Riemannian kernel based Nyström method for approximate infinite-dimensional covariance descriptors with application to image set classification
This work addresses computational efficiency and discriminative power issues in image set classification for pattern recognition applications, representing an incremental improvement.
The paper tackled the problem of high computational load and implicit form of infinite-dimensional covariance descriptors (CovDs) for image set classification by proposing a Riemannian kernel-based Nyström method to approximate them, resulting in improved performance over original CovDs on three benchmark datasets.
In the domain of pattern recognition, using the CovDs (Covariance Descriptors) to represent data and taking the metrics of the resulting Riemannian manifold into account have been widely adopted for the task of image set classification. Recently, it has been proven that infinite-dimensional CovDs are more discriminative than their low-dimensional counterparts. However, the form of infinite-dimensional CovDs is implicit and the computational load is high. We propose a novel framework for representing image sets by approximating infinite-dimensional CovDs in the paradigm of the Nyström method based on a Riemannian kernel. We start by modeling the images via CovDs, which lie on the Riemannian manifold spanned by SPD (Symmetric Positive Definite) matrices. We then extend the Nyström method to the SPD manifold and obtain the approximations of CovDs in RKHS (Reproducing Kernel Hilbert Space). Finally, we approximate infinite-dimensional CovDs via these approximations. Empirically, we apply our framework to the task of image set classification. The experimental results obtained on three benchmark datasets show that our proposed approximate infinite-dimensional CovDs outperform the original CovDs.