Related papers: Categorifying measure theory: a roadmap
Time series analysis has become crucial in various fields, from engineering and finance to healthcare and social sciences. Due to their multidimensional nature, time series often need to be embedded into a fixed-dimensional feature space to…
Creating a new Ontology: a Modular Approach
Classification tasks in machine learning involving more than two classes are known by the name of "multi-class classification". Performance indicators are very useful when the aim is to evaluate and compare different classification models…
We introduce a hierarchical classification of theories that describe systems with fundamentally limited information content. This property is introduced in an operational way and gives rise to the existence of mutually complementary…
We give a short introduction to category theory aimed at philosophers. We emphasize methodological issues and philosophical ramifications.
A systematic mapping is a way to identify, evaluate and interpret all relevant research available to a matter of particular research. One of the reasons for conducting systematic reviews is that it summarizes the existing evidence regarding…
The classifier chain is a widely used method for analyzing multi-labeled data sets. In this study, we introduce a generalization of the classifier chain: the classifier chain network. The classifier chain network enables joint estimation of…
In this paper, we propose a framework for graph signal processing using category theory. The aim is to generalize a few recent works on probabilistic approaches to graph signal processing, which handle signal and graph uncertainties.
There is growing acknowledgement within the software engineering community that a theory of software development is needed to integrate the myriad methodologies that are currently popular, some of which are based on opposing perspectives.…
The book gives a detailed exposition of basic concepts and results of a theory of processes. The presentation of theoretical concepts and results is accompanied with illustrations of their application to solving various problems of…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
Given a small category C, we show that there is a universal way of expanding C into a model category, essentially by formally adjoining homotopy colimits. The technique of localization becomes a method for imposing `relations' into these…
The paper "A General Theory of IR Evaluation Measures" develops a formal framework to determine whether IR evaluation measures are interval scales. This comment shows some limitations about its conclusions.
We develop notions of integrable functions within the theory of schemic motivic integration.
In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in…
This paper is simply a collection of process diagrams for further use and reference. These are diagrams about different approaches to research.
The unprecedented pace of machine learning research has lead to incredible advances, but also poses hard challenges. At present, the field lacks strong theoretical underpinnings, and many important achievements stem from ad hoc design…
In this paper we state some applications of Gr-category theory on the classification of crossed modules and on the classification of extensions of groups of the type of a crossed module.
A pretorsion theory for the category of all categories is presented. The associated prekernels and precokernels are calculated for every functor.