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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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. Principal component analysis (PCA) involves a mathematical procedure that transforms a number of possibly correlated variables into a smaller number of uncorrelated variables called principal components. The first principal component accounts for as much of the variability in the data as possible, and each succeeding component accounts for as much of the remaining variability as possible. Depending on the field of application, it is also named the discrete Karhunen Loève transform (K.L.T.), the Hotelling transform or proper orthogonal decomposition (POD).