Component SPD Matrices: A lower-dimensional discriminative data descriptor for image set classification

In the domain of pattern recognition, using the SPD (Symmetric Positive Definite) matrices to represent data and taking the metrics of resulting Riemannian manifold into account have been widely used for the task of image set classification. In this paper, we propose a new data representation framework for image sets named CSPD (Component Symmetric Positive Definite). Firstly, we obtain sub-image sets by dividing the image set into square blocks with the same size, and use traditional SPD model to describe them. Then, we use the results of the Riemannian kernel on SPD matrices as similarities of corresponding sub-image sets. Finally, the CSPD matrix appears in the form of the kernel matrix for all the sub-image sets, and CSPDi,j denotes the similarity between i-th sub-image set and j-th sub-image set. Here, the Riemannian kernel is shown to satisfy the Mercer's theorem, so our proposed CSPD matrix is symmetric and positive definite and also lies on a Riemannian manifold. On three benchmark datasets, experimental results show that CSPD is a lower-dimensional and more discriminative data descriptor for the task of image set classification.Comment: 8 pages,5 figures, Computational Visual Media, 201

Identification of neprilysin as a potential target of arteannuin using computational drug repositioning

The discovery of arteannuin (qinghaosu) in the 20th Century was a major advance for medicine. Besides functioning as a malaria therapy, arteannuin is a pharmacological agent in a range of other diseases, but its mechanism of action remains obscure. In this study, the reverse docking server PharmMapper was used to identify potential targets of arteannuin. The results were checked using the chemical-protein interactome servers DRAR-CPI and DDI-CPI, and verified by AutoDock Vina. The results showed that neprilysin (also known as CD10), a common acute lymphoblastic leukaemia antigen, was the top disease-related target of arteannuin. The chemical-protein interactome and docking results agreed with those of PharmMapper, further implicating neprilysin as a potential target. Although experimental verification is required, this study provides guidance for future pharmacological investigations into novel clinical applications for arteannuin

Riemannian kernel based Nystr\"om method for approximate infinite-dimensional covariance descriptors with application to image set classification

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 Nystr\"om 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 Nystr\"om 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.Comment: 6 pages, 3 figures, International Conference on Pattern Recognition 201

Approximation of Nonlinear Functionals Using Deep ReLU Networks

In recent years, functional neural networks have been proposed and studied in order to approximate nonlinear continuous functionals defined on $L^p([-1, 1]^s)$ for integers $s\ge1$ and $1\le p<\infty$. However, their theoretical properties are largely unknown beyond universality of approximation or the existing analysis does not apply to the rectified linear unit (ReLU) activation function. To fill in this void, we investigate here the approximation power of functional deep neural networks associated with the ReLU activation function by constructing a continuous piecewise linear interpolation under a simple triangulation. In addition, we establish rates of approximation of the proposed functional deep ReLU networks under mild regularity conditions. Finally, our study may also shed some light on the understanding of functional data learning algorithms