A Finite State Model for On-Line Analytical Processing in Triadic Contexts

Abstract

Abstract. About ten years ago, triadic contexts were presented by Lehmann and Wille as an extension of Formal Concept Analysis. However, they have rarely been used up to now, which may be due to the rather complex structure of the resulting diagrams. In this paper, we go one step back and discuss how traditional line diagrams of standard (dyadic) concept lattices can be used for exploring and navigating triadic data. Our approach is inspired by the slice & dice paradigm of On-Line-Analytical Processing (OLAP). We recall the basic ideas of OLAP, and show how they may be transferred to triadic contexts. For modeling the navigation patterns a user might follow, we use the formalisms of finite state machines. In order to present the benefits of our model, we show how it can be used for navigating the IT Baseline Protection Manual of the German Federal Office for Information Security.

Information Retrieval in Folksonomies: Search and Ranking

“…The ranking takes into account how early someone bookmarked an URL and how many people followed him or her. Other systems show popular sites (Populicious 11 ) or focus on graphical representations (Cloudalicious 12 , Grafolicious 13 ) of statistics about del.icio.us.…”

“…I. e., ≺= ∅, and we will simply note a folksonomy as a quadruple F := (U, T, R, Y ). This structure is known in Formal Concept Analysis [14,4] as a triadic context [7,13]. An equivalent view on folksonomy data is that of a tripartite (undirected) hypergraph G = (V, E), where V = U∪T∪R is the set of nodes, and E = {{u, t, r} | (u, t, r) ∈ Y } is the set of hyperedges.…”

Mining Association Rules in Folksonomies

“…I. e., ≺ = ∅, and we will simply note a folksonomy as a quadruple F := (U, T, R, Y ). This structure is known in Formal Concept Analysis (Wille (1982); Ganter and Wille (1999)) as a triadic context (Lehmann and Wille (1995);Stumme (2005)). An equivalent view on folksonomy data is that of a tripartite (undirected) hypergraph G = (V, E), where V = U∪T∪R is the set of nodes, and E = {{u, t, r} | (u, t, r) ∈ Y } is the set of hyperedges.…”

Social recommender systems for web 2.0 folksonomies

“…Typical examples of such measures are the clustering coefficient and the characteristic path length in the tripartite undirected hypergraph capturing relationships between users, annotations, and items. An equivalent common view on folksonomy data is known in Formal Concept Analysis [30,9] as a triadic context [17,26]. In many cases, suitable recommendations can be obtained by analyzing link-based authority measures of the folksonomy.…”