Related papers: Spatial Power Estimation via Riemannian Covariance…
This paper introduces sparse coding and dictionary learning for Symmetric Positive Definite (SPD) matrices, which are often used in machine learning, computer vision and related areas. Unlike traditional sparse coding schemes that work in…
Riemannian submanifold optimization with momentum is computationally challenging because, to ensure that the iterates remain on the submanifold, we often need to solve difficult differential equations. Here, we simplify such difficulties…
Symmetric Positive Definite (SPD) matrices have been widely used for data representation in many visual recognition tasks. The success mainly attributes to learning discriminative SPD matrices with encoding the Riemannian geometry of the…
In recent years, stochastic variance reduction algorithms have attracted considerable attention for minimizing the average of a large but finite number of loss functions. This paper proposes a novel Riemannian extension of the Euclidean…
Spatial modulation (SM) is a promising multiple-input multiple-output system used to increase spectral efficiency. The maximum likelihood (ML) decoder jointly detects the transmitted SM symbol, which is of high complexity. In this paper, a…
Multi-Task Learning (MTL) seeks to boost statistical power and learning efficiency by discovering structure shared across related tasks. State-of-the-art MTL representation methods, however, usually treat the latent representation matrix as…
We consider the problem of joint estimation of structured covariance matrices. Assuming the structure is unknown, estimation is achieved using heterogeneous training sets. Namely, given groups of measurements coming from centered…
In this paper, we develop a method for solving the problem of minimizing the $H^2$ error norm between the transfer functions of original and reduced systems on the set of stable matrices and two Euclidean spaces. That is, we develop a…
In this paper, we propose a nonlinear dimensionality reduction algorithm for the manifold of Symmetric Positive Definite (SPD) matrices that considers the geometry of SPD matrices and provides a low dimensional representation of the…
This study investigates the application of Riemannian geometry-based methods for brain decoding using invasive electrophysiological recordings. Although previously employed in non-invasive, the utility of Riemannian geometry for invasive…
As a representation learning method, nearest regularized subspace(NRS) algorithm is an effective tool to obtain both accuracy and speed for PolSAR image classification. However, existing NRS methods use the polarimetric feature vector but…
Spectral compressed sensing involves reconstructing a spectral-sparse signal from a subset of uniformly spaced samples, with applications in radar imaging and wireless channel estimation. By fully exploiting the signal structures, this…
We introduce a divergence measure between data distributions based on operators in reproducing kernel Hilbert spaces defined by kernels. The empirical estimator of the divergence is computed using the eigenvalues of positive definite Gram…
This paper proposes an uncalibrated photometric stereo method for non-Lambertian scenes based on deep learning. Unlike previous approaches that heavily rely on assumptions of specific reflectances and light source distributions, our method…
This work puts forth low-complexity Riemannian subspace descent algorithms for the minimization of functions over the symmetric positive definite (SPD) manifold. Different from the existing Riemannian gradient descent variants, the proposed…
Existing deep embedding methods in vision tasks are capable of learning a compact Euclidean space from images, where Euclidean distances correspond to a similarity metric. To make learning more effective and efficient, hard sample mining is…
We propose a novel estimation procedure for certain spectral distributions associated with a class of high dimensional linear time series. The processes under consideration are of the form $X_t = \sum_{\ell=0}^\infty \mathbf{A}_\ell…
Local feature matching remains a fundamental challenge in computer vision. Recent Area to Point Matching (A2PM) methods have improved matching accuracy. However, existing research based on this framework relies on inefficient pixel-level…
We introduce an approach to computing and comparing Covariance Descriptors (CovDs) in infinite-dimensional spaces. CovDs have become increasingly popular to address classification problems in computer vision. While CovDs offer some…
A novel linear classification method that possesses the merits of both the Support Vector Machine (SVM) and the Distance-weighted Discrimination (DWD) is proposed in this article. The proposed Distance-weighted Support Vector Machine method…