Alain Sigayret

A local approach to concept generation

Generating concepts defined by a binary relation between a set

Performances of galois sub-hierarchy-building algorithms

\mathcal{P}

Efficiently computing a linear extension of the sub-hierarchy of a concept lattice

of properties and a set

Maximal sub-triangulation in pre-processing phylogenetic data

\mathcal{O}

Hermes: a simple and efficient algorithm for building the AOC-poset of a binary relation

of objects is one of the important current problems encountered in Data Mining and Knowledge Discovery in Databases. We present a new algorithmic process which computes all the concepts, without requiring an exponential-size data structure, and with a good worst-time complexity analysis, which makes it competitive with the best existing algorithms for this problem. Our algorithm can be used to compute the edges of the lattice as well at no extra cost.

Very fast instances for concept generation

The Galois Sub-hierarchy (GSH) is a polynomial-size representation of a concept lattice which has been applied to several fields, such as software engineering and linguistics. In this paper, we analyze the performances, in terms of computation time, of three GSH-building algorithms with very different algorithmic strategies: Ares, Ceres and Pluton. We use Java and C++ as implementation languages and Galicia as our development platform. Our results show that implementations in C++ are significantly faster, and that in most cases Pluton is the best algorithm.

Faster dynamic algorithms for chordal graphs, and an application to phylogeny

Galois sub-hierarchies have been introduced as an interesting polynomial-size sub-order of a concept lattice, with useful applications. We present an algorithm which, given a context, efficiently computes an ordered partition which corresponds to a linear extension of this sub-hierarchy.

Clustering gene expression data using graph separators.

In order to help infer an evolutionary tree (phylogeny) from experimental data, we propose a new method for pre-processing the corresponding dissimilarity matrix, which is related to the property that the distance matrix of a phylogeny (called an additive matrix) describes a sandwich family of chordal graphs. As experimental data often yield distance values which are known to be under-estimated, we address the issue of correcting the data by increasing the distances which are incorrect. This is done by computing, for each graph of the sandwich family, a maximal chordal subgraph.

Representing a Concept Lattice By a Graph

Given a relation 𝓡 ⊆ 𝓞 × 𝓐 on a set 𝓞 of objects and a set 𝓐 of attributes, the AOC-poset (Attribute/Object Concept poset), is the partial order defined on the “introducers” of objects and attributes in the corresponding concept lattice. In this paper, we present Hermes, a simple and efficient algorithm for building an AOC-poset which runs in O(min{nm, nα}), where n is the number of objects plus the number of attributes, m is the size of the relation, and nα is the time required to perform matrix multiplication (currently α = 2.376). Finally, we compare the runtime of Hermes with the runtime of other algorithms computing the AOC-poset: Ares, Ceres and Pluton. We characterize the cases where each algorithm is the more relevant.

Hermes: an efficient algorithm for building Galois sub-hierarchies

Computing the maximal bicliques of a bipartite graph is equivalent to generating the concepts of the binary relation defined by the matrix of this graph. We study this problem for special classes of input relations for which concepts can be generated much more efficiently than in the general case; in some special cases, we can even say that the number of concepts is polynomially bounded, and all concepts can be generated particularly quickly.