Armstrong databases for functional and inclusion dependencies

An Armstrong database is a database that obeys precisely a given set of sentences (and their logical consequences) and no other sentences of a given type. It is shown that if the sentences of interest are inclusion dependencies and standard functional dependencies (functional dependencies for which the left-hand side is nonempty), then there is always an Armstrong database for each set of sentences. (An example of an inclusion dependency is the sentence that says that every $\text{MANAGER}$ is an $\text{EMPLOYEE}$.) If, however, the sentences of interest are inclusion dependencies and unrestricted functional dependencies, then there need not exist an Armstrong database. This result holds even if we allow only ‘full’ inclusion dependencies. Thus, a fairly sharp line is drawn, in a case of interest, as to when an Armstrong database must exist. These results hold whether we restrict our attention to finite databases (databases with a finite number of tuples), or whether we allow unrestricted databases.     

Membership problems for data dependencies in relational expressions

In relational databases, a query can be formulated in terms of a relational algebra expression using projection, selection, restriction, cross product and union. In this paper, we consider a problem, called the membership problem, of determining whether a given dependency d is valid in a given relational expression E over a given database scheme R that is, whether every instance of the view scheme defined by E satisfies d (assuming that the underlying constraints in R are always satisfied).Consider the case where each relation scheme in R is associated with functional dependencies (FDs) as constraints, and d is an FD. Then the complement of the membership problem is NP-complete. However, if E contains no union, then the membership problem can be solved in polynomial time. Furthermore, if E contains neither a union nor a projection, then we can construct in polynomial time a cover for valid FDs in E, that is, a set of FDs which implies every valid FD in E.Consider the case where each relation scheme in R is associated with multivalued dependencies (MVDs) as well as FDs, and d is an FD or an MVD. Even if E consists of selections and cross products only, the membership problem is NP-hard. However, if E contains no union, and each relation scheme name in R occurs in E at most once, then the membership problem can be solved in polynomial time. As a corollary of this result, it can be determined in polynomial time whether a given FD or MVD is valid in $\text{R}{}_1\text{???R}{}_{\mathrm{s}}$, where R₁,…,R_s are relation schemes with FDs and MVDs, and $\text{R}{}_{\mathrm{i}}\text{?R}{}_{\mathrm{j}}$ is the natural join of R_i and R_j.     

Restricted Bayesian classification networks

Bayesian networks are graphical models that describe dependency relationships between variables, and are powerful tools for studying probability classifiers. At present, the causal Bayesian network learning method is used in constructing Bayesian network classifiers while the contribution of attribute to class is over-looked. In this paper, a Bayesian network specifically for classification-restricted Bayesian classification networks is proposed. Combining dependency analysis between variables, classification accuracy evaluation criteria and a search algorithm, a learning method for restricted Bayesian classification networks is presented. Experiments and analysis are done using data sets from UCI machine learning repository. The results show that the restricted Bayesian classification network is more accurate than other well-known classifiers.     

单趟贝叶斯模糊聚类算法

对于概率模糊聚类,贝叶斯模糊聚类方法表现出良好的聚类性能,它从先验知识和贝叶斯理论的角度出发,采用最大后验概率理论处理模糊划分,进而获取最终的聚类结果.该方法有效地结合了概率论和模糊论两者的优点,较之传统的模糊聚类算法（如FCM算法）,该方法能够获取全局最优解并估计聚类个数.但在大数据时代,该方法较高的时间复杂度限制了它的实用性.针对此问题,首先在贝叶斯模糊聚类中引入加权机制,提出了加权贝叶斯模糊聚类算法;然后将其与单趟聚类框架相结合,提出了面向大规模数据的快速单趟贝叶斯模糊聚类算法,并从理论上对相关性质进行了较为深入的分析.所提出的单趟贝叶斯模糊聚类新算法较之贝叶斯模糊聚类算法在时间复杂度和收敛性上均有着不同程度的性能提升,同时继承了贝叶斯模糊聚类的良好的聚类性能.最后,相关实验结果亦验证了所提方法的有效性.     

