Related papers: Kernels on fuzzy sets: an overview

In recent years, various kernels have been proposed in the context of persistent homology to deal with persistence diagrams in supervised learning approaches. In this paper, we consider the idea of variably scaled kernels, for approximating…

A kernel density is an aggregate of kernel functions, which are itself densities and could be kernel densities. This is used to decompose a kernel into its constituent parts. Pearson's test for equality of proportions is applied to…

This paper introduces kdiff, a novel kernel-based measure for estimating distances between instances of time series, random fields and other forms of structured data. This measure is based on the idea of matching distributions that only…

Kernel methods give powerful, flexible, and theoretically grounded approaches to solving many problems in machine learning. The standard approach, however, requires pairwise evaluations of a kernel function, which can lead to scalability…

We introduce the loss kernel, an interpretability method for measuring similarity between data points according to a trained neural network. The kernel is the covariance matrix of per-sample losses computed under a distribution of…

We propose a kernelized classification layer for deep networks. Although conventional deep networks introduce an abundance of nonlinearity for representation (feature) learning, they almost universally use a linear classifier on the learned…

Especially in research areas of computer science such as data mining, image segmentation, clustering image capturing and networking. The interval-valued fuzzy graphs are more flexible and compatible than fuzzy graphs due to the fact that…

In practice, a ranking of objects with respect to given set of criteria is of considerable importance. However, due to lack of knowledge, information of time pressure, decision makers might not be able to provide a (crisp) ranking of…

Kernel embeddings have emerged as a powerful tool for representing probability measures in a variety of statistical inference problems. By mapping probability measures into a reproducing kernel Hilbert space (RKHS), kernel embeddings enable…

In this paper we propose a generalization of the concept of symmetric fuzzy measure based in a decomposition of the universal set in what we have called subsets of indifference. Some properties of these measures are studied, as well as…

The success of kernel methods has initiated the design of novel positive semidefinite functions, in particular for structured data. A leading design paradigm for this is the convolution kernel, which decomposes structured objects into their…

Determinantal point processes are point processes whose correlation functions are given by determinants of matrices. The entries of these matrices are given by one fixed function of two variables, which is called the kernel of the point…

The structure of transformation semigroups on a finite set is analyzed by introducing a hierarchy of functions mapping subsets to subsets. The resulting hierarchy of semigroups has a corresponding hierarchy of minimal ideals, or kernels.…

Kernel methods are among the most popular techniques in machine learning. From a frequentist/discriminative perspective they play a central role in regularization theory as they provide a natural choice for the hypotheses space and the…

Statistical depth is the act of gauging how representative a point is compared to a reference probability measure. The depth allows introducing rankings and orderings to data living in multivariate, or function spaces. Though widely applied…

The usual formulas for the correlation functions in orthogonal and symplectic matrix models express them as quaternion determinants. From this representation one can deduce formulas for spacing probabilities in terms of Fredholm…

This paper further studies the fuzzy rough sets based on fuzzy coverings. We first present the notions of the lower and upper approximation operators based on fuzzy coverings and derive their basic properties. To facilitate the computation…

A new class of fuzzy closed sets, namely fuzzy weakly closed set in a fuzzy topological space is introduced and it is established that this class of fuzzy closed sets lies between fuzzy closed sets and fuzzy generalized closed sets.…

The main objective of this paper is to develop a new semantic Network structure, based on the fuzzy sets theory, used in Artificial Intelligent system in order to provide effective on-line assistance to users of new technological systems.…

Most graph kernels are an instance of the class of $\mathcal{R}$-Convolution kernels, which measure the similarity of objects by comparing their substructures. Despite their empirical success, most graph kernels use a naive aggregation of…