Learning locality-constrained collaborative representation for robust face recognition

• A coding algorithm integrates the locality with the global similarity of data.
• A new formulation of local consistency derives from similar inputs has similar codes.
• Our algorithm has an analytical solution and does not involve local minima.
• Consider the tasks of modeling facial images with various corruption and occlusions.

The models of low-dimensional manifold and sparse representation are two well-known concise models that suggest that each data can be described by a few characteristics. Manifold learning is usually investigated for dimension reduction by preserving some expected local geometric structures from the original space into a low-dimensional one. The structures are generally determined by using pairwise distance, e.g., Euclidean distance. Alternatively, sparse representation denotes a data point as a linear combination of the points from the same subspace. In practical applications, however, the nearby points in terms of pairwise distance may not belong to the same subspace, and vice versa. Consequently, it is interesting and important to explore how to get a better representation by integrating these two models together. To this end, this paper proposes a novel coding algorithm, called Locality-Constrained Collaborative Representation (LCCR), which introduce a kind of local consistency into coding scheme to improve the discrimination of the representation. The locality term derives from a biologic observation that the similar inputs have similar codes. The objective function of LCCR has an analytical solution, and it does not involve local minima. The empirical studies based on several popular facial databases show that LCCR is promising in recognizing human faces with varying pose, expression and illumination, as well as various corruptions and occlusions.