Formal Methods For Mining Structured Objects

In the field of knowledge discovery, graphs of concepts are an expressive and versatile modeling technique providing ways to reason about information implicit in a set of data. Interesting examples of this can be found under the mathematical theory of formal concept analysis, dedicated to the construction of a lattice of concepts by defining a Galois connection on a binary relationship. This book present such graph of concepts under the more complex case of data that comes in a set of structured objects; e.g. a set of sequences, trees or graphs. Nodes of this graph will represent patterns in the data and edges will correspond to relationships of specificity. From this combinatorial object results are derived such as a full characterization of logical implications and closed partial orders. The results presented in this book are coupled with examples and empirical experiments that illustrate the derived theoretical contributions.