Characterization of order-like dependencies with formal concept analysis

Functional Dependencies (FDs) play a key role in many fields of the relational database model, one of the most widely used database systems. FDs have also been applied in data analysis, data quality, knowl- edge discovery and the like, but in a very limited scope, because of their fixed semantics. To overcome this limitation, many generalizations have been defined to relax the crisp definition of FDs. FDs and a few of their generalizations have been characterized with Formal Concept Analysis which reveals itself to be an interesting unified framework for charac- terizing dependencies, that is, understanding and computing them in a formal way. In this paper, we extend this work by taking into account order-like dependencies. Such dependencies, well defined in the database field, consider an ordering on the domain of each attribute, and not sim- ply an equality relation as with standard FDs.Peer ReviewedPostprint (published version

characterization of order-like dependencies with formal concept analysis

Functional Dependencies (FDs) play a key role in many fields of the relational database model, one of the most widely used database systems. FDs have also been applied in data analysis, data quality, knowledge discovery and the like, but in a very limited scope, because of their fixed semantics. To overcome this limitation, many generalizations have been defined to relax the crisp definition of FDs. FDs and a few of their generalizations have been characterized with Formal Concept Analysis which reveals itself to be an interesting unified framework for characterizing dependencies, that is, understanding and computing them in a formal way. In this paper, we extend this work by taking into account order-like dependencies. Such dependencies, well defined in the database field, consider an ordering on the domain of each attribute, and not simply an equality relation as with standard FDsPostprint (published version

Possibilistic functional dependencies and their relationship to possibility theory

This paper introduces possibilistic functional dependencies. These dependencies are associated with a particular possibility distribution over possible worlds of a classical database. The possibility distribution reflects a layered view of the database. The highest layer of the (classical) database consists of those tuples that certainly belong to it, while the other layers add tuples that only possibly belong to the database, with different levels of possibility. The relation between the confidence levels associated with the tuples and the possibility distribution over possible database worlds is discussed in detail in the setting of possibility theory. A possibilistic functional dependency is a classical functional dependency associated with a certainty level that reflects the highest confidence level where the functional dependency no longer holds in the layered database. Moreover, the relationship between possibilistic functional dependencies and possibilistic logic formulas is established. Related work is reviewed, and the intended use of possibilistic functional dependencies is discussed in the conclusion

Characterizing approximate-matching dependencies in formal concept analysis with pattern structures

Functional dependencies (FDs) provide valuable knowledge on the relations between attributes of a data table. A functional dependency holds when the values of an attribute can be determined by another. It has been shown that FDs can be expressed in terms of partitions of tuples that are in agreement w.r.t. the values taken by some subsets of attributes. To extend the use of FDs, several generalizations have been proposed. In this work, we study approximatematching dependencies that generalize FDs by relaxing the constraints on the attributes, i.e. agreement is based on a similarity relation rather than on equality. Such dependencies are attracting attention in the database field since they allow uncrisping the basic notion of FDs extending its application to many different fields, such as data quality, data mining, behavior analysis, data cleaning or data partition, among others. We show that these dependencies can be formalized in the framework of Formal Concept Analysis (FCA) using a previous formalization introduced for standard FDs. Our new results state that, starting from the conceptual structure of a pattern structure, and generalizing the notion of relation between tuples, approximate-matching dependencies can be characterized as implications in a pattern concept lattice. We finally show how to use basic FCA algorithms to construct a pattern concept lattice that entails these dependencies after a slight and tractable binarization of the original data.Postprint (author's final draft

Characterization of Order-like Dependencies with Formal Concept Analysis

Abstract. Functional Dependencies (FDs) play a key role in many fields of the relational database model, one of the most widely used database systems. FDs have also been applied in data analysis, data quality, knowledge discovery and the like, but in a very limited scope, because of their fixed semantics. To overcome this limitation, many generalizations have been defined to relax the crisp definition of FDs. FDs and a few of their generalizations have been characterized with Formal Concept Analysis which reveals itself to be an interesting unified framework for characterizing dependencies, that is, understanding and computing them in a formal way. In this paper, we extend this work by taking into account order-like dependencies. Such dependencies, well defined in the database field, consider an ordering on the domain of each attribute, and not simply an equality relation as with standard FDs

