The Equivalence Between Principal Component Analysis and Nearest Flat in the Least Square Sense
In this paper, we declare the equivalence between the principal component analysis and the nearest q-flat in the least square sense by showing that, for given m data points, the linear manifold with nearest distance is identical to the linear manifold with largest variance. Furthermore, from this observation, we give a new simpler proof for the approach to find the nearest q-flat.
principal component analysis nearest q-flat linear manifold unsupervised learning eigenvalue decomposition 15a18 58c40