Traditional Functional Dependencies Research Articles

Contextual Data Cleaning with Ontology Functional Dependencies

Functional Dependencies define attribute relationships based on syntactic equality, and when used in data cleaning, they erroneously label syntactically different but semantically equivalent values as errors. We explore dependency-based data cleaning with Ontology Functional Dependencies (OFDs), which express semantic attribute relationships such as synonyms defined by an ontology. We study the theoretical foundations of OFDs, including sound and complete axioms and a linear-time inference procedure. We then propose an algorithm for discovering OFDs (exact ones and ones that hold with some exceptions) from data that uses the axioms to prune the search space. Toward enabling OFDs as data quality rules in practice, we study the problem of finding minimal repairs to a relation and ontology with respect to a set of OFDs. We demonstrate the effectiveness of our techniques on real datasets and show that OFDs can significantly reduce the number of false positive errors in data cleaning techniques that rely on traditional Functional Dependencies.

Combining quantitative and logical data cleaning

Quantitative data cleaning relies on the use of statistical methods to identify and repair data quality problems while logical data cleaning tackles the same problems using various forms of logical reasoning over declarative dependencies. Each of these approaches has its strengths: the logical approach is able to capture subtle data quality problems using sophisticated dependencies, while the quantitative approach excels at ensuring that the repaired data has desired statistical properties. We propose a novel framework within which these two approaches can be used synergistically to combine their respective strengths. We instantiate our framework using (i) metric functional dependencies, a type of dependency that generalizes functional dependencies (FDs) to identify inconsistencies in domains where only large differences in metric data are considered to be a data quality problem, and (ii) repairs that modify the inconsistent data so as to minimize statistical distortion, measured using the Earth Mover's Distance. We show that the problem of computing a statistical distortion minimal repair is NP-hard. Given this complexity, we present an efficient algorithm for finding a minimal repair that has a small statistical distortion using EMD computation over semantically related attributes. To identify semantically related attributes, we present a sound and complete axiomatization and an efficient algorithm for testing implication of metric FDs. While the complexity of inference for some other FD extensions is co-NP complete, we show that the inference problem for metric FDs remains linear, as in traditional FDs. We prove that every instance that can be generated by our repair algorithm is set-minimal (with no unnecessary changes). Our experimental evaluation demonstrates that our techniques obtain a considerably lower statistical distortion than existing repair techniques, while achieving similar levels of efficiency.

Extracting Data Quality Rules Using Information Theoretic Measures

Data quality is of major concern in today’s information world. Poor data quality impacts information based businesses negatively. Conditional functional dependencies (CFDs) are extensions of functional dependencies (FDs) with semantics of data values and are used as quality assessment rules. Conditional functional dependencies contribute to the improvement of data quality by detecting data inconsistencies. CFDs extracted from data can be used as rules for data cleaning. Any violation of CFDs can be identified as inconsistencies and could be repaired by applying the rules. As mining traditional functional dependencies is computationally intensive, mining CFDs is still more costly. In this paper, we discuss an information theoretic approach (ITCFD) to detect CFDs, which is scalable to large datasets.

Effective Pruning for the Discovery of Conditional Functional Dependencies

Conditional functional dependencies (CFDs) have been proposed as a new type of semantic rules extended from traditional functional dependencies. They have shown great potential for detecting and repairing inconsistent data. Constant CFDs are 100% confidence association rules. The theoretical search space for the minimal set of CFDs is the set of minimal generators and their closures in data. This search space has been used in the currently most efficient constant CFD discovery algorithm. In this paper, we propose pruning criteria to further prune the theoretic search space, and design a fast algorithm for constant CFD discovery. We evaluate the proposed algorithm on a number of media to large real-world data sets. The proposed algorithm is faster than the currently most efficient constant CFD discovery algorithm, and has linear time performance in the size of a data set.

