Draft and proof of an algorithm computing incremental changes within a labeled layouted concept lattice upon insertion or removal of an attribute column in the underlying formal context. Furthermore some implementational details and mathematical background knowledge are presented. / Entwurf und Beweis eines Algorithmus zur Berechnung inkrementeller Änderungen in einem beschrifteten dargestellten Begriffsverband beim Einfügen oder Entfernen einer Merkmalsspalte im zugrundeliegenden formalen Kontext. Weiterhin sind einige Details zur Implementation sowie zum mathematischen Hintergrundwissen dargestellt.

Draft and proof of an algorithm computing incremental changes within a labeled layouted concept lattice upon insertion or removal of an attribute column in the underlying formal context. Furthermore some implementational details and mathematical background knowledge are presented.:1 Introduction 1.1 Acknowledgements 1.2 Supporting University: TU Dresden, Institute for Algebra 1.3 Supporting Corporation: SAP AG, Research Center Dresden 1.4 Research Project: CUBIST 1.5 Task Description und Structure of the Diploma Thesis I Mathematical Details 2 Fundamentals of Formal Concept Analysis 2.1 Concepts and Concept Lattice 2.2 Visualizations of Concept Lattices 2.2.1 Transitive Closure and Transitive Reduction 2.2.2 Neighborhood Relation 2.2.3 Line Diagram 2.2.4 Concept Diagram 2.2.5 Vertical Hybridization 2.2.6 Omitting the top and bottom concept node 2.2.7 Actions on Concept Diagrams 2.2.8 Metrics on Concept Diagrams 2.2.9 Heatmaps for Concept Diagrams 2.2.10 Biplots of Concept Diagrams 2.2.11 Seeds Selection 2.3 Apposition of Contexts 3 Incremental Updates for Concept Diagrams 3.1 Insertion & Removal of a single Attribute Column 3.1.1 Updating the Concepts 3.1.2 Structural Remarks 3.1.3 Updating the Order 3.1.4 Updating the Neighborhood 3.1.5 Updating the Concept Labels 3.1.6 Updating the Reducibility 3.1.7 Updating the Arrows 3.1.8 Updating the Seed Vectors 3.1.9 Complete IFOX Algorithm 3.1.10 An Example: Stepwise Construction of FCD(3) 3.2 Setting & Deleting a single cross 4 Iterative Exploration of Concept Lattices 4.1 Iceberg Lattices 4.2 Alpha Iceberg Lattices 4.3 Partly selections 4.3.1 Example with EMAGE data 4.4 Overview on Pruning & Interaction Techniques II Implementation Details 5 Requirement Analysis 5.1 Introduction 5.2 User-Level Requirements for Graphs 5.2.1 Select 5.2.2 Explore 5.2.3 Reconfigure 5.2.4 Encode 5.2.5 Abstract/Elaborate 5.2.6 Filter 5.2.7 Connect 5.2.8 Animate 5.3 Low-Level Requirements for Graphs 5.3.1 Panel 5.3.2 Node and Edge 5.3.3 Interface 5.3.4 Algorithm 5.4 Mapping of Low-Level Requirements to User-Level Requirements 5.5 Specific Visualization Requirements for Lattices 5.5.1 Lattice Zoom/Recursive Lattices/Partly Nested Lattices 5.5.2 Planarity 5.5.3 Labels 5.5.4 Selection of Ideals, Filters and Intervalls 5.5.5 Restricted Moving of Elements 5.5.6 Layout Algorithms 5.5.7 Additional Feature: Three Dimensions and Rotation 5.5.8 Additional Feature: Nesting 6 FCAFOX Framework for Formal Concept Analysis in JAVA 6.1 Architecture A Appendix A.1 Synonym Lexicon A.2 Galois Connections & Galois Lattices A.3 Fault Tolerance Extensions to Formal Concept Analysis / Entwurf und Beweis eines Algorithmus zur Berechnung inkrementeller Änderungen in einem beschrifteten dargestellten Begriffsverband beim Einfügen oder Entfernen einer Merkmalsspalte im zugrundeliegenden formalen Kontext. Weiterhin sind einige Details zur Implementation sowie zum mathematischen Hintergrundwissen dargestellt.:1 Introduction 1.1 Acknowledgements 1.2 Supporting University: TU Dresden, Institute for Algebra 1.3 Supporting Corporation: SAP AG, Research Center Dresden 1.4 Research Project: CUBIST 1.5 Task Description und Structure of the Diploma Thesis I Mathematical Details 2 Fundamentals of Formal Concept Analysis 2.1 Concepts and Concept Lattice 2.2 Visualizations of Concept Lattices 2.2.1 Transitive Closure and Transitive Reduction 2.2.2 Neighborhood Relation 2.2.3 Line Diagram 2.2.4 Concept Diagram 2.2.5 Vertical Hybridization 2.2.6 Omitting the top and bottom concept node 2.2.7 Actions on Concept Diagrams 2.2.8 Metrics on Concept Diagrams 2.2.9 Heatmaps for Concept Diagrams 2.2.10 Biplots of Concept Diagrams 2.2.11 Seeds Selection 2.3 Apposition of Contexts 3 Incremental Updates for Concept Diagrams 3.1 Insertion & Removal of a single Attribute Column 3.1.1 Updating the Concepts 3.1.2 Structural Remarks 3.1.3 Updating the Order 3.1.4 Updating the Neighborhood 3.1.5 Updating the Concept Labels 3.1.6 Updating the Reducibility 3.1.7 Updating the Arrows 3.1.8 Updating the Seed Vectors 3.1.9 Complete IFOX Algorithm 3.1.10 An Example: Stepwise Construction of FCD(3) 3.2 Setting & Deleting a single cross 4 Iterative Exploration of Concept Lattices 4.1 Iceberg Lattices 4.2 Alpha Iceberg Lattices 4.3 Partly selections 4.3.1 Example with EMAGE data 4.4 Overview on Pruning & Interaction Techniques II Implementation Details 5 Requirement Analysis 5.1 Introduction 5.2 User-Level Requirements for Graphs 5.2.1 Select 5.2.2 Explore 5.2.3 Reconfigure 5.2.4 Encode 5.2.5 Abstract/Elaborate 5.2.6 Filter 5.2.7 Connect 5.2.8 Animate 5.3 Low-Level Requirements for Graphs 5.3.1 Panel 5.3.2 Node and Edge 5.3.3 Interface 5.3.4 Algorithm 5.4 Mapping of Low-Level Requirements to User-Level Requirements 5.5 Specific Visualization Requirements for Lattices 5.5.1 Lattice Zoom/Recursive Lattices/Partly Nested Lattices 5.5.2 Planarity 5.5.3 Labels 5.5.4 Selection of Ideals, Filters and Intervalls 5.5.5 Restricted Moving of Elements 5.5.6 Layout Algorithms 5.5.7 Additional Feature: Three Dimensions and Rotation 5.5.8 Additional Feature: Nesting 6 FCAFOX Framework for Formal Concept Analysis in JAVA 6.1 Architecture A Appendix A.1 Synonym Lexicon A.2 Galois Connections & Galois Lattices A.3 Fault Tolerance Extensions to Formal Concept Analysis