Properties of Weakly Closed Itemsets and their Application to Knowledge Discovery

2020 Fiscal Year Final Research Report

• Project/Area Number: 17H01788
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Intelligent informatics
• Research Institution: Kyoto University
• Principal Investigator: Yamamoto Akihiro 京都大学, 情報学研究科, 教授 (30230535)
• Co-Investigator(Kenkyū-buntansha): 小林 靖明 京都大学, 情報学研究科, 助教 (60735083) ; 久保山 哲二 学習院大学, 付置研究所, 教授 (80302660)
• Project Period (FY): 2017-04-01 – 2020-03-31
• Keywords: 知識発見 / ２項関係 / 閉集合 / 弱閉集合

Outline of Final Research Achievements

In this research, in order to admit noise in closed sets in a binary relation between two discrete-valued attributes, we formulated weakly closed sets using set theory and constructed an algorithm for enumerating weakly closed sets. We defined weakly closed sets based on the fact that closed sets can be interpreted using graphs. We designed an algorithm for enumerating weakly closed sets with modifying the well-known fast enumeration algorithm for closed sets. Furthermore, by modifying the definition of weakly closed sets and the enumeration algorithm to the trajectory data collected from travelers, we succeeded in enumerating the routes frequently followed by them as weakly closed sets. We also showed that the fixpoint semantics of closed sets cannot be given to weakly closed sets in general.

Free Research Field

知能情報学

Academic Significance and Societal Importance of the Research Achievements

２つの離散値属性間の２項関係における閉集合は，知識発見における意味を持つだけでなく，数学的な性質を数多く持ち，しかも高速な列挙方法が開発されるなど，知識発見において重要な概念である．しかし，ノイズを全く認めないことが実用上の障害となることもあった．そこで，閉集合に対してノイズを許容する方法が必要であるが，離散値属性を扱う際にノイズを数量的に定義することは適切とは限らない．そこで，弱閉集合をグラフ理論を範にして集合論を用いて定式化した上で，弱閉集合を列挙するためのアルゴリズムを構築した．実応用として，旅行者の経路を集めた実データから旅行者がよく辿る経路を弱閉集合として列挙することに成功した．