We propose a machine learning approach to characterize the functional status of astrocytes, the most abundant cells in human brain, based on time-lapse Ca2+ imaging data. The interest in analyzing astrocyte Ca2+ dynamics is evoked by recent discoveries that astrocytes play proactive regulatory roles in neural information processing, and is enabled by recent technical advances in modern microscopy and ultrasensitive genetically encoded Ca2+ indicators. However, current analysis relies on eyeballing the time-lapse imaging data and manually drawing regions of interest, which not only limits the analysis throughput but also at risk to miss important information encoded in the big complex dynamic data. Thus, there is an increased demand to develop sophisticated tools to dissect Ca2+ signaling in astrocytes, which is challenging due to the complex nature of Ca2+ signaling and low signal to noise ratio. We develop Functional AStrocyte Phenotyping (FASP) to automatically detect functionally independent units (FIUs) and extract the corresponding characteristic curves in an integrated way. FASP is data-driven and probabilistically principled, flexibly accounts for complex patterns and accurately controls false discovery rates. We demonstrate the effectiveness of FASP on both synthetic and real data sets.