Extensions of Bordat's Algorithm for Attributes

In our works, we use a concept lattice as classifier of noised symbol images. On the contrary of others methods of classification based on Formal Concept Analysis [12], our approach is adapted to the special case of noisy since it is based on a navigation into the lattice structure to classify a noised symbol image : the navigation is performed from the minimal concept, until a final concept is reached, according to the cover-relation between concepts. Class of the input noised symbol is then the class associated to the reached final concept. We use Bordat’s algorithm to generate the concept lattice since it generates the cover relation of the lattice. In this paper, we present three extensions of Bordat’s algorithm : the first extension generates the reduction of the concept lattice to its attributes, i.e. a closure system on attributes ; the second extension generates concepts only when required during the navigation, thus a reduction of the total number of generated concepts ; the third extension generates the concept lattice together with the canonical direct basis, i.e. a basis of implication rules between attributes to describe them.