Sobre las interacciones: distancias e integrales

La definición de independencia de variables aleatorias se basa en la distribución de probabilidad conjunta. La distribución gausiana multivariante es un tipo de distribución conjunta en el que las variables pueden no ser independientes. Sin embargo son concebibles otros tipos de relaciones diferentes a la distribución gausiana. En un trabajo reciente mostramos que las medidas difusas pueden utilizarse para definir distribuciones de probabilidad con interacciones entre variables. En este trabajo se presenta un resumen de nuestros resultados recientes en este tipo de distribuciones.Se agradece el apoyo de los proyectos del MEC y MINECO ARES (CONSOLIDER INGENIO 2010 CSD2007-00004), eAEGIS (TSI2007-65406-C03-02) y COPRIVACY (TIN2011-27076-C03-03).Peer Reviewe

Some properties of Choquet integral based probability functions

The Choquet integral permits us to integrate a function with respect to a non-additive measure. When the measure is additive it corresponds to the Lebesgue integral. This integral was used recently to define families of probability-density functions. They are the exponential family of Choquet integral (CI) based class-conditional probability-density functions, and the exponential family of Choquet– Mahalanobis integral (CMI) based class-conditional probability-density functions. The latter being a generalization of the former, and also a generalization of the normal distribution.In this paper we study some properties of these distributions, and study the application of a few normality tests

An evolutionary algorithm to enhance multivariate Post-Randomization Method (PRAM) protections

The amount of public statistical information available is growing and more accurate protection methods are needed in order to achieve data confidentiality. The Post-Randomization Method (PRAM) protection method was introduced in 1997 as a very powerful method for categorical microdata, but it is still not widely used. This method has a Markov matrix as a parameter. The main problem of the application of this method is that it is difficult to find a good Markov matrix that performs changes in the microdata file producing low loss of valuable information and low risk of disclosure of sensitive data. In this paper we present a methodology that helps us to find a matrix to perform better protections. This is achieved by using an evolutionary algorithm with integrated Information Loss and Disclosure Risk measures. Experiments using three different datasets are also presented in order to empirically evaluate the application of this technique. © 2014 Elsevier Inc. All rights reserved.This work has been done under the PhD in Computer Science program of the Universitat Autònoma de Barcelona (UAB). It is also partially supported by the Spanish MEC ARES-CONSOLIDER INGENIO 2010 CSD2007-00004, and COPRIVACY TIN2011-27076-C03-03. The research leading to these results has also received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under Grant Agreement Num. 262608.Peer Reviewe

Reidentification and k-anonymity: A model for disclosure risk in graphs

In this article we provide a formal framework for reidentification in general. We define n-confusion as a concept for modeling the anonymity of a database table and we prove that n-confusion is a generalization of k-anonymity. After a short survey on the different available definitions of k-anonymity for graphs we provide a new definition for k-anonymous graph, which we consider to be the correct definition. We provide a description of the k-anonymous graphs, both for the regular and the non-regular case. We also introduce the more flexible concept of (k, l)-anonymous graph. Our definition of (k, l)-anonymous graph is meant to replace a previous definition of (k, l)-anonymous graph, which we here prove to have severe weaknesses. Finally, we provide a set of algorithms for k-anonymization of graphs. © 2012 Springer-Verlag.Partial support by the Spanish MEC projects ARES (CONSOLIDER INGENIO 2010 CSD2007-00004), eAEGIS (TSI2007-65406-C03-02), COPRIVACY (TIN2011-27076-C03-03), and RIPUP (TIN2009-11689) is acknowledged. One author is partially supported by the FPU grant (BOEs 17/11/2009 and 11/10/2010) and by the Government of Catalonia under grant 2009 SGR 1135Peer Reviewe

Generalization-Based k-Anonymization

Microaggregation is an anonymization technique consisting on partitioning the data into clusters no smaller than k elements and then replacing the whole cluster by its prototypical representant. Most of microaggregation techniques work on numerical attributes. However, many data sets are described by heterogeneous types of data, i.e., nu- merical and categorical attributes. In this paper we propose a new mi- croaggregation method for achieving a compliant k-anonymous masked file for categorical microdata based on generalization. The goal is to build a generalized description satisfied by at least k domain objects and to replace these domain objects by the description. The way to construct that generalization is similar that the one used in growing decision trees. Records that cannot be generalized satisfactorily are discarded, therefore some information is lost. In the experiments we performed we prove that the new approach gives good results. © Springer International Publishing Switzerland 2015.This research is partially funded by the Spanish MICINN projects COGNITIO (TIN-2012-38450-C03-03), EdeTRI (TIN2012-39348-C02-01) and COPRIVACY (TIN2011-27076-C03-03), the grant 2009-SGR-1434 from the Generalitat de Catalunya, and the European Project DwB (Grant Agreement Number 262608)Peer reviewe

Literature Review of the Recent Trends and Applications in various Fuzzy Rule based systems

Fuzzy rule based systems (FRBSs) is a rule-based system which uses linguistic fuzzy variables as antecedents and consequent to represent human understandable knowledge. They have been applied to various applications and areas throughout the soft computing literature. However, FRBSs suffers from many drawbacks such as uncertainty representation, high number of rules, interpretability loss, high computational time for learning etc. To overcome these issues with FRBSs, there exists many extensions of FRBSs. This paper presents an overview and literature review of recent trends on various types and prominent areas of fuzzy systems (FRBSs) namely genetic fuzzy system (GFS), hierarchical fuzzy system (HFS), neuro fuzzy system (NFS), evolving fuzzy system (eFS), FRBSs for big data, FRBSs for imbalanced data, interpretability in FRBSs and FRBSs which use cluster centroids as fuzzy rules. The review is for years 2010-2021. This paper also highlights important contributions, publication statistics and current trends in the field. The paper also addresses several open research areas which need further attention from the FRBSs research community.Comment: 49 pages, Accepted for publication in ijf