Progress in Artificial Intelligence

, Volume 3, Issue 1, pp 15–28 | Cite as

Constructing fading histograms from data streams

  • Raquel Sebastião
  • João Gama
  • Teresa Mendonça
Regular Paper


The ability to collect data is changing drastically. Nowadays, data are gathered in the form of transient and finite data streams. Memory restrictions preclude keeping all received data in memory. When dealing with massive data streams, it is mandatory to create compact representations of data, also known as synopses structures or summaries. Reducing memory occupancy is of utmost importance when handling a huge amount of data. This paper addresses the problem of constructing histograms from data streams under error constraints. When constructing online histograms from data streams there are two main characteristics to embrace: the updating facility and the error of the histogram. Moreover, in dynamic environments, besides the need of compact summaries to capture the most important properties of data, it is also essential to forget old data. Therefore, this paper presents sliding histograms and fading histograms, an abrupt and a smooth strategies to forget outdated data.


Data streams Online histograms  Error constraints Fading histograms 



The work of Raquel Sebastião was supported by FCT (Portuguese Foundation for Science and Technology) under the PhD Grant SFRH/BD/41569/2007. The authors acknowledge the support of the European Commission through the project MAESTRA (Grant number ICT-2013-612944). This work was also funded by the European Regional Development Fund through the COMPETE Program, by the Portuguese Funds through the FCT (Portuguese Foundation for Science and Technology) within project FCOMP-01-0124-FEDER-022701, and by the Projects NORTE-07-0124-FEDER-000056/000059 which is financed by the North Portugal Regional Operational Program (ON.2 O Novo Norte), under the National Strategic Reference Framework (NSRF).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Raquel Sebastião
    • 1
    • 2
  • João Gama
    • 1
    • 3
  • Teresa Mendonça
    • 2
    • 4
  1. 1.LIAAD, INESC TECPortoPortugal
  2. 2.Dep. MatemáticaFac. Ciências da Universidade do Porto (FCUP)PortoPortugal
  3. 3.Fac. Economia da Universidade do Porto (FEP)PortoPortugal
  4. 4.Dep. de MatemáticaCenter for Research and Developments in Mathematics and Applications (CIDMA)AveiroPortugal

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