Regression from uncertain labels and its applications to soft biometrics

In this paper, we investigate two soft-biometric problems: 1) age estimation and 2) pose estimation, within the scenario where uncertainties exist for the available labels of the training samples. These two tasks are generally formulated as the automatic design of a regressor from training samples with uncertain nonnegative labels. First, the nonnegative label is predicted as the Frobenius norm of a matrix, which is bilinearly transformed from the nonlinear mappings of a set of candidate kernels. Two transformation matrices are then learned for deriving such a matrix by solving two semidefinite programming (SDP) problems, in which the uncertain label of each sample is expressed as two inequality constraints. The objective function of SDP controls the ranks of these two matrices and, consequently, automatically determines the structure of the regressor. The whole framework for the automatic design of a regressor from samples with uncertain nonnegative labels has the following characteristics: 1) the SDP formulation makes full use of the uncertain labels, instead of using conventional fixed labels; 2) regression with the Frobenius norm of matrix naturally guarantees the nonnegativity of the labels, and greater prediction capability is achieved by integrating the squares of the matrix elements, which to some extent act as weak regressors; and 3) the regressor structure is automatically determined by the pursuit of simplicity, which potentially promotes the algorithmic generalization capability. Extensive experiments on two human age databases: 1) FG-NET and 2) Yamaha, and the Pointing'04 head pose database, demonstrate encouraging estimation accuracy improvements over conventional regression algorithms without taking the uncertainties within the labels into account.