  A novel approach for supervised classification analysis for high dimensional
and flat data (more variables than observations) is proposed. We use the
information of class-membership of observations to determine groups of
observations locally describing the group structure. By projecting the data on
the subspace spanned by those groups, local projections are defined based on
the projection concepts from Ortner et al. (2017a) and Ortner et al. (2017b).
For each local projection a local discriminant analysis (LDA) model is computed
using the information within the projection space as well as the distance to
the projection space. The models provide information about the quality of
separation for each class combination. Based on this information, weights are
defined for aggregating the LDA-based posterior probabilities of each subspace
to a new overall probability. The same weights are used for classifying new
observations.
  In addition to the provided methodology, implemented in the R-package lop, a
method of visualizing the connectivity of groups in high-dimensional spaces is
proposed on the basis of the posterior probabilities. A thorough evaluation is
performed using three different real-world datasets, underlining the strengths
of local projection based classification and the provided visualization
methodology.
