Principal geodesic analysis
Encyclopedia
In geometric data analysis
and statistical shape analysis
, principal geodesic analysis is a generalization of principal component analysis to a non-Euclidean
, non-linear setting of manifolds suitable for use with shape descriptors such as medial representations.
Geometric data analysis
Geometric data analysis can refer to geometric aspects of image analysis, pattern analysis and shape analysis or the approach of multivariate statistics that treats arbitrary data sets as clouds of points in n-dimensional space...
and statistical shape analysis
Statistical shape analysis
Statistical shape analysis is a geometrical analysis from a set of shapes in which statistics are measured to describe geometrical properties from similar shapes or different groups, for instance, the difference between male and female Gorilla skull shapes, normal and pathological bone shapes, etc...
, principal geodesic analysis is a generalization of principal component analysis to a non-Euclidean
Euclidean geometry
Euclidean geometry is a mathematical system attributed to the Alexandrian Greek mathematician Euclid, which he described in his textbook on geometry: the Elements. Euclid's method consists in assuming a small set of intuitively appealing axioms, and deducing many other propositions from these...
, non-linear setting of manifolds suitable for use with shape descriptors such as medial representations.