on using complex principal geodesic analysis to tackle variabilityamong angular data

Principal component analysis (pca) is one of the well-known tools formodeling and visualizing a data set with correlated variables. however, it cannot bedirectly employed for the data taking their values in non-euclidean space, such asangular data. an alternative option is to invoke the complex principal componentanalysis (cpca) which uses the euler formula to take the periodic feature of angles.another possibility is the dihedral angles principal geodesic analysis (dpga), consideringthe geodesic distance for the angles and then utilizing the pca. in this paper,we propose a new method called complex principal geodesic analysis (cpga), acombined version of dpga and cpca. it benefits from advantages of both tools toderive the complex covariance matrix and then invoke dimension reduction methods.the proposed method is applied to the dihedral angles of particular protein structure.