Coproduct Transformations on Lattices of Closed Partial Orders
Gemma Casas-Garriga and José Balcázar
In: 2nd. International Conference on Graph Transformations, Rome, Italy(2004).
In the field of Knowledge Discovery, graphs of concepts are an expressive and versatile
modeling technique that provides ways to reason about information implicit
in the data. Typically, nodes of these graphs represent unstructured closed patterns, such as
sets of items, and edges represent the relationships of specificity among them.
In this paper we want to consider the case where data keeps an order, and nodes of the concept
graph represent complex structured patterns. We contribute by first characterizing a lattice
of closed partial orders that precisely summarizes the original ordered data; and second,
we show that this lattice can be obtained via coproduct transformations on a simpler graph of
so-called stable sequences. In the practice, this graph transformation implies that
algorithms for mining plain sequences can efficiently transform the discovered patterns
into a lattice of closed partial orders, and so, avoiding the complexity of the mining
operation for the partial orders directly from the data.