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Generating Hierarchical link patterns based on concept lattice for Navigating the Web of Data

This paper proposes a concept lattice-based link pattern hierarchy for exploring Web data, organizing links effectively. Utilizing Formal Concept Analysis (FCA) theory, the approach helps users analyze intricate link relationships. The study presents methods for constructing link pattern hierarchies, comparing algorithms' performance in generating concept lattices. Key elements include defining formal contexts, link patterns, and the link pattern hierarchy construction process. Theoretical foundations and practical applications are discussed, aiming to enhance data navigation on the Web. Researchers Kuznetsov and Obiedkov's work is cited, highlighting algorithm comparisons in concept lattice generation.

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Generating Hierarchical link patterns based on concept lattice for Navigating the Web of Data

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  1. Generating Hierarchical link patterns based on concept lattice for Navigating the Web of Data Liang Zheng

  2. Navigational features have been largely recognized as fundamental for the Web of Data browsing, search and query. • Most existing navigation approaches are based on link-traversal. • However, current approaches for navigating can hardly expose deep relations of the links. • In this paper, a link pattern hierarchy based on concept lattice is proposed which effectively organizes the link space.

  3. Preliminaries

  4. LetUbe the set of all URIs and L the set of all literals. • Definition 1. (Web of Data T ) • The Web of Data (over U and L) is the set of triples(s, p, o) in UU  (U L). We will denote it by T.

  5. Let P  U be a finite set of properties. • Definition 2: Property Hierarchy H • A set P together with a partial ordering p is called a poset, and is denoted by H=( P, p) • Irreducible property set • A property set X  P, when u, v  X such that neitheru p v nor • v p u, is called irreducible property set.

  6. A partial ordering on the subset of P • Let X, Y be two irreducible property subsets of P, • X p Y iff  v  Y ,  u  X, such that u pv {mother} < {parents}  {mother, influencedBy} < {parents}  {mother, influencedBy} < {mother}  {mother, influencedBy} < {parents, influencedBy}  {mother, influencedBy} < {parents, knows} X

  7. Data analysis is performed to help users analyze the deep relations of the links, by taking advantage of a mathematical theory named Formal Concept Analysis (FCA) theory.

  8. Definition 3: Formal Context (形式背景) Let Es U be a finite set of URIs, indicating the starting points of the navigation. • a triple K=(G,M,I), where GU denotes a set of entities, M U a set of properties, and I ⊆ G×M a binary relation between G and M. • The ordered pair ( g, m) ∈ I iff •  es Es, such that (es, m, g) T or (g, m, es) T

  9. Example: K: G={e1, e2, e3, e4}, M={mother, father, knows, influencedBy}

  10. Definition 4: Link Pattern( a formal concept of the context K) • For X ⊆ G, Y ⊆ M, a pair lp= <X,Y>, such that X ‘= Y and Y’ = X, is called a link pattern (a formal concept of the context K) • In <X, Y>, the set X is called the extent and the set Y the intent of the link pattern lp. • Let LPK be a finite link pattern set of the context K, and Let ≤ be a partial ordering on LPK, lp1 ≤ lp2⇔ (X1,Y1) ≤ (X2,Y2) ⇔ Y1 p Y2 . Obviously:lp1 ≤ lp2  X1 ⊆ X2 • Then lp1 is called a sub_linkpattern of lp2,and lp2 is a super_linkpattern of lp1. • For two link pattern lp1 and lp2, if lp1 ≤ lp2 and there is no link pattern lp3 withlp3lp1, lp3lp2, lp1 ≤ lp3 ≤ lp2 ,the lp1 is called a child of lp2, and lp2 is called a parent of lp1. This relationship is denotedby lp1 ≺ lp2 .

  11. Definition 5: Link Pattern Hierarchy (concept lattices) • With respect to the partial order ≺ , the link pattern set LPK forms a lattice called the link pattern hierarchy of the formal context K,denoted by LPHk • The greatest element of LPHk (G, G’) • The least element of LPHk (M’ , M)

  12. Problem 1: Link Pattern Hierarchy Construction • Generating formal concepts • Constructing concept lattices

  13. Comparing Performance of Algorithms for Generating Concept Lattices [] • Batch Algorithm 批生成算法 • 首先生成形式背景所对应的所有概念,再生成概念之间的连接关系 • 静态的形式背景 • Incremental Algorithm 增量算法 • 动态形式背景(交易数据库) Kuznetsov S O, Obiedkov S A. Comparing performance of algorithms for generating concept lattices[J]. Journal of Experimental & Theoretical Artificial Intelligence, 2002, 14(2-3): 189-216. 被引用次数:415

  14. |M| = 100; |g'| = 4. |g‘ | : the number of attributes per object

  15. |M| = 100; |g'| = 25.

  16. |M| = 100; |g'| = 50.

  17. Bordat算法的基本思想是:对于形式背景K=(G, M,I),若概念节点为(Ak,Bk),找出属性子集Colk=M- Bk, 且Colk在Ak中能保持完全二元组的性质,即Colk为最大的子集,则Bki=Bk  Colk构成了当前节 点的一个子节点的内涵。

  18. The worst-case time complexity of Bordat is O(|G||M|2|L|), where |L| is the size of the concept lattice.

  19. References • Kuznetsov S O, Obiedkov S A. Comparing performance of algorithms for generating concept lattices[J]. Journal of Experimental & Theoretical Artificial Intelligence, 2002, 14(2-3): 189-216. • Heath, T., & Bizer, C. (2011). Linked data: Evolving the web into a global data space. Synthesis lectures on the semantic web: theory and technology, 1(1), 1-136.

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