Data Mining and Knowledge Discovery

, Volume 26, Issue 3, pp 574-619

First online:

Closed and noise-tolerant patterns in n-ary relations

  • Loïc CerfAffiliated withDepartment of Computer Science, Universidade Federal de Minas Gerais Email author 
  • , Jérémy BessonAffiliated withUniversity of Vilnius
  • , Kim-Ngan T. NguyenAffiliated withUniversité de Lyon, CNRS, INSA, LIRIS, UMR5205
  • , Jean-François BoulicautAffiliated withUniversité de Lyon, CNRS, INSA, LIRIS, UMR5205

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Binary relation mining has been extensively studied. Nevertheless, many interesting 0/1 data naturally appear as n-ary relations with n ≥ 3. A timely challenge is to extend local pattern extraction, eg, closed pattern mining, to such contexts. When considering higher arities, faint noise affects more and more the quality of the extracted patterns. We study a declarative specification of error-tolerant patterns by means of new primitive constraints and the design of an efficient algorithm to extract every solution pattern. It exploits the enumeration principles of the state-of-the-art Data-Peeler algorithm for n-ary relation mining. Efficiently enforcing error-tolerance crucially depends on innovative strategies to incrementally compute partial information on the data. Our prototype is tested on both synthetic and real datasets. It returns relevant collections of patterns even in the case of noisy ternary or 4-ary relations, eg, in the context of pattern discovery from dynamic networks.


Boolean tensor Multi-way set Fault-tolerance Cross-graph quasi-clique