12,725 research outputs found

    Parametric matroid of rough set

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    Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set family, with any subset of a universe as its parameter, to connect rough sets and matroids. On the one hand, for a universe and an equivalence relation on the universe, a parametric set family is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore it can generate a matroid, called a parametric matroid of the rough set. Three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, since partition-circuit matroids were well studied through the lower approximation number, we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.Comment: 15 page

    Soft data mining, computational theory of perceptions, and rough-fuzzy approach

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    Data mining and knowledge discovery is described from pattern recognition point of view along with the relevance of soft computing. Key features of the computational theory of perceptions and its significance in pattern recognition and knowledge discovery problems are explained. Role of fuzzy-granulation (f-granulation) in machine and human intelligence, and its modeling through rough-fuzzy integration are discussed. Merits of fuzzy granular computation, in terms of performance and computation time, for the task of case generation in large scale case-based reasoning systems are illustrated through an example

    Soft data mining, computational theory of perceptions, and rough-fuzzy approach

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    PriPeARL: A Framework for Privacy-Preserving Analytics and Reporting at LinkedIn

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    Preserving privacy of users is a key requirement of web-scale analytics and reporting applications, and has witnessed a renewed focus in light of recent data breaches and new regulations such as GDPR. We focus on the problem of computing robust, reliable analytics in a privacy-preserving manner, while satisfying product requirements. We present PriPeARL, a framework for privacy-preserving analytics and reporting, inspired by differential privacy. We describe the overall design and architecture, and the key modeling components, focusing on the unique challenges associated with privacy, coverage, utility, and consistency. We perform an experimental study in the context of ads analytics and reporting at LinkedIn, thereby demonstrating the tradeoffs between privacy and utility needs, and the applicability of privacy-preserving mechanisms to real-world data. We also highlight the lessons learned from the production deployment of our system at LinkedIn.Comment: Conference information: ACM International Conference on Information and Knowledge Management (CIKM 2018
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