data collection and mining system will then meet. Privacy-preserving methods are proposed for a core data mining task, namely finding dense spatio-temporal regions. An extensive set of experiments evaluate the methods, comparing them to their non- privacy-preserving equivalents. The experiments show that the framework still allows most patterns to be found, even when privacy is preserved.