Large Sparse Cone Non-negative Matrix Factorization for Image Annotation

Image annotation assigns relevant tags to query images based on their semantic contents. Since Non-negative Matrix Factorization (NMF) has the strong ability to learn parts-based representations, recently, a number of algorithms based on NMF have been proposed for image annotation and have achieved good performance. However, most of the efforts have focused on the representations of images and annotations. The properties of the semantic parts have not been well studied. In this article, we revisit the sparseness-constrained NMF (sNMF) proposed by Hoyer 2004. By endowing the sparseness constraint with a geometric interpretation and sNMF with theoretical analyses of the generalization ability, we show that NMF with such a sparseness constraint has three advantages for image annotation tasks: (i) The sparseness constraint is more ℓ 0 -norm oriented than the ℓ 1 -norm-based sparseness, which significantly enhances the ability of NMF to robustly learn semantic parts. (ii) The sparseness constraint has a large cone interpretation and thus allows the reconstruction error of NMF to be smaller, which means that the learned semantic parts are more powerful to represent images for tagging. (iii) The learned semantic parts are less correlated, which increases the discriminative ability for annotating images. Moreover, we present a new efficient large sparse cone NMF (LsCNMF) algorithm to optimize the sNMF problem by employing the Nesterov’s optimal gradient method. We conducted experiments on the PASCAL VOC07 dataset and demonstrated the effectiveness of LsCNMF for image annotation.