A novel locally linear KNN model for visual recognition

This paper presents a novel locally linear KNN model with the goal of not only developing efficient representation and classification methods, but also establishing a relation between them so as to approximate some classification rules, e.g. the Bayes decision rule. Towards that end, first, the proposed model represents the test sample as a linear combination of all the training samples and derives a new representation by learning the coefficients considering the reconstruction, locality and sparsity constraints. The theoretical analysis shows that the new representation has the grouping effect of the nearest neighbors, which is able to approximate the 'ideal representation'. And then the locally linear KNN model based classifier (LLKNNC), which shows its connection to the Bayes decision rule for minimum error in the view of kernel density estimation, is proposed for classification. Besides, the locally linear nearest mean classifier (LLNMC), whose relation to the LLKNNC is just like the nearest mean classifier to the KNN classifier, is also derived. Furthermore, to provide reliable kernel density estimation, the shifted power transformation and the coefficients cut-off method are applied to improve the performance of the proposed method. The effectiveness of the proposed model is evaluated on several visual recognition tasks such as face recognition, scene recognition, object recognition and action recognition. The experimental results show that the proposed model is effective and outperforms some other representative popular methods.