1 research outputs found
Optimal Algorithms for -subspace Signal Processing
We describe ways to define and calculate -norm signal subspaces which
are less sensitive to outlying data than -calculated subspaces. We start
with the computation of the maximum-projection principal component of a
data matrix containing signal samples of dimension . We show that while
the general problem is formally NP-hard in asymptotically large , , the
case of engineering interest of fixed dimension and asymptotically large
sample size is not. In particular, for the case where the sample size is
less than the fixed dimension (), we present in explicit form an optimal
algorithm of computational cost . For the case , we present an
optimal algorithm of complexity . We generalize to multiple
-max-projection components and present an explicit optimal subspace
calculation algorithm of complexity where is the
desired number of principal components (subspace rank). We conclude with
illustrations of -subspace signal processing in the fields of data
dimensionality reduction, direction-of-arrival estimation, and image
conditioning/restoration