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Deep convolutional neural networks are hindered by training instability and feature redundancy towards further performance improvement. A promising solution is to impose orthogonality on convolutional filters. We develop an efficient…

Incorporating spatial information into hyperspectral unmixing procedures has been shown to have positive effects, due to the inherent spatial-spectral duality in hyperspectral scenes. Current research works that consider spatial information…

This paper introduces a directional multiscale algorithm for the two dimensional $N$-body problem of the Helmholtz kernel with applications to high frequency scattering. The algorithm follows the approach in [Engquist and Ying, SIAM Journal…

Today, machine learning tools, particularly artificial neural networks, have become crucial for diverse applications. However, current digital computing tools to train and deploy artificial neural networks often struggle with massive data…

In this paper we revisit the kernel density estimation problem: given a kernel $K(x, y)$ and a dataset of $n$ points in high dimensional Euclidean space, prepare a data structure that can quickly output, given a query $q$, a…

We develop TwinKernel methods for nonparametric estimation of intensity functions of point processes. Building on the general TwinKernel framework and combining it with martingale techniques for counting processes, we construct estimators…

We give a kernel with $O(k^7)$ vertices for Trivially Perfect Editing, the problem of adding or removing at most $k$ edges in order to make a given graph trivially perfect. This answers in affirmative an open question posed by Nastos and…

This article is devoted to developing a theory for effective kernel interpolation and approximation in a general setting. For a wide class of compact, connected $C^\infty$ Riemannian manifolds, including the important cases of spheres and…

In most adaptive signal processing applications, system linearity is assumed and adaptive linear filters are thus used. The traditional class of supervised adaptive filters rely on error-correction learning for their adaptive capability.…

The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we…

Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…

Deep neural networks represent a powerful class of function approximators that can learn to compress and reconstruct images. Existing image compression algorithms based on neural networks learn quantized representations with a constant…

In recent years, kernel density estimation has been exploited by computer scientists to model machine learning problems. The kernel density estimation based approaches are of interest due to the low time complexity of either O(n) or…

Kernel matrix-vector product is ubiquitous in many science and engineering applications. However, a naive method requires $O(N^2)$ operations, which becomes prohibitive for large-scale problems. We introduce a parallel method that provably…

Introducing spatial prior information in hyperspectral imaging (HSI) analysis has led to an overall improvement of the performance of many HSI methods applied for denoising, classification, and unmixing. Extending such methodologies to…

Let $\mathcal{O}$ be a set of $k$ orientations in the plane, and let $P$ be a simple polygon in the plane. Given two points $p,q$ inside $P$, we say that $p$ $\mathcal{O}$-\emph{sees} $q$ if there is an $\mathcal{O}$-\emph{staircase}…

We present a method for efficiently searching long-duration gravitational wave signals from compact binary coalescences (CBCs). The approach exploits the smooth frequency-domain behavior of ratios between neighboring waveform templates. The…

Orthogonality regularization has been developed to prevent deep CNNs from training instability and feature redundancy. Among existing proposals, kernel orthogonality regularization enforces orthogonality by minimizing the residual between…

In this paper we combine the theory of reproducing kernel Hilbert spaces with the field of collocation methods to solve boundary value problems with special emphasis on reproducing property of kernels. From the reproducing property of…

In this paper, we study the feature learning ability of two-layer neural networks in the mean-field regime through the lens of kernel methods. To focus on the dynamics of the kernel induced by the first layer, we utilize a two-timescale…