  The use of orthogonal projections on high-dimensional input and target data
in learning frameworks is studied. First, we investigate the relations between
two standard objectives in dimension reduction, preservation of variance and of
pairwise relative distances. Investigations of their asymptotic correlation as
well as numerical experiments show that a projection does usually not satisfy
both objectives at once. In a standard classification problem we determine
projections on the input data that balance the objectives and compare
subsequent results. Next, we extend our application of orthogonal projections
to deep learning tasks and introduce a general framework of augmented target
loss functions. These loss functions integrate additional information via
transformations and projections of the target data. In two supervised learning
problems, clinical image segmentation and music information classification, the
application of our proposed augmented target loss functions increase the
accuracy.
