Factored principal components analysis, with applications to face recognition

Abstract

A dimension reduction technique is proposed for matrix data, with applications to face recognition from images. In particular, we propose a factored covariance model for the data under study, estimate the parameters using maximum likelihood, and then carry out eigendecompositions of the estimated covariance matrix. We call the resulting method factored principal components analysis. We also develop a method for classification using a likelihood ratio criterion, which has previously been used for evaluating the strength of forensic evidence. The methodology is illustrated with applications in face recognition.

Bilinear Probabilistic Principal Component Analysis

“…Comparing (11), (12), (27), and (30), we can find that G c and G r are different from S c and S r . Therefore, the principal components by BPPCA and GLRAM are in general different.…”

“…For example, for linear discriminant analysis (LDA), the even more restrictive diagonal covariance assumption leads to the diagonal LDA [26], which is found to perform well on high-dimensional microarray data. Recently, Dryden et al [27] proposed a related dimension reduction technique for 2-D data called factored PCA (FPCA) which also assumes separable covariance. Indeed, it can be seen from (15) …”

“…N d c (0, c ). The covariance of these Nd r transformed observations is S c in (27). Thus, CM-step 1 performs PPCA on these transformed observations.…”

“…The most expensive computations are on the formations of S c in (27), S r in (30) and their eigen-decompositions. Using…”

Isotone additive latent variable models

“…PCA and its extensions are used in many applications such as pattern recognition (see e.g. Dryden et al 2009), chemometrics, and biomedical studies.…”