Related papers: K-Means as a Radial Basis function Network: a Vari…
Support Vector Machines (SVMs) rely heavily on the choice of the kernel function to map data into high-dimensional feature spaces. While the Gaussian Radial Basis Function (RBF) is the industry standard, its exponential decay makes it…
Radial basis functions (RBFs) are prominent examples for reproducing kernels with associated reproducing kernel Hilbert spaces (RKHSs). The convergence theory for the kernel-based interpolation in that space is well understood and optimal…
K-FAC (arXiv:1503.05671, arXiv:1602.01407) is a tractable implementation of Natural Gradient (NG) for Deep Learning (DL), whose bottleneck is computing the inverses of the so-called ``Kronecker-Factors'' (K-factors). RS-KFAC…
Federated clustering, an integral aspect of federated machine learning, enables multiple data sources to collaboratively cluster their data, maintaining decentralization and preserving privacy. In this paper, we introduce a novel federated…
This work analyzes the solution trajectory of gradient-based algorithms via a novel basis function decomposition. We show that, although solution trajectories of gradient-based algorithms may vary depending on the learning task, they behave…
The fuzzy $K$-means problem is a generalization of the classical $K$-means problem to soft clusterings, i.e. clusterings where each points belongs to each cluster to some degree. Although popular in practice, prior to this work the fuzzy…
This paper developed a systematic strategy establishing RBF on the wavelet analysis, which includes continuous and discrete RBF orthonormal wavelet transforms respectively in terms of singular fundamental solutions and nonsingular general…
K-FAC is a successful tractable implementation of Natural Gradient for Deep Learning, which nevertheless suffers from the requirement to compute the inverse of the Kronecker factors (through an eigen-decomposition). This can be very…
Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered datasets in d-dimensional space. It is non-separable approximation, as it is…
Deep neural networks work well at approximating complicated functions when provided with data and trained by gradient descent methods. At the same time, there is a vast amount of existing functions that programmatically solve different…
$K$-means, a simple and effective clustering algorithm, is one of the most widely used algorithms in multimedia and computer vision community. Traditional $k$-means is an iterative algorithm---in each iteration new cluster centers are…
We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the…
We present a generalization of the RBF-FD method that computes RBF-FD weights in finite-sized neighborhoods around the centers of RBF-FD stencils by introducing an overlap parameter $\delta \in [0,1]$ such that $\delta=1$ recovers the…
In the classical Gaussian SVM classification we use the feature space projection transforming points to normal distributions with fixed covariance matrices (identity in the standard RBF and the covariance of the whole dataset in Mahalanobis…
Clustering is a hard discrete optimization problem. Nonconvex approaches such as low-rank semidefinite programming (SDP) have recently demonstrated promising statistical and local algorithmic guarantees for cluster recovery. Due to the…
Generative Adversarial Networks (GANs) have achieved great success in generating realistic images. Most of these are conditional models, although acquisition of class labels is expensive and time-consuming in practice. To reduce the…
The $k$-means algorithm is a prevalent clustering method due to its simplicity, effectiveness, and speed. However, its main disadvantage is its high sensitivity to the initial positions of the cluster centers. The global $k$-means is a…
Deep learning self-supervised algorithms that can segment an image in a fixed number of hard labels such as the k-means algorithm and relying only on deep learning techniques are still lacking. Here, we introduce the k-textures algorithm…
Most neural networks are trained using first-order optimization methods, which are sensitive to the parameterization of the model. Natural gradient descent is invariant to smooth reparameterizations because it is defined in a…
Quantum kernel methods are a promising branch of quantum machine learning, yet their effectiveness on diverse, high-dimensional, real-world data remains unverified. Current research has largely been limited to low-dimensional or synthetic…