相关论文: Quality-diversity in dissimilarity spaces

We propose a definition of magnitude for a length space with a Borel measure, which involves integrals over the set of geodesics. This quantity agrees with the magnitude of finite metric spaces, up to re-scaling the metric to ensure the…

Magnitude is a numerical invariant of metric spaces introduced by Leinster, motivated by considerations from category theory. This paper extends the original definition for finite spaces to compact spaces, in an equivalent but more natural…

Quantile-based classifiers can classify high-dimensional observations by minimising a discrepancy of an observation to a class based on suitable quantiles of the within-class distributions, corresponding to a unique percentage for all…

The concept of diversity has received increasing attention in natural language processing (NLP) in recent years. It became an advocated property of datasets and systems, and many measures are used to quantify it. However, it is often…

The necessity to find the global optimum of multiextremal functions arises in many applied problems where finding local solutions is insufficient. One of the desirable properties of global optimization methods is \emph{strong homogeneity}…

Dynamical systems of a new kind are described, which are motivated by the problem of constructing diffeomorphism invariant quantum theories. These are based on the extremization of a non-local and non-additive quantity that we call the…

Diversification in a set of solutions has become a hot research topic in the evolutionary computation community. It has been proven beneficial for optimisation problems in several ways, such as computing a diverse set of high-quality…

Exploratory landscape analysis and fitness landscape analysis in general have been pivotal in facilitating problem understanding, algorithm design and endeavors such as automated algorithm selection and configuration. These techniques have…

There is an implicit assumption in software testing that more diverse and varied test data is needed for effective testing and to achieve different types and levels of coverage. Generic approaches based on information theory to measure and…

This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…

Machine learning methods have achieved good performance and been widely applied in various real-world applications. They can learn the model adaptively and be better fit for special requirements of different tasks. Generally, a good machine…

A global optimization framework, acronymed COMBEO (Change OfMeasure Based Evolutionary Optimization), is proposed. An important aspect in the development is a set of derivative-free additive directional terms obtainable through a change of…

We introduce the framework of qualitative optimization problems (or, simply, optimization problems) to represent preference theories. The formalism uses separate modules to describe the space of outcomes to be compared (the generator) and…

We introduce classifiers based on directional quantiles. We derive theoretical results for selecting optimal quantile levels given a direction, and, conversely, an optimal direction given a quantile level. We also show that the…

Recent work on dissimilarity-based hierarchical clustering has led to the introduction of global objective functions for this classical problem. Several standard approaches, such as average linkage, as well as some new heuristics have been…

The Multiverse is collection of parallel universes. In this article a formal theory and a topos-theoretic models of the multiverse are given. For this the Lawvere-Kock Synthetic Differential Geometry and topos models for smooth…

The majority of standard approaches to financial portfolio optimization (PO) are based on the mean-variance (MV) framework. Given a risk aversion coefficient, the MV procedure yields a single portfolio that represents the optimal trade-off…

We propose an alternative framework for quantifying coherence. The framework is based on a natural property of coherence, the additivity of coherence for subspace-independent states, which is described by an operation-independent equality…

The resource theory of quantum coherence studies the off-diagonal elements of a density matrix in a distinguished basis, whereas the resource theory of purity studies all deviations from the maximally mixed state. We establish a direct…

We characterize countable dimensionality and strong countable dimensionality by means of an infinite game.