ABSTRACT
Throughout this text, a number of locally homogeneous spaces (see Patrange-
naru (1994) [264]) have been discussed that arise as sample spaces in data
analysis. These manifolds are smooth, including Rp for multivariate analysis
and the spheres Sp−1 for directional data analysis. Certain Lie groups, such as the special orthogonal groups for the analysis of the movement of tectonic
plates (see Chang (1988) [63]) and the group of positive definite symmetric
matrices for DTI analysis (see Osborne et al. (2013) [258]), also fall into this
category. Additionally, real and complex Grassmann manifolds arise for the
analysis of affine shape spaces (see Patrangenaru and Mardia (2002) [274]),
Kendall’s similarity shape spaces (see Kendall (1984) [177]), and in signal
tracking problems. Products of real projective spaces are found in projective
shape analysis (see Mardia and Patrangenaru (2005) [233]).
