Global Positioning System (GPS) measurements reveal rapid incoherent crustal motions at various points in the longitudinal valley along the eastern coast of Taiwan, exhibiting a strong effect of the collision between the Philippine sea plate and the Eurasian plate. Dynamic Time Warping (DTW) can identify the subtle crustal motion patterns by comparing two GPS position daily fluctuations (non-tidal, non-seasonal and non-CME). We applied a nonparametric, hierarchical agglomerative clustering algorithm based on the DTW for 27 three-component, GPS daily fluctuations from 2007 to 2018 near the eastern coast of Taiwan. Agglomerative Clustering algorithm categorized the east coast tectonics of Taiwan into 3 geographical clusters based on pairwise DTW distance metrics - on the Chengkung Fault (related to 2003 Mw6.8 Chengkung Earthquake), inside Longitudinal Valley, others. Principal Component Analysis on the clustered three-component time series delineates their group movement patterns.