Features

Context manipulation

Galicia provides advanced features for data manipulation which allow various types of contexts to be processed. Thus, besides the classical binary tables, multi-valued contexts are admitted. More advanced data types such as the relational context families (RCF) can be handled by Galicia as well (see Figure 1 on the left).

The contexts can be either loaded from an external storage device or composed with an interactive context editor. The editor which covers all the above context types (see Figure1, on the right) allows even loaded contexts to be modified if necessary. Modifications include any change in the number of objects/attributes/relation elements (i.e., object - attribute pairs), as well as changes in the identifiers of objects and attributes. For RCF, the editor offers the possibility of manipulating not only the involved contexts, but also the binary relations linking the object sets of the member contexts.

Data formats

Several external formats are available in Galicia. So far, implemented formats include the IBM formats for transaction databases, popular among the data mining community, proprietary formats used to store contexts (SCF) and lattices (SLF) in a human-readable form, and two XML DTDs describing classical contexts and partial orders (lattices, icebergs, GSH, etc.), respectively.

Partial order manipulations

In the sequel, we describe briefly our recent achievements in the field of constructing lattices and other related posets and their current availability within the platform.

Lattice manipulations

The lattice construction functions of the platform cover most of the classical algorithms for lattice construction [10] as well as a large set of recent lattice-related techniques which have been designed by members of our team.

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Lattice construction

Galicia provides the access to a whole family of incremental algorithms. One the one hand, the initial algorithm of Godin et al. is included together with some later versions designed to reduce complexity. On the other hand, the platform features more recent methods based on deeper insight in the lattice substructures related to incrementation. The earliest method has been presented in [15] while more recent work and algorithmic designs may be found in [16].

Lattice assembly/slicing

Moreover, the platform supports direct operations on lattices such as assembly, or merge, and split, or decomposition, of lattices. In fact, in a general study on lattice manipulations within FCA, the construction has been revisited as a bare transition from a unique context, either known beforehand or gradually acquired, to a complete structure.

For example, the assembly of lattices has been proposed as a generalization of the incremental lattice construction, since it considers a set of new elements as added to a context at once [15]. The underlying methods put together two lattices corresponding to contexts which share either their object or their attribute set, and thus compute the lattice of the global context in a direct manner, i.e., with no preliminary compilation of the data.

The assembly methods provide the basis for a divide-and-conquer method for lattice construction which proceeds by first divide a contexts into fragments until single lines/columns are reached, and then assemble the corresponding lattices until the global one is obtained.

Both techniques, i.e., assembly and divide-and-conquer, have been included in the platform design and their implementation is in progress. In addition, the reverse operation of lattice split into smaller lattices upon a partition of either the attribute set or the object one, is also a part of Galicia.

Lattice maintenance at large

The work on lattice assembly/slicing has led to the a logical question about all the possible evolutions of a lattice during an analysis process which are triggered by changes in the data. Being able to provide efficient support for such evolutions is of high importance for FCA tools intended for exploratory tasks. As an approach to the problem, we specified of a set of operation which allow an arbitrary modification in data to be propagated to the lattice with minimal effort. Implementations of these operations support the interactive lattice construction mode of Galicia in which the user gradually refines his/her view on which parts of the data are worth analyzing.

Multi-constructions of lattices

Yet different problems arise with a relational context family, where several lattice constructions must be carried out simultaneously. This is realized by including relations into concept descriptions (intentional dimension of concept definition) and thus linking concepts in a way similar to UML associations between classes. To solve the underlying algorithmic problem of several lattice constructions, we devised a generic method which deals with a family of mutually related contexts in a coherent way, called Multi-FCA (see [11] for details). The implementation of Multi-FCA within Galicia is still in progress, although the related function of constructing several related GSH is already available.