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In this paper, we developed a new robust part-based model for facial landmark localization and detection via affine transformation. In contrast to the existing works, the new algorithm incorporates affine transformations with the robust regression to tackle the potential effects of outliers and heavy sparse noises, occlusions and illuminations. As such, the distorted or misaligned objects can be rectified by affine transformations and the patterns of occlusions and outliers can be explicitly separated from the true underlying objects in big data. Moreover, the search of the optimal parameters and affine transformations is cast as a constrained optimization programming. To mitigate the computations, a new set of equations is derived to update the parameters involved and the affine transformations iteratively in a round-robin manner. Our way to update the parameters compared to the state of the art of the works is relatively better, as we employ a fast alternating direction method for multiplier (ADMM) algorithm that solves the parameters separately. Simulations show that the proposed method outperforms the state-of-the-art works on facial landmark localization and detection on the COFW, HELEN, and LFPW datasets. [ABSTRACT FROM AUTHOR]