Hanika, T., Kibanov, M., Kropf, J., Laser, S.: Ich denke, es ist wichtig zu verstehen, warum die Netzwerkanalyse jetzt populär und besonders interessant für die Forschung geworden ist. In: Kropf, J. and Laser, S. (eds.) Digitale Bewertungspraktiken. p. 165--188. Springer (2019).
It is well known that any bipartite (social) network can be regarded as a
formal context $(G,M,I)$. Therefore, such networks give raise to formal concept
lattices which can be investigated utilizing the toolset of Formal Concept
Analysis (FCA). In particular, the notion of clones in closure systems on $M$,
i.e., pairwise interchangeable attributes that leave the closure system
unchanged, suggests itself naturally as a candidate to be analyzed in the realm
of FCA based social network analysis. In this study, we investigate the notion
of clones in social networks. After building up some theoretical background for
the clone relation in formal contexts we try to find clones in real word data
sets. To this end, we provide an experimental evaluation on nine mostly well
known social networks and provide some first insights on the impact of clones.
We conclude our work by nourishing the understanding of clones by generalizing
those to permutations of higher order.
Geometric analysis is a very capable theory to understand the influence of
the high dimensionality of the input data in machine learning (ML) and
knowledge discovery (KD). With our approach we can assess how far the
application of a specific KD/ML-algorithm to a concrete data set is prone to
the curse of dimensionality. To this end we extend V.~Pestov's axiomatic
approach to the instrinsic dimension of data sets, based on the seminal work by
M.~Gromov on concentration phenomena, and provide an adaptable and
computationally feasible model for studying observable geometric invariants
associated to features that are natural to both the data and the learning
procedure. In detail, we investigate data represented by formal contexts and
give first theoretical as well as experimental insights into the intrinsic
dimension of a concept lattice. Because of the correspondence between formal
concepts and maximal cliques in graphs, applications to social network analysis
are at hand.
Hanika, T., Zumbrägel, J.: Towards Collaborative Conceptual Exploration. In: Chapman, P., Endres, D., and Pernelle, N. (eds.) ICCS. pp. 120-134. Springer (2018).
The curse of dimensionality in the realm of association rules is twofold.
Firstly, we have the well known exponential increase in computational
complexity with increasing item set size. Secondly, there is a related
curse concerned with the distribution of (spare) data itself in high
dimension. The former problem is often coped with by projection, i.e., feature
selection, whereas the best known strategy for the latter is avoidance. This
work summarizes the first attempt to provide a computationally feasible method
for measuring the extent of dimension curse present in a data set with respect
to a particular class machine of learning procedures. This recent development
enables the application of various other methods from geometric analysis to be
investigated and applied in machine learning procedures in the presence of high
Borchmann, D., Hanika, T., Obiedkov, S.: Probably approximately correct learning of Horn envelopes from queries.CoRR.abs/1807.06149, (2018).
We propose an algorithm for learning the Horn envelope of an arbitrary domain using an expert, or an oracle, capable of answering certain types of queries about this domain. Attribute exploration from formal concept analysis is a procedure that solves this problem, but the number of queries it may ask is exponential in the size of the resulting Horn formula in the worst case. We recall a well-known polynomial-time algorithm for learning Horn formulas with membership and equivalence queries and modify it to obtain a polynomial-time probably approximately correct algorithm for learning the Horn envelope of an arbitrary domain.
Felde, M., Hanika, T.: Formal Context Generation using Dirichlet Distributions.CoRR.abs/1809.11160, (2018).
For localization and mapping of indoor environments through WiFi signals,
locations are often represented as likelihoods of the received signal strength
indicator. In this work we compare various measures of distance between such
likelihoods in combination with different methods for estimation and
representation. In particular, we show that among the considered distance
measures the Earth Mover's Distance seems the most beneficial for the
localization task. Combined with kernel density estimation we were able to
retain the topological structure of rooms in a real-world office scenario.
Borchmann, D., Hanika, T., Obiedkov, S.: On the Usability of Probably Approximately Correct Implication Bases. In: Bertet, K., Borchmann, D., Cellier, P., and Ferré, S. (eds.) ICFCA. pp. 72-88. Springer (2017).
Borchmann, D., Hanika, T.: Individuality in Social Networks. In: Missaoui, R., Kuznetsov, S.O., and Obiedkov, S. (eds.) Formal Concept Analysis of Social Networks. p. 19--40. Springer International Publishing, Cham (2017).
We consider individuality in bi-modal social networks, a facet that has not been considered before in the mathematical analysis of social networks. We use methods from formal concept analysis to develop a natural definition for individuality, and provide experimental evidence that this yields a meaningful approach for additional insights into the nature of social networks.
Borchmann, D., Hanika, T.: Some Experimental Results on Randomly Generating Formal Contexts. In: Huchard, M. and Kuznetsov, S. (eds.) CLA. pp. 57-69. CEUR-WS.org (2016).