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The transcriptomics of cancer tumors are characterized with tens of thousands of gene expression features. Patient prognosis or tumor stage can be assessed by machine learning techniques like supervised classification tasks given a gene…

This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…

Learning in Riemannian orbifolds is motivated by existing machine learning algorithms that directly operate on finite combinatorial structures such as point patterns, trees, and graphs. These methods, however, lack statistical…

We consider discretized two-dimensional PDE-constrained shape optimization problems, in which shapes are represented by triangular meshes. Given the connectivity, the space of admissible vertex positions was recently identified to be a…

Lithography is fundamental to integrated circuit fabrication, necessitating large computation overhead. The advancement of machine learning (ML)-based lithography models alleviates the trade-offs between manufacturing process expense and…

In this note we present criteria on both symbols and integral kernels ensuring that the corresponding operators on compact manifolds belong to Schatten classes. A specific test for nuclearity is established as well as the corresponding…

We study positive definiteness of kernels $K(x,y)$ on two-point homogeneous spaces. As opposed to the classical case, which has been developed and studied in the existing literature, we allow the kernel to have an (integrable) singularity…

Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are…

Deep kernel learning provides an elegant and principled framework for combining the structural properties of deep learning algorithms with the flexibility of kernel methods. By means of a deep neural network, we learn a parametrized kernel…

In this paper, we propose a multi-kernel classifier learning algorithm to optimize a given nonlinear and nonsmoonth multivariate classifier performance measure. Moreover, to solve the problem of kernel function selection and kernel…

Low rank representation (LRR) has recently attracted great interest due to its pleasing efficacy in exploring low-dimensional subspace structures embedded in data. One of its successful applications is subspace clustering which means data…

Random feature maps are used to decrease the computational cost of kernel machines in large-scale problems. The Mondrian kernel is one such example of a fast random feature approximation of the Laplace kernel, generated by a computationally…

Understanding the spectral properties of kernels offers a principled perspective on generalization and representation quality. While deep models achieve state-of-the-art accuracy in molecular property prediction, kernel methods remain…

Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different…

Quantum computing, with its potential to enhance various machine learning tasks, allows significant advancements in kernel calculation and model precision. Utilizing the one-class Support Vector Machine alongside a quantum kernel, known for…

Positive definite operator-valued kernels generalize the well-known notion of reproducing kernels, and are naturally adapted to multi-output learning situations. This paper addresses the problem of learning a finite linear combination of…

We present sufficient condition for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their representation as a series of spherical harmonics. The family analyzed is a…

We introduce a family of positive definite kernels specifically optimized for the manipulation of 3D structures of molecules with kernel methods. The kernels are based on the comparison of the three-points pharmacophores present in the 3D…

We briefly summarize the kernel regression approach, as used recently in materials modelling, to fitting functions, particularly potential energy surfaces, and highlight how the linear algebra framework can be used to both predict and train…

Image reconstruction for positron emission tomography (PET) is challenging because of the ill-conditioned tomographic problem and low counting statistics. Kernel methods address this challenge by using kernel representation to incorporate…