Mean variants on matrix manifolds
The geometrically elegant Stiefel and Grassmann manifolds have become organizational tools for data applications, such as illumination spaces for faces in digital photography. Modern data analysis involves increasingly large-scale data sets, both in terms of number of samples and number of features per sample. In circumstances such as when large-scale data has been mapped to a Stiefel or Grassmann manifold, the computation of mean representatives for clusters of points on these manifolds is a valuable tool. We derive three algorithms for determining mean representatives for a cluster of points ...
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Marks, Justin D.
Peterson, Chris; Kirby, Michael