Fundamentals and applications of order dependencies

Business-intelligence queries often involve SQL functions and algebraic expressions. There can be clear semantic relationships between a column's values and the values of a function over that column. A common property is monotonicity: as the column's values ascend, so do the function's values (or the other column's values). This we call an order dependency (OD). Queries can be evaluated more efficiently when the query optimizer uses order dependencies. They can be run even faster when the optimizer can also reason over known ODs to infer new ones. Order dependencies can be declared as integrity constraints, and they can be detected automatically for many types of SQL functions and algebraic expressions. We present optimization techniques using ODs for queries that involve join, order by, group by, partition by, and distinct. Essentially, ODs can further exploit interesting orders to eliminate or simplify potentially expensive sorts in the query plan. We evaluate these techniques over our prototype implementation in IBM® DB2® using the TPC-DS® benchmark schema and some customer inspired queries. Our experimental results demonstrate a significant performance gain. Dependencies have played an important role in database theory. We study the theoretical aspects of order dependencies-and unidirectional order dependencies (UODs), a proper sub-class of ODs-which describe the relationships among lexicographical orderings of sets of tuples. We investigate the inference problem for order dependencies. We establish the following: (i) a sound and complete axiomatization for UODs which is sound for ODs; (ii) a hierarchy of order dependency classes; (iii) a proof of co-NP-completeness of the inference problem for ODs and for the subclass of UODs; (iv) a proof of co-NP-completeness of the inference problem of functional dependencies (FDs) from ODs in general, but demonstrate linear time complexity for the inference of FDs from UODs; (v) a sound and complete elimination procedure for testing logical implication over ODs; and (vi) a sound and complete polynomial inference algorithm for sets of UODs over natural domains