Discovering Conditional Functional Dependencies

This paper investigates the discovery of conditional functional dependencies (CFDs). CFDs are a recent extension of functional dependencies (FDs) by supporting patterns of semantically related constants, and can be used as rules for cleaning relational data. However, finding quality CFDs is an expensive process that involves intensive manual effort. To effectively identify data cleaning rules, we develop techniques for discovering CFDs from relations. Already hard for traditional FDs, the discovery problem is more difficult for CFDs. Indeed, mining patterns in CFDs introduces new challenges. We provide three methods for CFD discovery. The first, referred to as CFDMiner, is based on techniques for mining closed item sets, and is used to discover constant CFDs, namely, CFDs with constant patterns only. Constant CFDs are particularly important for object identification, which is essential to data cleaning and data integration. The other two algorithms are developed for discovering general CFDs. One algorithm, referred to as CTANE, is a levelwise algorithm that extends TANE, a well-known algorithm for mining FDs. The other, referred to as FastCFD, is based on the depth-first approach used in FastFD, a method for discovering FDs. It leverages closed-item-set mining to reduce the search space. As verified by our experimental study, CFDMiner can be multiple orders of magnitude faster than CTANE and FastCFD for constant CFD discovery. CTANE works well when a given relation is large, but it does not scale well with the arity of the relation. FastCFD is far more efficient than CTANE when the arity of the relation is large; better still, leveraging optimization based on closed-item-set mining, FastCFD also scales well with the size of the relation. These algorithms provide a set of cleaning-rule discovery tools for users to choose for different applications.

Propagating functional dependencies with conditions

The dependency propagation problem is to determine, given a view defined on data sources and a set of dependencies on the sources, whether another dependency is guaranteed to hold on the view. This paper investigates dependency propagation for recently proposed conditional functional dependencies (CFDs). The need for this study is evident in data integration, exchange and cleaning since dependencies on data sources often only hold conditionally on the view. We investigate dependency propagation for views defined in various fragments of relational algebra, CFDs as view dependencies, and for source dependencies given as either CFDs or traditional functional dependencies (FDs). (a) We establish lower and upper bounds, all matching , ranging from PTIME to undecidable. These not only provide the first results for CFD propagation, but also extend the classical work of FD propagation by giving new complexity bounds in the presence of finite domains. (b) We provide the first algorithm for computing a minimal cover of all CFDs propagated via SPC views; the algorithm has the same complexity as one of the most efficient algorithms for computing a cover of FDs propagated via a projection view, despite the increased expressive power of CFDs and SPC views. (c) We experimentally verify that the algorithm is efficient.

Conditional functional dependencies for capturing data inconsistencies

We propose a class of integrity constraints for relational databases, referred to as conditional functional dependencies (CFDs), and study their applications in data cleaning. In contrast to traditional functional dependencies (FDs) that were developed mainly for schema design, CFDs aim at capturing the consistency of data by enforcing bindings of semantically related values. For static analysis of CFDs we investigate the consistency problem , which is to determine whether or not there exists a nonempty database satisfying a given set of CFDs, and the implication problem , which is to decide whether or not a set of CFDs entails another CFD. We show that while any set of transitional FDs is trivially consistent, the consistency problem is NP-complete for CFDs, but it is in PTIME when either the database schema is predefined or no attributes involved in the CFDs have a finite domain. For the implication analysis of CFDs, we provide an inference system analogous to Armstrong's axioms for FDs, and show that the implication problem is coNP-complete for CFDs in contrast to the linear-time complexity for their traditional counterpart. We also present an algorithm for computing a minimal cover of a set of CFDs. Since CFDs allow data bindings, in some cases CFDs may be physically large, complicating the detection of constraint violations. We develop techniques for detecting CFD violations in SQL as well as novel techniques for checking multiple constraints by a single query. We also provide incremental methods for checking CFDs in response to changes to the database. We experimentally verify the effectiveness of our CFD-based methods for inconsistency detection. This work not only yields a constraint theory for CFDs but is also a step toward a practical constraint-based method for improving data quality.

Dependencies and generalized relations

A combinatorial, data-oriented approach is suggested to study generalized relational databases (GRDs) and generalized functional dependencies (GFDs). GRDs, as defined here, extend the traditional relational model by Codd. Also, certain aspects of nonfirst-normal-form databases and databases with null values can be captured in the setting of GRDs. We show that, after a suitable transformation, GFDs can be described in the framework of traditional functional dependencies (FDs). This leads to a convenient description of GFDs in terms of propositional logic.