On the implication problem for cardinality constraints and functional dependencies

In database design, integrity constraints are used to express database semantics. They specify the way by that the elements of a database are associated to each other. The implication problem asks whether a given set of constraints entails further constraints. In this paper, we study the finite implication problem for cardinality constraints. Our main result is a complete characterization of closed sets of cardinality constraints. Similar results are obtained for constraint sets containing cardinality constraints, but also key and functional dependencies. Moreover, we construct Armstrong databases for these constraint sets, which are of special interest for example-based deduction in database design.     

Fast algorithms of mining probability functional dependency rules in relational database

This paper defines a new kind of rule,probability functional dependency rule.The functional dependency degree can be depicted by this kind of rule.Five algorithms,from the simple to the complex,are presented to mine this kind of rule in different condition.The related theorems are proved to ensure the high efficiency and the correctness of the above algorithms.     

基于相关性分析的不完整数据函数依赖挖掘方法

函数依赖（FD）挖掘方法通常专注于发现所有满足函数依赖语法特征的结果,在数据不完整的情况下常导致大量成立但无意义的FD。针对挖掘无效FD的问题,提出基于相关性分析的不完整数据FD挖掘方法。利用概率图模型构建具有缺失值属性的概率分布,通过相关性分析捕捉属性之间的关联关系,避免枚举所有可能性,以挖掘具有统计学意义的FD。实验结果表明,提出方法可以更准确的定位到有意义的FD,与最先进的FD发现方法相比F1分数平均提高1.5倍。     

XML弱函数依赖及单依赖集合研究

XML弱函数依赖是在XML数据库中引入空值理论后的函数依赖。在空值、不完全树元组等概念的基础上,定义了弱函数依赖、单依赖集合,证明了单依赖集合判定定理和单依赖集合判定可终止定理。     

The theory of functional and subset dependencies over relational expressions

A formal system for reasoning about functional dependencies (FDs) and subset dependencies (SDs) defined over relational expressions is described. An FD e:X → Y indicates that Y is functionally dependent on X in the relation denoted by expression e; an SD e ? f indicates that the relation denoted by e is a subset of that denoted by f. The system is shown to be sound and complete by resorting to the analytic tableaux method. Applications of the system include the problem of determining if a constraint of a subschema is implied by the constraints of the base schema and the development of database design methodologies similar to normalization.     

Method of probabilistic inference from learning data in Bayesian networks

Bayesian networks (BN) are a powerful tool for various data-mining systems. The available methods of probabilistic inference from learning data have shortcomings such as high computation complexity and cumulative error. This is due to a partial loss of information in transition from empiric information to conditional probability tables. The paper presents a new simple and exact algorithm for probabilistic inference in BN from learning data. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 93–99, May–June 2007.     

On interpreting and inferring propositional formulas of data dependencies in a relational database

This paper concerns generally the satisfaction and the inference problem involving functional and/or multivalued dependencies in a relational database. In particular, two independent aids in solving an inference problem, concerning the logical counterparts of functional as well as multivalued dependencies, are introduced. The first aid is provided by establishing a pair of complementary inequivalence and equivalence theorems between the propositional formula corresponding to the difference, U-X, in set theory and the propositional formula not(X) where U is a relation scheme and X is a subset of U. By applying these theorems, correctness of solving an inference problem is assured. The second aid is the application of a Venn diagram for simplifying a propositional formula involving conjunctions, differences, etc., for solving an inference problem. A guideline for constructing simplified Venn diagrams is also given and discussed.     

Bayesian selection probability estimation for probabilistic Boolean networks

A Bayesian approach to estimate selection probabilities of probabilistic Boolean networks is developed in this study. The concepts of inverse Boolean function and updatable set are introduced to specify states which can be used to update a Bayesian posterior distribution. The analysis on convergence of the posteriors is carried out by exploiting the combination of semi‐tensor product technique and state decomposition algorithm for Markov chain. Finally, some numerical examples demonstrate the proposed estimation algorithm.     

