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New depth sensors, like the Microsoft Kinect, produce streams of human pose data. These discrete pose streams can be viewed as noisy samples of an underlying continuous ideal curve that describes a trajectory through high-dimensional pose space. This paper introduces a technique for generalized curvature analysis (GCA) that determines features along the trajectory which can be used to characterize change and segment motion. Tools are developed for approximating generalized curvatures at mean points along a curve in terms of the singular values of local mean-centered data balls. The features of the GCA algorithm are illustrated on both synthetic and real examples, including data collected from a Kinect II sensor. We also applied GCA to the Carnegie Mellon University Motion Capture (MoCaP) database. Given that GCA scales linearly with the length of the time series we are able to analyze large data sets without down sampling. It is demonstrated that the generalized curvature approximations can be used to segment pose streams into motions and transitions between motions. The GCA algorithm can identify 94.2% of the transitions between motions without knowing the set of possible motions in advance, even though the subjects do not stop or pause between motions.