Related papers: Geometrically Inspired Kernel Machines for Collabo…

The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and…

Image harmonization aims to solve the visual inconsistency problem in composited images by adaptively adjusting the foreground pixels with the background as references. Existing methods employ local color transformation or region matching…

Recent advances suggest that a wide range of computer vision problems can be addressed more appropriately by considering non-Euclidean geometry. This paper tackles the problem of sparse coding and dictionary learning in the space of…

3D generative modeling is accelerating as the technology allowing the capture of geometric data is developing. However, the acquired data is often inconsistent, resulting in unregistered meshes or point clouds. Many generative learning…

Metric and kernel learning are important in several machine learning applications. However, most existing metric learning algorithms are limited to learning metrics over low-dimensional data, while existing kernel learning algorithms are…

In this paper, the framework of kernel machines with two layers is introduced, generalizing classical kernel methods. The new learning methodology provide a formal connection between computational architectures with multiple layers and the…

Multiscale Models are known to be successful in uncovering and analyzing the structures in data at different resolutions. In the current work we propose a feature driven Reproducing Kernel Hilbert space (RKHS), for which the associated…

Multi-task learning is a natural approach for computer vision applications that require the simultaneous solution of several distinct but related problems, e.g. object detection, classification, tracking of multiple agents, or denoising, to…

In this work, we consider the problem of learning a hierarchical generative model of an object from a set of images which show examples of the object in the presence of variable background clutter. Existing approaches to this problem are…

State-of-the-art neural networks are heavily over-parameterized, making the optimization algorithm a crucial ingredient for learning predictive models with good generalization properties. A recent line of work has shown that in a certain…

In this paper, a geometric framework for neural networks is proposed. This framework uses the inner product space structure underlying the parameter set to perform gradient descent not in a component-based form, but in a coordinate-free…

We present a novel approach to learn a kernel-based regression function. It is based on the useof conical combinations of data-based parameterized kernels and on a new stochastic convex optimization procedure of which we establish…

Quantum support vector machines have the potential to achieve a quantum speedup for solving certain machine learning problems. The key challenge for doing so is finding good quantum kernels for a given data set -- a task called kernel…

Kernel approximation via nonlinear random feature maps is widely used in speeding up kernel machines. There are two main challenges for the conventional kernel approximation methods. First, before performing kernel approximation, a good…

A structure-preserving kernel ridge regression method is presented that allows the recovery of nonlinear Hamiltonian functions out of datasets made of noisy observations of Hamiltonian vector fields. The method proposes a closed-form…

Supervised learning in reproducing kernel Hilbert space (RKHS) and vector-valued RKHS (vvRKHS) has been investigated for more than 30 years. In this paper, we provide a new twist to this rich literature by generalizing supervised learning…

In this paper, we focus on subspace-based learning problems, where data elements are linear subspaces instead of vectors. To handle this kind of data, Grassmann kernels were proposed to measure the space structure and used with classifiers,…

We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…

Gaussian Processes (GPs) are known to provide accurate predictions and uncertainty estimates even with small amounts of labeled data by capturing similarity between data points through their kernel function. However traditional GP kernels…

Many supervised learning problems involve high-dimensional data such as images, text, or graphs. In order to make efficient use of data, it is often useful to leverage certain geometric priors in the problem at hand, such as invariance to…