  In this paper a novel efficient method for representation of facial action
units by encoding an image sequence as a fourth-order tensor is presented. The
multilinear tensor-based extension of the biased discriminant analysis (BDA)
algorithm, called multilinear biased discriminant analysis (MBDA), is first
proposed. Then, we apply the MBDA and two-dimensional BDA (2DBDA) algorithms,
as the dimensionality reduction techniques, to Gabor representations and the
geometric features of the input image sequence respectively. The proposed
scheme can deal with the asymmetry between positive and negative samples as
well as curse of dimensionality dilemma. Extensive experiments on Cohn-Kanade
database show the superiority of the proposed method for representation of the
subtle changes and the temporal information involved in formation of the facial
expressions. As an accurate tool, this representation can be applied to many
areas such as recognition of spontaneous and deliberate facial expressions,
multi modal/media human computer interaction and lie detection efforts.
