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On GROUSE and Incremental SVD
GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an incremental
algorithm for identifying a subspace of Rn from a sequence of vectors in this
subspace, where only a subset of components of each vector is revealed at each
iteration. Recent analysis has shown that GROUSE converges locally at an
expected linear rate, under certain assumptions. GROUSE has a similar flavor to
the incremental singular value decomposition algorithm, which updates the SVD
of a matrix following addition of a single column. In this paper, we modify the
incremental SVD approach to handle missing data, and demonstrate that this
modified approach is equivalent to GROUSE, for a certain choice of an
algorithmic parameter
Packing ellipsoids with overlap
The problem of packing ellipsoids of different sizes and shapes into an
ellipsoidal container so as to minimize a measure of overlap between ellipsoids
is considered. A bilevel optimization formulation is given, together with an
algorithm for the general case and a simpler algorithm for the special case in
which all ellipsoids are in fact spheres. Convergence results are proved and
computational experience is described and illustrated. The motivating
application - chromosome organization in the human cell nucleus - is discussed
briefly, and some illustrative results are presented
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