Related papers: K-Means as a Radial Basis function Network: a Vari…
In this article we present a modification of classical Radial Basis Function (RBF) interpolation techniques aimed at reducing oscillations near discontinuities in one and two dimensions. Our approach introduces an adaptive mechanism by…
Recent developments have made it possible to overcome grid-based limitations of finite difference (FD) methods by adopting the kernel-based meshless framework using radial basis functions (RBFs). Such an approach provides a meshless…
We formally prove the connection between k-means clustering and the predictions of neural networks based on the softmax activation layer. In existing work, this connection has been analyzed empirically, but it has never before been…
One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are `flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct)…
K-means defines one of the most employed centroid-based clustering algorithms with performances tied to the data's embedding. Intricate data embeddings have been designed to push $K$-means performances at the cost of reduced theoretical…
We present adaptive finite difference ENO/WENO methods by adopting infinitely smooth radial basis functions (RBFs). This is a direct extension of the non-polynomial finite volume ENO/WENO method proposed by authors in \cite{GuoJung} to the…
We address the problem of simultaneously learning a k-means clustering and deep feature representation from unlabelled data, which is of interest due to the potential of deep k-means to outperform traditional two-step feature extraction and…
This thesis aims to invent new approaches for making inferences with the k-means algorithm. k-means is an iterative clustering algorithm that randomly assigns k centroids, then assigns data points to the nearest centroid, and updates…
This paper introduces a novel parametric activation function based on Wendland radial basis functions (RBFs) for deep neural networks. Wendland RBFs, known for their compact support, smoothness, and positive definiteness in approximation…
We propose a differential radial basis function (RBF) network termed RBF-DiffNet -- whose hidden layer blocks are partial differential equations (PDEs) linear in terms of the RBF -- to make the baseline RBF network robust to noise in…
Clustering is a long-standing problem area in data mining. The centroid-based classical approaches to clustering mainly face difficulty in the case of high dimensional inputs such as images. With the advent of deep neural networks, a common…
This note carries three purposes involving our latest advances on the radial basis function (RBF) approach. First, we will introduce a new scheme employing the boundary knot method (BKM) to nonlinear convection-diffusion problem. It is…
Support Vector Machines (SVMs) are still one of the most popular and precise classifiers. The Radial Basis Function (RBF) kernel has been used in SVMs to separate among classes with considerable success. However, there is an intrinsic…
Three-dimensional object recognition has recently achieved great progress thanks to the development of effective point cloud-based learning frameworks, such as PointNet and its extensions. However, existing methods rely heavily on fully…
We introduce the {\it diffusion $K$-means} clustering method on Riemannian submanifolds, which maximizes the within-cluster connectedness based on the diffusion distance. The diffusion $K$-means constructs a random walk on the similarity…
Radial basis function neural networks (RBFs) are prime candidates for pattern classification and regression and have been used extensively in classical machine learning applications. However, RBFs have not been integrated into contemporary…
This paper introduces a novel meshfree methodology based on Radial Basis Function-Finite Difference (RBF-FD) approximations for the numerical solution of partial differential equations (PDEs) on surfaces of codimension 1 embedded in…
In this paper, we present a method based on Radial Basis Function (RBF)-generated Finite Differences (FD) for numerically solving diffusion and reaction-diffusion equations (PDEs) on closed surfaces embedded in $\mathbb{R}^d$. Our method…
Some response surface functions in complex engineering systems are usually highly nonlinear, unformed, and expensive-to-evaluate. To tackle this challenge, Bayesian optimization, which conducts sequential design via a posterior distribution…
We propose a Gradient Boosting algorithm for learning an ensemble of kernel functions adapted to the task at hand. Unlike state-of-the-art Multiple Kernel Learning techniques that make use of a pre-computed dictionary of kernel functions to…