Related papers: Kernels on fuzzy sets: an overview

In this paper we show how specific families of positive definite kernels serve as powerful tools in analyses of iteration algorithms for multiple layer feedforward Neural Network models. Our focus is on particular kernels that adapt well to…

Modeling relations between components of 3D objects is essential for many geometry editing tasks. Existing techniques commonly rely on labeled components, which requires substantial annotation effort and limits components to a dictionary of…

We introduce propagation kernels, a general graph-kernel framework for efficiently measuring the similarity of structured data. Propagation kernels are based on monitoring how information spreads through a set of given graphs. They leverage…

Deep kernel learning refers to a Gaussian process that incorporates neural networks to improve the modelling of complex functions. We present a method that makes this approach feasible for problems where the data consists of line integral…

We present the first comprehensive and large-scale evaluation of classical (NN), fuzzy (FNN) and fuzzy rough (FRNN) nearest neighbour classification. We standardise existing proposals for nearest neighbour weighting with kernel functions,…

In this work, we first define relations on the fuzzy parametrized soft sets and study their properties. We also give a decision making method based on these relations. In approximate reasoning, relations on the fuzzy parametrized soft sets…

Classical machine learning has succeeded in the prediction of both classical and quantum phases of matter. Notably, kernel methods stand out for their ability to provide interpretable results, relating the learning process with the physical…

In this article, we first define the concept of ordered intervals, then introduce ordered fuzzy inner product and describe some of its properties.

This paper introduces a new kernel-based classifier by viewing kernel matrices as generalized graphs and leveraging recent progress in graph embedding techniques. The proposed method facilitates fast and scalable kernel matrix embedding,…

We interpret a fuzzy set as a random availability function and provide sufficient conditions under which a preference relation over the set of all random availability functions can be represented by a utility function.

The heat kernel expansion can be used as a tool to obtain the effective geometric quantities in fuzzy spaces. Generalizing the efficient method presented in the previous work on the global quantities, it is applied to the effective local…

Deep neural networks have become essential for numerous applications due to their strong empirical performance such as vision, RL, and classification. Unfortunately, these networks are quite difficult to interpret, and this limits their…

Given a reproducing kernel Hilbert space H of real-valued functions and a suitable measure mu over the source space D (subset of R), we decompose H as the sum of a subspace of centered functions for mu and its orthogonal in H. This…

Complex models are often used to understand interactions and drivers of human-induced and/or natural phenomena. It is worth identifying the input variables that drive the model output(s) in a given domain and/or govern specific model…

The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel polynomial, and using properties of the curve, the kernel curve,…

We present new classes of positive definite kernels on non-standard spaces that are integrally strictly positive definite or characteristic. In particular, we discuss radial kernels on separable Hilbert spaces, and introduce broad classes…

The Weisfeiler-Lehman graph kernels are among the most prevalent graph kernels due to their remarkable time complexity and predictive performance. Their key concept is based on an implicit comparison of neighborhood representing trees with…

We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…

Applying machine learning to biological sequences - DNA, RNA and protein - has enormous potential to advance human health, environmental sustainability, and fundamental biological understanding. However, many existing machine learning…

Quantum kernel method is a machine learning model exploiting quantum computers to calculate the quantum kernels (QKs) that measure the similarity between data. Despite the potential quantum advantage of the method, the commonly used…