Local Principal Curves

Principal components are a well established tool in dimension
reduction. The extension to principal curves allows for general
smooth curves which pass through the middle of a p-dimensional data
cloud. In this paper local principal curves are introduced, which
are based on the localization of principal component analysis. The
proposed algorithm is able to identify closed curves as well as
multiple curves which may or may not be connected. For the
evaluation of performance of data reduction obtained by principal
curves a measure of coverage is suggested. The selection of tuning
parameters is considered explicitely yielding an algorithm which is
easy to apply. By use of simulated and real data sets the approach
is compared to various alternative concepts of principal curves.