*Paper ID sheet*
- TITLE:
**Design of continuous-time flows on intertwined orbit spaces**
- AUTHORS: P.-A. Absil, C. Lageman, J. H. Manton
- ABSTRACT:

Consider a space $M$ endowed with two or more Lie group actions. Under
a certain condition on the orbits of the Lie group actions, we show
how to construct a flow on $M$ that projects to prescribed flows on
the orbit spaces of the group actions. Hence, in order to design a
flow that converges to the intersection of given orbits, it suffices
to design flows on the various orbit spaces that display convergence
to the desired orbits, and then to lift these flows to $M$ using the
proposed procedure. We illustrate the technique by creating a flow for
principal component analysis. The flow projects to a flow on the
Grassmann manifold that achieves principal subspace analysis and to a
flow on the ``shape'' manifold that converges to the set of
orthonormal matrices.
- KEY WORDS:
- STATUS: Proceedings of the 46th IEEE Conference on Decision and Control (CDC 2007), pp. 6244-6249, 2007.

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