Fast approximate factor analysis

The principal orthogonal factor analysis or Karhunen-Loeve algorithm may be sped up by a low-complexity preprocessing step. A fast transform is selected from a large library of wavelet-like orthonormal bases, so as to maximize transform coding gain for an ensemble of vectors. Only the top few coefficients in the new basis, in order of variance across the ensemble, are then decorrelated by diagonalizing the autocovariance matrix. The method has computational complexity O(d² log d + d³) and 0(d log d + d'²) respectively for training and classifying a d-dimensional system, where d' <C d. One application is described, the reduction of an ensemble of 16,384-pixel face images to a 10-parameter space using a desktop computer, retaining 90% of the variance of the ensemble.