Discovery and application of data dependencies

Orientador: Prof. Dr. Eduardo Cunha de AlmeidaTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa : Curitiba, 08/09/2020Inclui referências: p. 126-140Área de concentração: Ciência da ComputaçãoResumo: D ependências de dados (ou, simplesmente, dependências) têm um papel fundamental em muitos aspectos do gerenciam ento de dados. Em consequência, pesquisas recentes têm desenvolvido contribuições para im portante problem as relacionados à dependências. Esta tese traz contribuições que abrangem dois desses problemas. O prim eiro problem a diz respeito à descoberta de dependências com alto poder de expressividade. O objetivo é substituir o projeto m anual de dependências, o qual é sujeito a erros, por um algoritmo capaz de descobrir dependências a partir de dados apenas. N esta tese, estudamos a descoberta de restrições de negação, um tipo de dependência que contorna muitos problemas relacionados ao poder de expressividade de depêndencias. As restrições de negação têm poder de expressividade suficiente para generalizar outros tipos importantes de dependências, e expressar com plexas regras de negócios. No entanto, sua descoberta é com putacionalm ente difícil, pois possui um espaço de busca m aior do que o espaço de busca visto na descoberta de dependências mais simples. Esta tese apresenta novas técnicas na forma de um algoritmo para a descoberta de restrições de negação. Avaliamos o projeto de nosso algoritmo em uma variedade de cenários: conjuntos de dados reais e sintéticos; e núm eros variáveis de registros e colunas. N ossa avaliação m ostra que, em com paração com soluções do estado da arte, nosso algoritmo m elhora significativamente a eficiência da descoberta de restrição de negação em term os de tempo de execução. O segundo problem a diz respeito à aplicação de dependências no gerenciam ento de dados. Primeiro, estudamos a aplicação de dependências na melhoraria da consistência de dados, um aspecto crítico da qualidade dos dados. Uma m aneira comum de m odelar inconsistências é identificando violações de dependências. N esse contexto, esta tese apresenta um m étodo que estende nosso algoritm o para a descoberta de restrições de negação de form a que ele possa retornar resultados confiáveis, m esm o que o algoritm o execute sobre dados contendo alguns registros inconsistentes. M ostram os que é possível extrair evidências dos conjuntos de dados para descobrir restrições de negação que se mantêm aproximadamente. Nossa avaliação mostra que nosso método retorna dependências de negação que podem identificar, com boa precisão e recuperação, inconsistências no conjunto de dados de entrada. Esta tese traz mais um a contribuição no que diz respeito à aplicação de dependências para m elhorar a consistência de dados. Ela apresenta um sistem a para detectar violações de dependências de form a eficiente. Realizam os um a extensa avaliação de nosso sistem a usando comparações com várias abordagens; dados do mundo real e sintéticos; e vários tipos de restrições de negação. Mostramos que os sistemas de gerenciamento de banco de dados comerciais testados com eçam a apresentar baixo desem penho para conjuntos de dados relativam ente pequenos e alguns tipos de restrições de negação. Nosso sistema, por sua vez, apresenta execuções até três ordens de magnitude mais rápidas do que as de outras soluções relacionadas, especialmente para conjuntos de dados maiores e um grande número de violações identificadas. N ossa contribuição final diz respeito à aplicação de dependências na otim ização de consultas. Em particular, esta tese apresenta um sistema para a descoberta automática e seleção de dependências funcionais que potencialmente melhoram a execução de consultas. Nosso sistema com bina representações das dependências funcionais descobertas em um conjunto de dados com representações extraídas de cargas de trabalho de consulta. Essa com binação direciona a seleção de dependências funcionais que podem produzir reescritas de consulta para as consultas de entrada. N ossa avaliação experim ental m ostra que nosso sistem a seleciona dependências funcionais relevantes que podem ajudar na redução do tempo de resposta geral de consultas. Palavras-chave: Perfilamento de dados. Qualidade de dados. Limpeza de dados. Depenência de dados. Execução de consulta.Abstract: Data dependencies (or dependencies, for short) have a fundamental role in many facets of data management. As a result, recent research has been continually driving contributions to central problem s in connection w ith dependencies. This thesis makes contributions that reach two of these problems. The first problem regards the discovery of dependencies of high expressive power. The goal is to replace the error-prone process of m anual design of dependencies with an algorithm capable of discovering dependencies using only data. In this thesis, we study the discovery of denial constraints, a type of dependency that circumvents many expressiveness drawbacks. Denial constraints have enough expressive pow er to generalize other im portant types of dependencies and to express com plex business rules. However, their discovery is com putationally hard since it regards a search space that is bigger than the search space seen in the discovery of sim pler dependencies. This thesis introduces novel algorithm ic techniques in the form of an algorithm for the discovery of denial constraints. We evaluate the design of our algorithm in a variety of scenarios: real and synthetic datasets; and a varying num ber of records and columns. Our evaluation shows that, com pared to state-of-the-art solutions, our algorithm significantly improves the efficiency of denial constraint discovery in terms of runtime. The second problem concerns the application of dependencies in data management. We first study the application of dependencies for improving data consistency, a critical aspect of data quality. A com m on way to m odel data inconsistencies is by identifying violations of dependencies. in that context, this thesis presents a m ethod that extends our algorithm for the discovery of denial constraints such that it can return reliable results even if the algorithm runs on data containing some inconsistent records. A central insight is that it is possible to extract evidence from datasets to discover denial constraints that alm ost hold in the dataset. Our evaluation shows that our method returns denial dependencies that can identify, with good precision and recall, inconsistencies in the input dataset. This thesis makes one m ore contribution regarding the application of dependencies for im proving data consistency. it presents a system for detecting violations of dependencies efficiently. We perform an extensive evaluation of our system that includes comparisons with several different approaches; real-world and synthetic data; and various kinds of denial constraints. We show that the tested com m ercial database m anagem ent systems start underperform ing for relatively small datasets and production dependencies in the form of denial constraints. Our system, in turn, is up to three orders-of-m agnitude faster than related solutions, especially for larger datasets and massive numbers of identified violations. Our final contribution regards the application of dependencies in query optimization. In particular, this thesis presents a system for the automatic discovery and selection of functional dependencies that potentially improve query executions. Our system combines representations from the functional dependencies discovered in a dataset with representations of the query workloads that run for that dataset. This combination guides the selection of functional dependencies that can produce query rewritings for the incoming queries. Our experimental evaluation shows that our system selects relevant functional dependencies, which can help in reducing the overall query response time. Keywords: D ata profiling. D ata quality. D ata cleaning. D ata dependencies. Query execution