Related papers: Kernels on fuzzy sets: an overview
We consider a kernel based harmonic analysis of "boundary," and boundary representations. Our setting is general: certain classes of positive definite kernels. Our theorems extend (and are motivated by) results and notions from classical…
Universal kernels, whose Reproducing Kernel Hilbert Space is dense in the space of continuous functions are of great practical and theoretical interest. In this paper, we introduce an explicit construction of universal kernels on compact…
Quantum kernel methods, i.e., kernel methods with quantum kernels, offer distinct advantages as a hybrid quantum-classical approach to quantum machine learning (QML), including applicability to Noisy Intermediate-Scale Quantum (NISQ)…
Probability-generating function (PGF) kernels are introduced, which constitute a class of kernels supported on the unit hypersphere, for the purposes of spherical data analysis. PGF kernels generalize RBF kernels in the context of spherical…
In this article we investigate a way in which quantum computing can be used to extend the class of fuzzy sets. The core idea is to see states of a quantum register as characteristic functions of quantum fuzzy subsets of a given set. As the…
Since categories are graphs with additional "structure", one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility…
This study intends to introduce kernel mean embedding of probability measures over infinite-dimensional separable Hilbert spaces induced by functional response statistical models. The embedded function represents the concentration of…
The nature of an atom in a bonded structure -- such as in molecules, in nanoparticles or solids, at surfaces or interfaces -- depends on its local atomic environment. In atomic-scale modeling and simulation, identifying groups of atoms with…
The concepts of fuzzy objects and their classes are described that make it possible to structurally represent knowledge about fuzzy and partially-defined objects and their classes. Operations over such objects and classes are also proposed…
Similarity plays a fundamental role in many areas, including data mining, machine learning, statistics and various applied domains. Inspired by the success of ensemble methods and the flexibility of trees, we propose to learn a similarity…
This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning,…
This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as…
We consider the problem of computation of the correlation functions for the z-measures with the deformation (Jack) parameters 2 or 1/2. Such measures on partitions are originated from the representation theory of the infinite symmetric…
Kernel methods have great promise for learning rich statistical representations of large modern datasets. However, compared to neural networks, kernel methods have been perceived as lacking in scalability and flexibility. We introduce a…
In this paper we introduce a fuzzy version of symport/antiport membrane systems. Our fuzzy membrane systems handle possibly inexact copies of reactives and their rules are endowed with threshold functions that determine whether a rule can…
In granular computing, fuzzy sets can be approximated by granularly representable sets that are as close as possible to the original fuzzy set w.r.t. a given closeness measure. Such sets are called granular approximations. In this article,…
Graph-structured data are an integral part of many application domains, including chemoinformatics, computational biology, neuroimaging, and social network analysis. Over the last two decades, numerous graph kernels, i.e. kernel functions…
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…
A fuzzy theoretic analytical approach was recently introduced that leads to efficient and robust models while addressing automatically the typical issues associated to parametric deep models. However, a formal conceptualization of the fuzzy…
WordNet lexical-database groups English words into sets of synonyms called "synsets." Synsets are utilized for several applications in the field of text-mining. However, they were also open to criticism because although, in reality, not all…