相关论文: Sparse Coding and Dictionary Learning for Symmetri…

Many approaches to transform classification problems from non-linear to linear by feature transformation have been recently presented in the literature. These notably include sparse coding methods and deep neural networks. However, many of…

A popular approach within the signal processing and machine learning communities consists in modelling signals as sparse linear combinations of atoms selected from a learned dictionary. While this paradigm has led to numerous empirical…

This paper tackles algorithmic and theoretical aspects of dictionary learning from incomplete and random block-wise image measurements and the performance of the adaptive dictionary for sparse image recovery. This problem is related to…

Over the past decade, learning a dictionary from input images for sparse modeling has been one of the topics which receive most research attention in image processing and compressed sensing. Most existing dictionary learning methods…

We address the non-convex optimisation problem of finding a sparse matrix on the Stiefel manifold (matrices with mutually orthogonal columns of unit length) that maximises (or minimises) a quadratic objective function. Optimisation problems…

Dictionary learning methods continue to gain popularity for the solution of challenging inverse problems. In the dictionary learning approach, the computational forward model is replaced by a large dictionary of possible outcomes, and the…

Encoding time-series with Linear Dynamical Systems (LDSs) leads to rich models with applications ranging from dynamical texture recognition to video segmentation to name a few. In this paper, we propose to represent LDSs with…

We tackle the problem of optimizing over all possible positive definite radial kernels on Riemannian manifolds for classification. Kernel methods on Riemannian manifolds have recently become increasingly popular in computer vision. However,…

Sparse dictionary coding represents signals as linear combinations of a few dictionary atoms. It has been applied to images, time series, graph signals and multi-way spatio-temporal data by jointly employing temporal and spatial…

These notes provide a self-contained introduction to kernel methods and their geometric foundations in machine learning. Starting from the construction of Hilbert spaces, we develop the theory of positive definite kernels, reproducing…

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…

We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear…

Sparse coding, which is the decomposition of a vector using only a few basis elements, is widely used in machine learning and image processing. The basis set, also called dictionary, is learned to adapt to specific data. This approach has…

Many imaging science tasks can be modeled as a discrete linear inverse problem. Solving linear inverse problems is often challenging, with ill-conditioned operators and potentially non-unique solutions. Embedding prior knowledge, such as…

Sparse coding has been proposed as a theory of visual cortex and as an unsupervised algorithm for learning representations. We show empirically with the MNIST dataset that sparse codes can be very sensitive to image distortions, a behavior…

Dictionary learning is the task of determining a data-dependent transform that yields a sparse representation of some observed data. The dictionary learning problem is non-convex, and usually solved via computationally complex iterative…

We study Sparse Multiple Kernel Learning (SMKL), which is the problem of selecting a sparse convex combination of prespecified kernels for support vector binary classification. Unlike prevailing l1 regularized approaches that approximate a…

We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…

In this paper, a novel framework of sparse kernel learning for Support Vector Data Description (SVDD) based anomaly detection is presented. In this work, optimal sparse feature selection for anomaly detection is first modeled as a Mixed…

Multi-channel sparse blind deconvolution, or convolutional sparse coding, refers to the problem of learning an unknown filter by observing its circulant convolutions with multiple input signals that are sparse. This problem finds numerous…