贝叶斯网络结构学习的发展与展望

从最初的概率贝叶斯网络构建阶段到涌现大量研究成果的因果贝叶斯网络结构学习阶段,本文完整地回顾了贝叶斯网络结构学习的整个发展历程,并对该领域当前存在的问题及相关研究进行分析论述,给出了研究展望.值得一提的是,贝叶斯网络结构学习正在成为因果数据挖掘的主流.     

Parallel algorithms for solving the satisfaction problem of functional and multivalued data dependencies

Parallel algorithms for solving the satisfaction problem of non-trivial functional and multivalued data dependencies (FDs and MVDs) in a relation of N tuples by M processors are developed in this paper. Algorithms performing, in a parallel manner, batch or interactive checking of these data dependencies are also discussed. The M processors are organized as a linear systolic array. The time complexities of the first two algorithms for solving the FD satisfaction problem under M N are both O(N), and that of Algorithm (3) or (4) for solving the FD or MVD satisfaction problem under N M is O(N²/M). The latter complexity reduced to O(N) if N = M and is at least not worse than O(N log N) if N = M (N/log N).     

不含非平凡函数依赖或多值依赖的关系的势

本文讨论了一类特殊的Armstrong关系－不含非平凡函数依赖或多值依赖的关系，给出了这类关系的判定条件，得到了这类关系的势的下界值，并使用基于关系的投影运算方法，得到了精确的下界值，同时还涉及到了多值依赖的情形。     

XML弱函数依赖及其推理规则

XML函数依赖问题是进行XML数据库后续研究的基础。首先基于M.Arenas等人给定的XML中DTD和XML树的定义,提出空值、不完全树元组、数据值偏序、最小扩展树等概念,在此基础上,给出弱函数依赖及其满足性的定义;其次研究了XML弱函数依赖的逻辑蕴含问题,提出一组适合XML空值模型的函数依赖推理规则集;最后给出推理规则集的正确性和完备性证明。     

Probability propagation in fuzzy Bayesian belief networks with nondeterministic states

The conceptual basis of fuzzy Bayesian belief networks with nondeterministic states is considered. The concept of a fuzzy probability estimate as a fuzzy relation of special type is introduced and its geometrical interpretation is given. Functional transformations of fuzzy probability estimates are defined and a multidimensional linear interpolation procedure is developed. Fundamental aspects of information distribution in fuzzy Bayesian belief networks with nondeterministic states are considered. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 153–169, November–December 2008.     

Asymptotic properties of keys and functional dependencies in random databases

Practical database applications give the impression that sets of constraints are rather small and that large sets are unusual and are caused by bad design decisions. Theoretical investigations, however, show that minimal constraint sets are potentially very large. Their size can be estimated to be exponential in terms of the number of attributes. The gap between observation in practice and theory results in the rejection of theoretical results. However, practice is related to average cases and is not related to worst cases.

The theory used until now considered the worst-case complexity. This paper aims to develop a theory for the average-case complexity. Several probabilistic models and asymptotics of corresponding probabilities are investigated for random databases formed by independent random tuples with a common discrete distribution. Poisson approximations are studied for the distributions of some characteristics for such databases where the number of tuples is sufficiently large. We intend to prove that the exponential complexity of key sets and sets of functional dependencies is rather unusual and almost all minimal keys in a relation have a length which depends mainly on the size of the relation.     

XML文档在关系数据库中的规范化存储

提出了一种存储方法，首先把XML文档映射为泛关系模式，再利用算法DeriveFDs推导出XML键所蕴含的泛关系模式上函数依赖集的规范覆盖，根据此规范覆盖，最后将泛关系模式保持函数依赖地分解为3NF模式集。得到了保持XML键约束的规范化存储模式，实现了XML文档在关系数据库中的规范化存储。实验研究表明文中提出的方法是有效的。