| 1. |
- Izquierdo, Milagros, 1963-, et al.
(författare)
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Isometric Point-Circle Configurations on Surfaces from Uniform Maps
- 2016
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Ingår i: Springer Proceedings in Mathematics and Statistics. - Cham : Springer-Verlag New York. - 2194-1009. ; 159, s. 201-212, s. 201-212
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Tidskriftsartikel (refereegranskat)abstract
- We embed neighborhood geometries of graphs on surfaces as point-circle configurations. We give examples coming from regular maps on surfaces with a maximum number of automorphisms for their genus, and survey geometric realization of pentagonal geometries coming from Moore graphs. An infinite family of point-circle v4'>v4v4 configurations on p-gonal surfaces with two p-gonal morphisms is given. The image of these configurations on the sphere under the two p-gonal morphisms is also described.
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| 2. |
- Conder, Marston, et al.
(författare)
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New methods for finding minimum genus embeddings of graphs on orientable and non-orientable surfaces
- 2019
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Ingår i: Ars Mathematica Contemporanea. - : Drustvo Matematikov, Fizikov in Astronomov,Society of Mathematicians, Physicists and Astronomers. - 1855-3966 .- 1855-3974. ; 17:1, s. 1-35
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Tidskriftsartikel (refereegranskat)abstract
- The question of how to find the smallest genus of all embeddings of a given finite connected graph on an orientable (or non-orientable) surface has a long and interesting history. In this paper we introduce four new approaches to help answer this question, in both the orientable and non-orientable cases. One approach involves taking orbits of subgroups of the automorphism group on cycles of particular lengths in the graph as candidates for subsets of the faces of an embedding. Another uses properties of an auxiliary graph defined in terms of compatibility of these cycles. We also present two methods that make use of integer linear programming, to help determine bounds for the minimum genus, and to find minimum genus embeddings. This work was motivated by the problem of finding the minimum genus of the Hoffman-Singleton graph, and succeeded not only in solving that problem but also in answering several other open questions.
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| 3. |
- Boström, Henrik
(författare)
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Maximizing the Area under the ROC Curve with Decision Lists and Rule Sets
- 2007
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Ingår i: Proceedings of the 7th SIAM International Conference on Data Mining. - : Society for Industrial and Applied Mathematics. - 9780898716306 ; , s. 27-34
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Konferensbidrag (refereegranskat)abstract
- Decision lists (or ordered rule sets) have two attractive properties compared to unordered rule sets: they require a simpler classi¯cation procedure and they allow for a more compact representation. However, it is an open question what effect these properties have on the area under the ROC curve (AUC). Two ways of forming decision lists are considered in this study: by generating a sequence of rules, with a default rule for one of the classes, and by imposing an order upon rules that have been generated for all classes. An empirical investigation shows that the latter method gives a significantly higher AUC than the former, demonstrating that the compactness obtained by using one of the classes as a default is indeed associated with a cost. Furthermore, by using all applicable rules rather than the first in an ordered set, an even further significant improvement in AUC is obtained, demonstrating that the simple classification procedure is also associated with a cost. The observed gains in AUC for unordered rule sets compared to decision lists can be explained by that learning rules for all classes as well as combining multiple rules allow for examples to be ranked according to a more fine-grained scale compared to when applying rules in a fixed order and providing a default rule for one of the classes.
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| 4. |
- Stokes, Klara, et al.
(författare)
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On some clustering approaches for graphs
- 2011
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Ingår i: Fuzzy Systems (FUZZ), 2011. - : IEEE. - 9781424473151 - 9781424473168 - 9781424473175 ; , s. 409-415
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Konferensbidrag (refereegranskat)abstract
- In this paper we discuss some tools for graph perturbation with applications to data privacy. We present and analyse two different approaches. One is based on matrix decomposition and the other on graph partitioning. We discuss these methods and show that they belong to two traditions in data protection: noise addition/microaggregation and k-anonymity.
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| 5. |
- Stokes, Klara, et al.
(författare)
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On the Relationship Between Clustering and Coding Theory
- 2012
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Ingår i: 2012 IEEE International Conference on Fuzzy Systems. - : IEEE. - 9781467315074 - 9781467315050 - 9781467315067 ; , s. Article number 6250783-
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Konferensbidrag (refereegranskat)abstract
- In this paper we discuss the relations between clustering and error correcting codes. We show that clustering can be used for constructing error correcting codes. We review the previous works found in the literature about this issue, and propose a modification of a previous work that can be used for code construction from a set of proposed codewords.
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| 6. |
- Stokes, Klara, et al.
(författare)
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Reidentification and k-anonymity : a model for disclosure risk in graphs
- 2012
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Ingår i: Soft Computing - A Fusion of Foundations, Methodologies and Applications. - : Springer. - 1432-7643 .- 1433-7479. ; 16:10, s. 1657-1670
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Tidskriftsartikel (refereegranskat)abstract
- In this article we provide a formal framework for reidentification in general. We define n-confusion as a concept for modeling the anonymity of a database table and we prove that n-confusion is a generalization of k-anonymity. After a short survey on the different available definitions of k-anonymity for graphs we provide a new definition for k-anonymous graph, which we consider to be the correct definition. We provide a description of the k-anonymous graphs, both for the regular and the non-regular case. We also introduce the more flexible concept of (k, l)-anonymous graph. Our definition of (k, l)-anonymous graph is meant to replace a previous definition of (k, l)-anonymous graph, which we here prove to have severe weaknesses. Finally, we provide a set of algorithms for k-anonymization of graphs.
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