A Novel Locally Linear KNN Method with Applications to Visual Recognition

A locally linear K Nearest Neighbor (LLK) method is presented in this paper with applications to robust visual recognition. Specifically, the concept of an ideal representation is first presented, which improves upon the traditional sparse representation in many ways. The objective function based on a host of criteria for sparsity, locality, and reconstruction is then optimized to derive a novel representation, which is an approximation to the ideal representation. The novel representation is further processed by two classifiers, namely, an LLK-based classifier and a locally linear nearest mean-based classifier, for visual recognition. The proposed classifiers are shown to connect to the Bayes decision rule for minimum error. Additional new theoretical analysis is presented, such as the nonnegative constraint, the group regularization, and the computational efficiency of the proposed LLK method. New methods such as a shifted power transformation for improving reliability, a coefficients' truncating method for enhancing generalization, and an improved marginal Fisher analysis method for feature extraction are proposed to further improve visual recognition performance. Extensive experiments are implemented to evaluate the proposed LLK method for robust visual recognition. In particular, eight representative data sets are applied for assessing the performance of the LLK method for various visual recognition applications, such as action recognition, scene recognition, object recognition, and face recognition.