A tool for creating and visualising formal concept trees

This paper presents a tool for creating and visualising formal concept trees. The concept tree provides an alternative visualisation to the more commonly known concept lattice. The tool described here is an extension of the In-Close formal concept mining program, where concepts are output in a format that can be visualised in a Web Browser using the Collapsible Tree Layout from the D3.js JavaScript library. Because the visualisation is expandable and collapsible, the tool is able to deal with large trees and the user is able to explore branches with single mouse clicks and by panning and zooming the tree. So-called ‘iceberg trees’ can also be produced, by specifying a minimum support for objects

Making Use of Empty Intersections to Improve the Performance of CbO-Type Algorithms

This paper describes how improvements in the performance of Close-by-One type algorithms can be achieved by making use of empty intersections in the computation of formal concepts. During the computation, if the intersection between the current concept extent and the next attribute-extent is empty, this fact can be simply inherited by subsequent children of the current concept. Thus subsequent intersections with the same attribute-extent can be skipped. Because these intersections require the testing of each object in the current extent, significant time savings can be made by avoiding them. The paper also shows how further time savings can be made by forgoing the traditional canonicity test for new extents, if the intersection is empty. Finally, the paper describes how, because of typical optimizations made in the implementation of CbO-type algorithms, even more time can be saved by amalgamating inherited attributes with inherited empty intersections into a single, simple test

A ‘Best-of-Breed’ approach for designing a fast algorithm for computing fixpoints of Galois Connections

The fixpoints of Galois Connections form patterns in binary relational data, such as object-attribute relations, that are important in a number of data analysis fields, including Formal Concept Analysis (FCA), Boolean factor analysis and frequent itemset mining. However, the large number of such fixpoints present in a typical dataset requires efficient computation to make analysis tractable, particularly since any particular fixpoint may be computed many times. Because they can be computed in a canonical order, testing the canonicity of fixpoints to avoid duplicates has proven to be a key factor in the design of efficient algorithms. The most efficient of these algorithms have been variants of the Close-By-One (CbO) algorithm. In this article, the algorithms CbO, FCbO, In-Close, In-Close2 and a new variant, In-Close3, are presented together for the first time, with in-Close2 and In-Close3 being the results of breeding In-Close with FCbO. To allow them to be easily compared, the algorithms are presented in the same style and notation. The important advances in CbO are described and compared graphically using a simple example. For the first time, the algorithms are implemented using the same structures and techniques to provide a level playing field for evaluation. Their performance is tested and compared using a range of data sets and the most important features identified for a CbO ‘Best-of-Breed’. This article also presents, for the first time, the ‘partial-closure’ canonicity test

A new method for inheriting canonicity test failures in Close-by-One type algorithms

Close-by-One type algorithms are effcient algorithms for computing formal concepts. They use a mathematical canonicity test to avoid the repeated computation of the same concept, which is far more effcient than methods based on searching. Nevertheless, the canonicity test is still the most labour intensive part of Close-by-One algorithms and various means of avoiding the test have been devised, including the ability to inherit test failures at the next level of recursion. This paper presents a new method for inheriting canonicity test failures in Close- by-One type algorithms. The new method is simpler than the existing method and can be amalgamated with other algorithm features to further improve effciency. The paper recaps an existing algorithm that does not feature test failure inheritance and an algorithm that features the existing method. The paper then presents the new method and a new algorithm that incorporates it. The three algorithms are implemented on a `level playing field' with the same level of optimisation. Experiments are carried out on the implemented algorithms, using a representative range of data sets, to compare the number of inherited canonicity test failures and the computation times. It is shown that the new algorithm, incorporating the new method of inheriting canonicity test failures, gives the best performance

A conceptual approach to gene expression analysis enhanced by visual analytics

The analysis of gene expression data is a complex task for biologists wishing to understand the role of genes in the formation of diseases such as cancer. Biologists need greater support when trying to discover, and comprehend, new relationships within their data. In this paper, we describe an approach to the analysis of gene expression data where overlapping groupings are generated by Formal Concept Analysis and interactively analyzed in a tool called CUBIST. The CUBIST workflow involves querying a semantic database and converting the result into a formal context, which can be simplified to make it manageable, before it is visualized as a concept lattice and associated charts

Combining Business Intelligence with Semantic Technologies: The CUBIST Project

This paper describes the European Framework Seven CUBIST project, which ran from October 2010 to September 2013. The project aimed to combine the best elements of traditional BI with the newer, semantic, technologies of the Sematic Web, in the form of RDF and FCA. CUBIST’s purpose was to provide end-users with "conceptually relevant and user friendly visual analytics" to allow them to explore their data in new ways, discovering hidden meaning and solving hitherto difficult problems. To this end, three of the partners in CUBIST were use-cases: recruitment consultancy, computational biology and the space industry. Each use-case provided their own requirements and evaluated how well the CUBIST outcomes addressed them