2 research outputs found
Principal Component Analysis Based on T-norm Maximization
Classical principal component analysis (PCA) may suffer from the sensitivity
to outliers and noise. Therefore PCA based on -norm and -norm
() have been studied. Among them, the ones based on -norm
seem to be most interesting from the robustness point of view. However, their
numerical performance is not satisfactory. Note that, although T-norm
is similar to -norm () in some sense, it has the stronger
suppression effect to outliers and better continuity. So PCA based on
T-norm is proposed in this paper. Our numerical experiments have shown
that its performance is superior than PCA- and SPCA as well as
PCA, PCA- obviously
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