Extracting and Visualising Tree-like Structures from Concept Lattices Cassio Melo 1 , Bénédicte Le-Grand 2 , Marie-Aude Aufaure 1 and Anastasia Bezerianos 1 1 École Centrale Paris – MAS Laboratoire, 2 Laboratoire d’Informatique 6 – LIP6 {cassio.melo, marie-aude.aufaure, anastasia.bezerianos}@ecp.fr, benedicte.le-grand@lip6.fr Abstract Concept lattices built with Formal Concept Analysis are usually represented by Hasse diagrams illustrating the groupings of objects described by common attributes. Hasse diagrams display the relations of partial order between concepts in a hierarchical fashion, where each concept may have several parent concepts. Lattice visualization becomes a problem as the number of clusters grows significantly with the number of objects and attributes. Interpreting the lattice through a direct visualization of the line diagram rapidly becomes impossible and more synthetic representations are needed. In this work we propose several methods to enhance the readability of concept lattices firstly though colouring and distortion techniques, and secondly by extracting and visualizing trees derived from concept lattices structures. Keywords--- Concept Lattices, Formal Concept Analysis, Tree Extraction. 1. Introduction The vast amount of data generated over the last decades has brought new challenges to the analytics science. Visual data analysis and knowledge representation employ methods such as Formal Concept Analysis (FCA) in order to identify groupings of patterns from the analysis process [26]. FCA provides an intuitive understanding of generalization and specialization relationships among objects and their attributes in a structure known as a concept lattice. A concept lattice is traditionally represented by a Hasse diagram illustrating the groupings of objects described by common attributes. A Hasse diagram is a graph where concepts appear as vertices on the plane connected by line segments or curves. The layout of the partially ordered set may be seen as a layered diagram [2]. Lattices visualization becomes a problem as the number of clusters grows significantly with the number of objects and attributes. Interpreting the lattice through a direct visualization of the line diagram rapidly becomes impossible and more synthetic representations are needed. In this work we propose alternatives to the traditional lattice representation, firstly by enhancing the readability of concept lattices though colouring and distortion techniques; secondly by extracting and visualizing trees derived from the lattices structure. The tree extraction from the original lattice has some unique advantages: it eliminates all edges crossing and the resulting hierarchy is also easier to interpret and to represent. Moreover, this representation still provides an overview of the dataset, highlighting significant properties of the lattice. In order to extract trees from lattices, we define a set of parent concept selection criteria, including the stability and support indexes [1,4] provided by FCA literature, confidence index as well as topological features of the lattice. The paper is organized as follows. Section 2 provides background on lattice representations; Section 3 proposes a set of criteria for transforming concept lattices into trees; Section 4 discusses colouring and distortion techniques for enhancing interpretations of lattices. Section 5 presents instantiations of the suggested criteria and visualizations in the biology domain, followed by a discussion in section 6. Section 7 finally concludes and presents perspectives for future work. 2. Visual Representation of Concept Lattices As mentioned above, FCA analysis produces lattices, usually represented as layered directed acyclic graph graphs, named Hasse diagrams illustrating the groupings of objects described by common attributes. Hasse diagrams display the partially ordered sets (posets) between concepts in a hierarchical fashion, where each concept may have several parent concepts. In the following example about animal’s features, the formal context in table 1 generated the concept lattice illustrated in figure 1. The partial order among concepts of the lattice is materialized through the generalization and specialization relationships: for instance Concept 4 (representing the set of flying birds, containing Finch and Eagle objects), is more specific than Concept 1 (which contains all birds –flying or not-), and thus contains a smaller number of objects (Concept 1 has an extra one, the ostrich). This partial order provides different levels of abstraction and native navigation links from a given concept.