  Subspace models play an important role in a wide range of signal processing
tasks, and this paper explores how the pairwise geometry of subspaces
influences the probability of misclassification. When the mismatch between the
signal and the model is vanishingly small, the probability of misclassification
is determined by the product of the sines of the principal angles between
subspaces. When the mismatch is more significant, the probability of
misclassification is determined by the sum of the squares of the sines of the
principal angles. Reliability of classification is derived in terms of the
distribution of signal energy across principal vectors. Larger principal angles
lead to smaller classification error, motivating a linear transform that
optimizes principal angles. The transform presented here (TRAIT) preserves some
specific characteristic of each individual class, and this approach is shown to
be complementary to a previously developed transform (LRT) that enlarges
inter-class distance while suppressing intra-class dispersion. Theoretical
results are supported by demonstration of superior classification accuracy on
synthetic and measured data even in the presence of significant model mismatch.
