Semi-supervised learning on closed set lattices

We propose a new approach for semi-supervised learning using closed set lattices, which have been recently used for frequent pattern mining within the framework of the data analysis technique of Formal Concept Analysis (FCA). We present a learning algorithm, called SELF (SEmi-supervised Learning via FCA), which performs as a multiclass classifier and a label ranker for mixed-type data containing both discrete and continuous variables, while only few learning algorithms such as the decision tree-based classifier can directly handle mixed-type data. From both labeled and unlabeled data, SELF constructs a closed set lattice, which is a partially ordered set of data clusters with respect to subset inclusion, via FCA together with discretizing continuous variables, followed by learning classification rules through finding maximal clusters on the lattice. Moreover, it can weight each classification rule using the lattice, which gives a partial order of preference over class labels. We illustrate experimentally the competitive performance of SELF in classification and ranking compared to other learning algorithms using UCI datasets

Convergence and quantale-enriched categories

Generalising Nachbin's theory of "topology and order", in this paper we continue the study of quantale-enriched categories equipped with a compact Hausdorff topology. We compare these $\mathcal{V}$-categorical compact Hausdorff spaces with ultrafilter-quantale-enriched categories, and show that the presence of a compact Hausdorff topology guarantees Cauchy completeness and (suitably defined) codirected completeness of the underlying quantale enriched category

Clones in Graphs

Finding structural similarities in graph data, like social networks, is a far-ranging task in data mining and knowledge discovery. A (conceptually) simple reduction would be to compute the automorphism group of a graph. However, this approach is ineffective in data mining since real world data does not exhibit enough structural regularity. Here we step in with a novel approach based on mappings that preserve the maximal cliques. For this we exploit the well known correspondence between bipartite graphs and the data structure formal context $(G,M,I)$ from Formal Concept Analysis. From there we utilize the notion of clone items. The investigation of these is still an open problem to which we add new insights with this work. Furthermore, we produce a substantial experimental investigation of real world data. We conclude with demonstrating the generalization of clone items to permutations.Comment: 11 pages, 2 figures, 1 tabl

Metric and latticial medians

This paper presents the -linked- notions of metric and latticial medians and it explains what is the median procedure for the consensus problems, in particular in the case of the aggregation of linear orders. First we consider the medians of a v-tuple of arbitrary or particular binary relations.. Then we study in depth the difficult (in fact NP-difficult) problem of finding the median orders of a profile of linear orders. More generally, we consider the medians of v-tuples of elements of a semilattice and we describe the median semilattices, i.e. the semilattices were medians are easily computable.Ce texte présente les notions -reliées- de médianes métriques et latticielles et explique le rôle de la procédure médiane dans les problèmes de consensus, notamment dans le cas de l'agrégation d'ordres totaux.. Après avoir étudié les médianes d'un v-uple de relations binaires arbitraires ou particulières, on étudie en détail le problème -difficile (NP-difficile)- d'obtention des ordres médians d'un profil d'ordres totaux. Plus généralement on considère les médianes de v-uples d'éléments d'un demi-treillis (ou d'un treillis) et l'on décrit les demi-treillis à médianes,i.e. ceux où l'obtention des médianes est aisée

A Core Reference Hierarchical Primitive Ontology for Electronic Medical Records Semantics Interoperability

Currently, electronic medical records (EMR) cannot be exchanged among hospitals, clinics, laboratories, pharmacies, and insurance providers or made available to patients outside of local networks. Hospital, laboratory, pharmacy, and insurance provider legacy databases can share medical data within a respective network and limited data with patients. The lack of interoperability has its roots in the historical development of electronic medical records. Two issues contribute to interoperability failure. The first is that legacy medical record databases and expert systems were designed with semantics that support only internal information exchange. The second is ontological commitment to the semantics of a particular knowledge representation language formalism. This research seeks to address these interoperability failures through demonstration of the capability of a core reference, hierarchical primitive ontological architecture with concept primitive attributes definitions to integrate and resolve non-interoperable semantics among and extend coverage across existing clinical, drug, and hospital ontologies and terminologies