Characterization of image sets: the Galois Lattice approach

This paper presents a new method for supervised image classification. One or several landmarks are attached to each class, with the intention of characterizing it and discriminating it from the other classes. The different features, deduced from image primitives, and their relationships with the sets of images are structured and organized into a hierarchy thanks to an original method relying on a mathematical formalism called Galois (or Concept) Lattices. Such lattices allow us to select features as landmarks of specific classes. This paper details the feature selection process and illustrates this through a robotic example in a structured environment. The class of any image is the room from which the image is shot by the robot camera. In the discussion, we compare this approach with decision trees and we give some issues for future research

Galois lattice theory for probabilistic visual landmarks

This paper presents an original application of the Galois lattice theory, the visual landmark selection for topological localization of an autonomous mobile robot, equipped with a color camera. First, visual landmarks have to be selected in order to characterize a structural environment. Second, such landmarks have to be detected and updated for localization. These landmarks are combinations of attributes, and the selection process is done through a Galois lattice. This paper exposes the landmark selection process and focuses on probabilistic landmarks, which give the robot thorough information on how to locate itself. As a result, landmarks are no longer binary, but probabilistic. The full process of using such landmarks is described in this paper and validated through a robotics experiment

Visualizing and Interacting with Concept Hierarchies

Concept Hierarchies and Formal Concept Analysis are theoretically well grounded and largely experimented methods. They rely on line diagrams called Galois lattices for visualizing and analysing object-attribute sets. Galois lattices are visually seducing and conceptually rich for experts. However they present important drawbacks due to their concept oriented overall structure: analysing what they show is difficult for non experts, navigation is cumbersome, interaction is poor, and scalability is a deep bottleneck for visual interpretation even for experts. In this paper we introduce semantic probes as a means to overcome many of these problems and extend usability and application possibilities of traditional FCA visualization methods. Semantic probes are visual user centred objects which extract and organize reduced Galois sub-hierarchies. They are simpler, clearer, and they provide a better navigation support through a rich set of interaction possibilities. Since probe driven sub-hierarchies are limited to users focus, scalability is under control and interpretation is facilitated. After some successful experiments, several applications are being developed with the remaining problem of finding a compromise between simplicity and conceptual expressivity

In-Close, a fast algorithm for computing formal concepts

This paper presents an algorithm, called In-Close, that uses incremental closure and matrix searching to quickly compute all formal concepts in a formal context. In-Close is based, conceptually, on a well known algorithm called Close-By-One. The serial version of a recently published algorithm (Krajca, 2008) was shown to be in the order of 100 times faster than several well-known algorithms, and timings of other algorithms in reviews suggest that none of them are faster than Krajca. This paper compares In-Close to Krajca, discussing computational methods, data requirements and memory considerations. From experiments using several public data sets and random data, this paper shows that In-Close is in the order of 20 times faster than Krajca. In-Close is small, straightforward, requires no matrix pre-processing and is simple to implement.</p

Distributed Computation of Generalized One-Sided Concept Lattices on Sparse Data Tables

In this paper we present the study on the usage of distributed version of the algorithm for generalized one-sided concept lattices (GOSCL), which provides a special case for fuzzy version of data analysis approach called formal concept analysis (FCA). The methods of this type create the conceptual model of the input data based on the theory of concept lattices and were successfully applied in several domains. GOSCL is able to create one-sided concept lattices for data tables with different attribute types processed as fuzzy sets. One of the problems with the creation of FCA-based models is their computational complexity. In order to reduce the computation times, we have designed the distributed version of the algorithm for GOSCL. The algorithm is able to work well especially for data where the number of newly generated concepts is reduced, i.e., for sparse input data tables which are often used in domains like text-mining and information retrieval. Therefore, we present the experimental results on sparse data tables in order to show the applicability of the algorithm on the generated data and the selected text-mining datasets