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We present a new method for the automatic classification of Persistent Scatters Interferometry (PSI) time series based on a conditional sequence of statistical tests. Time series are classified into distinctive predefined target trends, such as uncorrelated, linear, quadratic, bilinear and discontinuous, that describe different styles of ground deformation. Our automatic analysis overcomes limits related to the visual classification of PSI time series, which cannot be carried out systematically for large datasets. The method has been tested with reference to landslides using PSI datasets covering the northern Apennines of Italy. The clear distinction between the relative frequency of uncorrelated, linear and non-linear time series with respect to mean velocity distribution suggests that different target trends are related to different physical processes that are likely to control slope movements. The spatial distribution of classified time series is also consistent with respect the known distribution of flat areas, slopes and landslides in the tests area. Classified time series enhances the radar interpretation of slope movements at the site scale, pointing out significant advantages in comparison with the conventional analysis based solely on the mean velocity. The test application also warns against potentially misleading classification outputs in case of datasets affected by systematic errors. Although the method was developed and tested to investigate landslides, it should be also useful for the analysis of other ground deformation processes such as subsidence, swelling/shrinkage of soils, or uplifts due to deep injections in reservoirs.