Local analysis. In addition to an overall analysis of quality of physical exercises GymSkill aims for unveiling interesting and
informative portions of the recorded sensor data streams. When analyzing re-occurring movements, which are smooth in
the ideal case, the term ‘interesting’ refers to those sections where the sensor data appear unusual compared to the rest.
This is e.g. the case when a participant hesitates or gets stuck while exercising.
Unlike standard techniques for time-series analysis (e.g. [28,29]) our approach processes sensor data of arbitrary
dimensionality. This is crucial since flattening sensor data to one-dimensional sequences (e.g. using the Euclidean norm) can
destroy potentially important information of the original signals. Our basic assumption is that sensor data for a particularly
analyzed movement should share certain (unknown) statistical properties. Unusual portions of a sequence will violate this
assumption and can thus be identified as such.
Algorithm 1 describes the local quality assessment algorithm — Principal Component Breakdown Analysis (PCBA). It is
based on a PCA of a sensor data sequence utilizing local neighborhoods. By means of a sliding window technique all analysis
windows of length w are extracted and a PCA model is learned. It is applied to project all frames to a lower-dimensional subspace
whose dimensionality is determined by the analysis of the eigenvalue spectrum. Given a pre-defined threshold for
reconstruction quality (typically 95% of the variance shall be preserved) the target dimensionality for a particular frame-size
is chosen. Using the lower-dimensional projection then the original frames are reconstructed. The resulting reconstruction
errors are then used as measure for the quality of the underlying movement, which is sample-wise assigned to the original
sequence. The idea behind this quality measure is that PCA models will require more eigenvectors to preserve a certain