  Representation based classification (RC) methods such as sparse RC (SRC) have
shown great potential in face recognition in recent years. Most previous RC
methods are based on the conventional regression models, such as lasso
regression, ridge regression or group lasso regression. These regression models
essentially impose a predefined assumption on the distribution of the noise
variable in the query sample, such as the Gaussian or Laplacian distribution.
However, the complicated noises in practice may violate the assumptions and
impede the performance of these RC methods. In this paper, we propose a modal
regression based atomic representation and classification (MRARC) framework to
alleviate such limitation. Unlike previous RC methods, the MRARC framework does
not require the noise variable to follow any specific predefined distributions.
This gives rise to the capability of MRARC in handling various complex noises
in reality. Using MRARC as a general platform, we also develop four novel RC
methods for unimodal and multimodal face recognition, respectively. In
addition, we devise a general optimization algorithm for the unified MRARC
framework based on the alternating direction method of multipliers (ADMM) and
half-quadratic theory. The experiments on real-world data validate the efficacy
of MRARC for robust face recognition.
