Juan-Carlos Cubero

A new definition of fuzzy functional dependency in fuzzy relational databases

The need to incorporate and treat information given in fuzzy terms in Relational Databases has concentrated a great effort in the last years. This article focuses on the treatment of functional dependencies (f.d.) between attributes of a relation scheme. We review other approaches to this problem and present some of its missfunctions concerning intuitive properties a fuzzy extension of f.d. should verify. Then we introduce a fuzzy extension of this concept to overcome the previous anomalous behaviors and study its properties. of primary interest is the completeness of our fuzzy version of Armstrong axioms in order to derive all the fuzzy functional dependencies logically implied by a set of f.f.d. just using these axioms.

TBAR: An efficient method for association rule mining in relational databases

Abstract In this paper, we propose a new algorithm for efficient association rule mining, which we apply in order to discover interesting patterns in relational databases. Our algorithm, which is called Tree-Based Association Rule mining (TBAR), redefines the notion of item and employs an effective tree data structure. It can also use techniques such as Direct Hashing and Pruning (DHP). Experiments with real-life datasets show that TBAR outperforms Apriori, a well-known and widely used algorithm.

Towards the implementation of a generalized fuzzy relational database model

This paper shows the necessary elements for the effective implementation of the generalized fuzzy relational database model. From the model described in Medina et al. (1994) some criteria for representation and handling of imprecise information are introduced, the most important aspect being the simplicity of the implementation. The paper shows a series of mechanisms to implement imprecise information in a classical RDBMS. Having the information represented in a classical RDBMS data structure and having the implementation of procedural knowledge about such information, we will be able to build a FRDBMS on a host RDBMS.

Data summarization in relational databases through fuzzy dependencies

In this paper we deal with the problem of treating with dependencies in relational databases which do not hold in an exact manner as classical functional dependencies but in a weaker sense, i.e., we face with relations which satisfy dependencies such that ‘people with similar age and height have similar weight’. We model this relationship through the concept of fuzzy dependency. We see that these dependencies imply some kind of fuzzy redundancy, and, in order to avoid it, we propose to use a projection operator which leads us to partition a relation r into two projections, say r1 and r2 with a less amount of information. Then, we proceed to replace the original relation by these projections. In this process we must guarantee that we can recover the data we had in the original relation. This will be possible by using a special join operator applied to r1 and r2. We must also guarantee that we can test the fuzzy dependency for new entries to the database in the same way either if we consider the original relation r or if we work with the projections r1 and r2. We also show that this definition of dependency maintains the good properties of completeness of the classical case. ” 1999 Elsevier Science Inc. All rights reserved.

Building multi-way decision trees with numerical attributes

Decision trees are probably the most popular and commonly used classification model. They are recursively built following a top-down approach (from general concepts to particular examples) by repeated splits of the training dataset. When this dataset contains numerical attributes, binary splits are usually performed by choosing the threshold value which minimizes the impurity measure used as splitting criterion (e.g. C4.5 gain ratio criterion or CART Ginis index). In this paper we propose the use of multi-way splits for continuous attributes in order to reduce the tree complexity without decreasing classification accuracy. This can be done by intertwining a hierarchical clustering algorithm with the usual greedy decision tree learning.

ART: A Hybrid Classification Model

This paper presents a new family of decision list induction algorithms based on ideas from the association rule mining context. ART, which stands for ‘Association Rule Tree’, builds decision lists that can be viewed as degenerate, polythetic decision trees. Our method is a generalized “Separate and Conquer” algorithm suitable for Data Mining applications because it makes use of efficient and scalable association rule mining techniques.

A conceptual approach for dealing with imprecision and uncertainty in object-based data models

This article treats the problem of vagueness in databases from a general point of view. Several kinds of attribute imprecise values are considered, including the case where such values are fuzzy set of objects. The possibility of managing uncertain data is also taken into account and both sources of the lack of information are studied jointly. All these vague elements are represented in a unified manner by using a semantic data model. The article shows how this representation is possible and opens the way for implementing this kind of information by using a classic object‐oriented database system.

AN ALTERNATIVE APPROACH TO DISCOVER GRADUAL DEPENDENCIES

In this paper we propose a new definition of gradual dependence as a special kind of association rule. We propose a way to adapt existing association rule mining algorithms for the new task of mining such dependencies, and we discuss about its complexity. Some experiments in a real database illustrate the usefulness of the approach.

A Survey of Link Prediction in Complex Networks

Networks have become increasingly important to model complex systems composed of interacting elements. Network data mining has a large number of applications in many disciplines including protein-protein interaction networks, social networks, transportation networks, and telecommunication networks. Different empirical studies have shown that it is possible to predict new relationships between elements attending to the topology of the network and the properties of its elements. The problem of predicting new relationships in networks is called link prediction. Link prediction aims to infer the behavior of the network link formation process by predicting missed or future relationships based on currently observed connections. It has become an attractive area of study since it allows us to predict how networks will evolve. In this survey, we will review the general-purpose techniques at the heart of the link prediction problem, which can be complemented by domain-specific heuristic methods in practice.

On the quest for easy-to-understand splitting rules

Decision trees are probably the most popular and commonly used classification model. They are built recursively following a top-down approach (from general concepts to particular examples) by repeated splits of the training dataset. The chosen splitting criterion may affect the accuracy of the classifier, but not significantly. In fact, none of the proposed splitting criteria in the literature has proved to be universally better than the rest. Although they all yield similar results, their complexity varies significantly, and they are not always suitable for multi-way decision trees. Here we propose two new splitting rules which obtain similar results to other well-known criteria when used to build multi-way decision trees, while their simplicity makes them ideal for non-expert users.