Related papers: A Categorical Unification for Multi-Model Data: Pa…
This paper has proposed a Graph - semantic based conceptual model for semi-structured database system, called GOOSSDM, to conceptualize the different facets of such system in object oriented paradigm. The model defines a set of graph based…
This paper presents the current version of our (Elementary) Mathematical Data Model ((E)MDM), which is based on the na\"ive theory of sets, relations, and functions, as well as on the first-order predicate calculus with equality. Many…
Clustering data objects into homogeneous groups is one of the most important tasks in data mining. Spectral clustering is arguably one of the most important algorithms for clustering, as it is appealing for its theoretical soundness and is…
The integration of knowledge extracted from different models described by domain experts or from models generated by machine learning algorithms is strongly conditioned by the lack of an appropriated framework to specify and integrate…
Stock and flow diagrams are already an important tool in epidemiology, but category theory lets us go further and treat these diagrams as mathematical entities in their own right. In this chapter we use communicable disease models created…
The goal of this paper is to show that generalizing the notion of frequent patterns can be useful in extending association analysis to more complex higher order patterns. To that end, we describe a general framework for modeling a complex…
Providing machine learning (ML) over relational data is a mainstream requirement for data analytics systems. While almost all the ML tools require the input data to be presented as a single table, many datasets are multi-table, which forces…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
In many areas of science multiple sets of data are collected pertaining to the same system. Examples are food products which are characterized by different sets of variables, bio-processes which are on-line sampled with different…
The problem of complex data analysis is a central topic of modern statistical science and learning systems and is becoming of broader interest with the increasing prevalence of high-dimensional data. The challenge is to develop statistical…
We apply foundation models to data discovery and exploration tasks. Foundation models include large language models (LLMs) that show promising performance on a range of diverse tasks unrelated to their training. We show that these models…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
This article introduces a novel nonparametric methodology for Generalized Linear Models which combines the strengths of the binary regression and latent variable formulations for categorical data, while overcoming their disadvantages.…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
The primary goal of this paper is to abstract notions, results and constructions from the theory of categories to the broader setting of plots. Loosely speaking, a plot can be thought of as a non-associative non-unital category with a…
This paper explores Bayesian estimation for categorical data, focusing on simple yet effective models that provide a foundation for applying more advanced methods accurately and reliably in real-world applications. We begin by revisiting…
Category theory offers a mathematical foundation for knowledge representation and database systems. Popular existing approaches model a database instance as a functor into the category of sets and functions, or as a 2-functor into the…
Graph clustering aims at discovering a natural grouping of the nodes such that similar nodes are assigned to a common cluster. Many different algorithms have been proposed in the literature: for simple graphs, for graphs with attributes…
Modeling generics in object-oriented programming languages such as Java and C# is a challenge. Recently we proposed a new order-theoretic approach to modeling generics. Given the strong relation between order theory and category theory, in…
We consider a database composed of a set of conceptual graphs. Using conceptual graphs and graph homomorphism it is possible to build a basic query-answering mechanism based on semantic search. Graph homomorphism defines a partial order…