This special issue includes extended versions of a selection of papers presented at the Tenth International Conference on Concept Lattices and Their Applications (CLA 2013) held in La Rochelle (France) in October 15–18, 2013. This event was a small conference with a workshop-like atmosphere in which informal relations lead to discussions which, in turn, generate new ideas and approaches. The conference consisted of the presentation of 22 full papers, five poster papers and four invited talks by Vincent Duquenne, Ralph Freese, Bart Goethals and Michel Grabisch.
The CLA conference series started in 2002 and has been held in different countries (Czech Republic, Tunisia, France and Spain), with the special focus on applications of concept lattices, hence its name. The concept lattices (also called Galois lattices) were formally introduced in the 1980s by Rudolf Wille and have provided, for many years now, a formal basis for the development of an applied theory of lattices, nowadays called formal concept analysis (FCA). Since its introduction, FCA has found its way in many disciplines, such as data and knowledge processing, information retrieval, data mining, reasoning and software engineering. With the depth and maturity of methodologies, formalisms, procedures and their applications available today, this claim is stronger than ever, as witnessed by a lot of papers on these and related topics that are published every year.
A total of 37 papers were submitted to CLA 2013, out of which 22 papers were accepted as full papers. For this special issue, the authors of the best-rated papers were invited to submit extended versions of their papers, and eight were ultimately accepted after the reviewing process.
Short descriptions of the contents of the papers included in this special issue are given below:
Bazin and Ganascia introduce an algorithm for choosing the order in which pseudo-intents are enumerated when computing the Duquenne–Guigues basis of a formal context, together with an empirical evaluation of its time and space complexity using, respectively, the number of logical closures and the number of sets in memory as measures.
Valverde-Albacete and Peláez-Moreno focus on the relation between L-valued extensions of FCA and the spectra of some matrices related to L-valued contexts. In this paper, the authors consider the spectra of reducible matrices over completed idempotent semifields and dioids, giving, as a result, a constructive solution to the all eigenvectors problem for matrices over complete idempotent semifields.
Krídlo et al. focus on second-order formal contexts as contexts in which their object and attribute sets are disjoint unions of object and attribute sets of external formal contexts. The paper provides a method to compute such second-order formal concepts by either using bonds between external formal contexts or by using methods based on heterogeneous formal contexts. The paper also shows how this structure generalizes homogeneous fuzzy formal contexts and their derivation operators.
Buzmakov et al. introduce a novel approach for analysing sequential data based on the formalism of sequential pattern structures and projections, and show how it is possible to enumerate more meaningful patterns and increase the computing efficiency of the approach. The applicability of the method for discovering and analysing patterns is tested on a real-world data-set with patient hospitalization trajectories. Interesting patterns answering questions of an expert are extracted and interpreted, showing the feasibility and usefulness of the approach. Particularly, projections play an important role, in that they provide means to select patterns of a special interest and they help to save computation time.
Konecny and Ojeda-Aciego deal with suitable generalizations of the notion of bond between contexts. Different generalizations of the notion of bond within the L-fuzzy setting are analysed: specifically, given a formal context there are three prototypical pairs of concept-forming operators, and this immediately leads to three possible versions of the notion of bond (so-called homogeneous bond wrt certain pair of concept-forming operators). The first results show a close correspondence between homogeneous bonds between two contexts and certain special types of mappings between the sets of extents (or intents) of the corresponding concept lattices. Then, the so-called heterogeneous bonds are introduced (considering simultaneously two types of concept-forming operators) and generalize the previous relationship to mappings between the sets of extents (or intents) of the corresponding concept lattices.
The paper by Dolques et al. considers data analysis methods for knowledge extraction from large water data-sets, the specific problem being to find a connection between physicochemical parameters and the characteristics of taxons living in sample sites. The authors introduce a variant of the relational concept analysis process based on attribute-object-concept posets rather than concept lattices, as the former lead to smaller combinatorial problems. Experiments are performed with various scaling operators, and a specific operator is introduced to deal with noisy data. The approach proved to be efficient and revealed relevant rules.
Outrata introduces an efficient algorithm for updating the concept lattice of a changed formal context (with new objects or attributes introduced or existing ones deleted or altered) from the context only, not requiring the possibly large concept lattice for the computation as the so-called incremental concept lattice algorithms do. The algorithm results as a modification and extension of Kuznetsov’s CbO algorithm for computing the set of all formal concepts, or its recent derivatives like FCbO, PCbO or PFCbO. An experimental performance evaluation included in the paper shows that the update is performed significantly faster than recomputing the whole concept lattice over again and without memory requirements proportional to the size of the lattice.
Glodeanu presents a knowledge discovery method for graded attributes that is based on an interactive determination of if–then rules between the attributes of a given data-set. The method enables not just to find a minimal list of implications between the attributes but also facilitates the process of enumerating the representative examples. The results of some applications of the method on different real-life applications for discrete data are presented as well. As a result, the paper shows that attribute exploration with background information can be conveniently generalized for graded attributes.
Last but not least, we would like to thank the authors for their contributions, the members of the programme and steering committees for keeping the highest scientific level of the conference, the conference participants for their support, the local organizers of the conference for making it a successful event and, in particular, the reviewers of both the conference and this special issue for their hard work of carefully reviewing the papers.