Local Coordinate Concept Factorization for Image Representation

Learning sparse representation of high-dimensional data is a state-of-the-art method for modeling data. Matrix factorization-based techniques, such as nonnegative matrix factorization and concept factorization (CF), have shown great advantages in this area, especially useful for image representation. Both of them are linear learning problems and lead to a sparse representation of the images. However, the sparsity obtained by these methods does not always satisfy locality conditions. For example, the learned new basis vectors may be relatively far away from the original data. Thus, we may not be able to achieve the optimal performance when using the new representation for other learning tasks, such as classification and clustering. In this paper, we introduce a locality constraint into the traditional CF. By requiring the concepts (basis vectors) to be as close to the original data points as possible, each datum can be represented by a linear combination of only a few basis concepts. Thus, our method is able to achieve sparsity and locality simultaneously. We analyze the complexity of our novel algorithm and demonstrate the effectiveness in comparison with the state-of-the-art approaches through a set of evaluations based on real-world applications.