Related papers: Complexity Analysis of a Fast Directional Matrix-V…

It is well-known that the high computational complexity and the insufficient samples in large-scale array signal processing restrict the real-world applications of the conventional full-dimensional adaptive beamforming (sample matrix…

A new method for hierarchical clustering is presented. It combines treelets, a particular multiscale decomposition of data, with a projection on a reproducing kernel Hilbert space. The proposed approach, called kernel treelets (KT),…

Matrix completion and extrapolation (MCEX) are dealt with here over reproducing kernel Hilbert spaces (RKHSs) in order to account for prior information present in the available data. Aiming at a faster and low-complexity solver, the task is…

We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…

We have performed a detailed analysis of the fast multipole method (FMM) in the adaptive case, in which the depth of the FMM tree is non-uniform. Previous works in this area have focused mostly on special types of adaptive distributions,…

Large-scale floating-point matrix multiplication is a fundamental kernel in many scientific and engineering applications. Most existing work only focus on accelerating matrix multiplication on FPGA by adopting a linear systolic array. This…

In this paper, we study the problem of sparse multiple kernel learning (MKL), where the goal is to efficiently learn a combination of a fixed small number of kernels from a large pool that could lead to a kernel classifier with a small…

We introduce a novel class of explicit feature maps based on topological indices that represent each graph by a compact feature vector, enabling fast and interpretable graph classification. Using radial basis function kernels on these…

Matrix multiplication is a fundamental computation in many scientific disciplines. In this paper, we show that novel fast matrix multiplication algorithms can significantly outperform vendor implementations of the classical algorithm and…

Kernel methods are used frequently in various applications of machine learning. For large-scale high dimensional applications, the success of kernel methods hinges on the ability to operate certain large dense kernel matrix K. An enormous…

In this paper, we discuss the solution of certain matrix-valued partial differential equations. Such PDEs arise, for example, when constructing a Riemannian contraction metric for a dynamical system given by an autonomous ODE. We develop…

We investigate the parallel one-level overlapping Schwarz method for solving finite element discretization of high-frequency Helmholtz equations. The resulting linear systems are large, indefinite, ill-conditioned, and complex-valued. We…

We develop a fast divided-and-conquer indirect collocation method for the homogeneous Dirichlet boundary value problem of variable-order space-fractional diffusion equations. Due to the impact of the space-dependent variable order, the…

We introduce Mercator, a reliable embedding method to map real complex networks into their hyperbolic latent geometry. The method assumes that the structure of networks is well described by the Popularity$\times$Similarity…

In this work we consider the problem of numerical integration, i.e., approximating integrals with respect to a target probability measure using only pointwise evaluations of the integrand. We focus on the setting in which the target…

Developing efficient hardware accelerators for mathematical kernels used in scientific applications and machine learning has traditionally been a labor-intensive task. These accelerators typically require low-level programming in Verilog or…

The fast multipole method (FMM) has had great success in reducing the computational complexity of solving the boundary integral form of the Helmholtz equation. We present a formulation of the Helmholtz FMM that uses Fourier basis functions…

In this paper we consider the problem of approximating vector-valued functions over a domain $\Omega$. For this purpose, we use matrix-valued reproducing kernels, which can be related to Reproducing kernel Hilbert spaces of vectorial…

Density-based clustering methodology has been widely considered in the statistical literature for classifying Euclidean observations. However, this approach has not been contemplated for directional data yet. In this work, directional…

We propose a novel stochastic algorithm that randomly samples entire rows and columns of the matrix as a way to approximate an arbitrary matrix function using the power series expansion. This contrasts with existing Monte Carlo methods,…