Related papers: Parametric Hierarchical Matrix Approximations to K…

Pseudo-hermitian matrices are matrices hermitian with respect to an indefinite metric. They can be thought of as the truncation of pseudo-hermitian operators, defined over some Krein space, together with the associated metric, to a finite…

Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition…

Many matrices appearing in numerical methods for partial differential equations and integral equations are rank-structured, i.e., they contain submatrices that can be approximated by matrices of low rank. A relatively general class of…

Tree kernels have demonstrated their ability to deal with hierarchical data, as the intrinsic tree structure often plays a discriminative role. While such kernels have been successfully applied to various domains such as nature language…

Kernel methods are powerful tools in various data analysis tasks. Yet, in many cases, their time and space complexity render them impractical for large datasets. Various kernel approximation methods were proposed to overcome this issue,…

In the iterative solution of dense linear systems from boundary integral equations or systems involving kernel matrices, the main challenges are the expensive matrix-vector multiplication and the storage cost which are usually tackled by…

Low-rank approximation is a common tool used to accelerate kernel methods: the $n \times n$ kernel matrix $K$ is approximated via a rank-$k$ matrix $\tilde K$ which can be stored in much less space and processed more quickly. In this work…

Generalized sparse matrix-matrix multiplication is a key primitive for many high performance graph algorithms as well as some linear solvers such as multigrid. We present the first parallel algorithms that achieve increasing speedups for an…

Numerical algorithms for elliptic partial differential equations frequently employ error estimators and adaptive mesh refinement strategies in order to reduce the computational cost. We can extend these techniques to general vectors by…

Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…

We consider the problem of high-dimensional non-linear variable selection for supervised learning. Our approach is based on performing linear selection among exponentially many appropriately defined positive definite kernels that…

Hierarchical data representations in the context of classi cation and data clustering were put forward during the fties. Recently, hierarchical image representations have gained renewed interest for segmentation purposes. In this paper, we…

The Hierarchical Heavy Hitters problem extends the notion of frequent items to data arranged in a hierarchy. This problem has applications to network traffic monitoring, anomaly detection, and DDoS detection. We present a new streaming…

In this paper, we present a kernel subspace clustering method that can handle non-linear models. In contrast to recent kernel subspace clustering methods which use predefined kernels, we propose to learn a low-rank kernel matrix, with which…

We present a data-driven method for computing approximate forward reachable sets using separating kernels in a reproducing kernel Hilbert space. We frame the problem as a support estimation problem, and learn a classifier of the support as…

Partitioning graphs into blocks of roughly equal size such that few edges run between blocks is a frequently needed operation when processing graphs on a parallel computer. When a topology of a distributed system is known an important task…

In this era of large-scale data, distributed systems built on top of clusters of commodity hardware provide cheap and reliable storage and scalable processing of massive data. Here, we review recent work on developing and implementing…

Enhancing classical machine learning (ML) algorithms through quantum kernels is a rapidly growing research topic in quantum machine learning (QML). A key challenge in using kernels -- both classical and quantum -- is that ML workflows…

In this paper, we develop a new technique which we call representation theory of the real hyperrectangle, which describes how to compute the eigenvectors and eigenvalues of certain matrices arising from hyperrectangles. We show that these…

We consider the approximation of the inverse of the finite element stiffness matrix in the data sparse $\mathcal{H}$-matrix format. For a large class of shape regular but possibly non-uniform meshes including graded meshes, we prove that…