Christophe Демко

selected publications

1. NPC

   NᴇxᴛPʀɪᴏʀɪᴛʏCᴏɴᴄᴇᴘᴛ: A new and generic algorithm computing concepts from complex and heterogeneous data

   Christophe Demko, Karell Bertet, Cyril Faucher, and 2 more authors

   Theoretical Computer Science 2020

   Abs Bib

   In this article, we present a new data type agnostic algorithm calculating a concept lattice from heterogeneous and complex data. Our NᴇxᴛPʀɪᴏʀɪᴛʏCᴏɴᴄᴇᴘᴛ algorithm is first introduced and proved in the binary case as an extension of Bordat’s algorithm with the notion of strategies to select only some predecessors of each concept, avoiding the generation of unreasonably large lattices. The algorithm is then extended to any type of data in a generic way. It is inspired by the pattern structure theory, where data are locally described by predicates independent of their types, allowing the management of heterogeneous data.

   @article{fca:Demko2020,
     title = {NᴇxᴛPʀɪᴏʀɪᴛʏCᴏɴᴄᴇᴘᴛ: A new and generic algorithm computing concepts from complex and heterogeneous data},
     journal = {Theoretical Computer Science},
     volume = {845},
     pages = {1 - 20},
     year = {2020},
     issn = {0304-3975},
     doi = {https://doi.org/10.1016/j.tcs.2020.08.026},
     url = {http://www.sciencedirect.com/science/article/pii/S0304397520304837},
     author = {Demko, Christophe and Bertet, Karell and Faucher, Cyril and Viaud, Jean-François and Kuznetsov, Sergei O.},
     keywords = {Formal Concept Analysis, Lattice, Pattern structures, Strategies, Heterogeneous data}
   }

2. GALACTIC

   GALACTIC: A python3 framework for studying Formal Concept Analysis

   Christophe Demko, Karell Bertet, and  others

   Jan 2019

   Bib HTML

   @misc{fca:Demko2019-2,
     author = {Demko, Christophe and Bertet, Karell and others},
     howpublished = {https://galactic.univ-lr.fr},
     month = jan,
     title = {{GALACTIC}: {A} python3 framework for studying {F}ormal {C}oncept {A}nalysis},
     year = {2019},
   }

3. FC+2M

   The fuzzy c+2-means: solving the ambiguity rejection in clustering

   Michel Ménard, Christophe Demko, and Pierre Loonis

   Pattern Recognition Jan 2000

   Abs Bib

   In this paper we deal with the clustering problem whose goal consists of computing a partition of a family of patterns into disjoint classes. The method that we propose is formulated as a constrained minimization problem, whose solution depends on a fuzzy objective function in which reject options are introduced. Two types of rejection have been included: the ambiguity rejection which concerns patterns lying near the class boundaries and the distance rejection dealing with patterns that are far away from all the classes. To compute these rejections, we propose an extension of the fuzzy c-means (FcM) algorithm of Bezdek, Pattern Recognition with Fuzzy Objective Function Algorithms, Plenum Press, New York, 1981. This algorithm is called the fuzzy c+2-means (Fc+2M). These measures allow to manage uncertainty due both to imprecise and incomplete definition of the classes. The advantages of our method are (1) the degree of membership to the reject classes for a pattern xk are learned in the iterative clustering problem; (2) it is not necessary to compute other characteristics to determine the reject and ambiguity degrees; (3) the partial ambiguity rejections introduce a discounting process between the classical FcM membership functions in order to avoid the memberships to be spread across the classes; (4) the membership functions are more immune to noise and correspond more closely to the notion of compatibility. Preliminary computational experiences on the developed algorithm are encouraging and compared favorably with results from other methods as FcM, FPcM and F(c+1)M (fuzzy c+1-means: clustering with solely distance rejection) algorithms on the same data sets. The differences in the performance can be attributed to the fact that ambiguous patterns are less accounted in for the computing of the centers.

   @article{fuzzy-clustering:Menard1999,
     title = {The fuzzy c+2-means: solving the ambiguity rejection in clustering},
     journal = {Pattern Recognition},
     volume = {33},
     number = {7},
     pages = {1219-1237},
     year = {2000},
     issn = {0031-3203},
     doi = {https://doi.org/10.1016/S0031-3203(99)00110-7},
     url = {https://www.sciencedirect.com/science/article/pii/S0031320399001107},
     author = {Ménard, Michel and Demko, Christophe and Loonis, Pierre},
     keywords = {Fuzzy clustering, Fuzzy c-means, Ambiguity rejection, Distance rejection}
   }