Drawing Area-Proportional Venn and Euler Diagrams

Chow, Stirling; Ruskey, Frank

doi:10.1007/978-3-540-24595-7_44

Cited by 98 publications

(160 citation statements)

References 3 publications

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“…An implementation of the algorithm was also provided which had a limited guarantee of being able to draw any such diagram with up to four contours in any one connected component. In [1] the relaxation of the wellformedness conditions to allow multiple points and concurrent contours was adopted, and although no conversion from theory to practise was provided, it was shown that the Euler diagram generation problem is NP-Complete in this case. Since imposing some wellformedness conditions implies that some abstract descriptions are not realisable as Euler diagrams, in [1] the notion of an Euler diagram was extended so that any abstract description with at most nine sets could be drawn: they used Euler diagrams that had holes, which are a restricted version of allowing duplicate curve labels.…”

Section: A Amentioning

confidence: 99%

“…To guarantee to find a wellconnected planar dual where one exists is an NPComplete problem [1]. Therefore we resort to heuristics to do as good a job as possible.…”

Section: Edge Removal To Achieve Planaritymentioning

confidence: 99%

“…For the purposes of embedding we treat the dual as the dual of an Euler graph [1]. An Euler graph can be formed from an Euler diagram by placing a node at each point where curves meet or cross, and connecting them up with edges that parallel the curve segments.…”

Section: Edge Addition To Remove Tangential Intersectionsmentioning

confidence: 99%

“…As shown in [1], not all Euler diagrams can be embedded in the plane with simple, uniquely labelled curves. The reason is that there are abstract descriptions for which any wellconnected dual graph is non-planar.…”

Section: Duplicate Curve Labelsmentioning

confidence: 99%

“…The motivation for this work comes from the use of Euler diagrams in a wide variety of applications, including the visualization of statistical data [2,13], displaying the results of database queries [1] and representing non-hierarchical computer file systems [3]. They have been used in a visual semantic web editing environment [18] and for viewing clusters which contain concepts from multiple ontologies [11].…”

Section: Introductionmentioning

confidence: 99%

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General Euler Diagram Generation

Rodgers

Zhang

Fish

Lecture Notes in Computer Science

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Abstract. Euler diagrams are a natural method of representing set-theoretic data and have been employed in diverse areas such as visualizing statistical data, as a basis for diagrammatic logics and for displaying the results of database search queries. For effective use of Euler diagrams in practical computer based applications, the generation of a diagram as a set of curves from an abstract description is necessary. Various practical methods for Euler diagram generation have been proposed, but in all of these methods the diagrams that can be produced are only for a restricted subset of all possible abstract descriptions. We describe a method for Euler diagram generation, demonstrated by implemented software, and illustrate the advances in methodology via the production of diagrams which were difficult or impossible to draw using previous approaches. To allow the generation of all abstract descriptions we may be required to have some properties of the final diagram that are not considered nice. In particular we permit more than two curves to pass though a single point, permit some curve segments to be drawn concurrently, and permit duplication of curve labels. However, our method attempts to minimize these bad properties according to a chosen prioritization.

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Section: A Amentioning

confidence: 99%

“…To guarantee to find a wellconnected planar dual where one exists is an NPComplete problem [1]. Therefore we resort to heuristics to do as good a job as possible.…”

Section: Edge Removal To Achieve Planaritymentioning

confidence: 99%

Section: Edge Addition To Remove Tangential Intersectionsmentioning

confidence: 99%

Section: Duplicate Curve Labelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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General Euler Diagram Generation

Rodgers

Zhang

Fish

Lecture Notes in Computer Science

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American College of Rheumatology classification criteria for Sjögren's syndrome: A data‐driven, expert consensus approach in the Sjögren's International Collaborative Clinical Alliance Cohort

Shiboski

Criswell

et al. 2012

Arthritis Care & Research

1,227

875

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Objectives We propose new classification criteria for Sjögren’s Syndrome (SS), which are needed considering the emergence of biological agents as potential treatments and their associated co-morbidity. These criteria target individuals with signs/symptoms suggestive of SS. Methods Criteria are based on expert opinion elicited using the Nominal Group Technique, and analyses of data from the Sjögren’s International Collaborative Clinical Alliance. Preliminary criteria validation included comparisons with classifications based on the American-European-Consensus-Group (AECG) criteria, a model-based “gold standard” obtained from Latent Class Analysis (LCA) of data from a range of diagnostic tests, and a comparison with cases and controls collected from sources external to the population used for criteria development Results Validation results indicate high levels of sensitivity and specificity for the criteria. Case definition requires at least 2 out of the following 3: Positive serum anti-SSA and/or anti-SSB or [positive rheumatoid factor and ANA ≥ 1:320]; Ocular staining score ≥ 3; Presence of focal lymphocytic sialadenitis with focus score ≥ 1 focus/4mm2 in labial salivary gland biopsies. Observed agreement with the AECG criteria is high when these are applied using all objective tests. However, AECG classification based on allowable substitutions of symptoms for objective tests results in poor agreement with the proposed and LCA-derived classifications. Conclusion These classification criteria developed from registry data collected using standardized measures are based on objective tests. Validation indicates improved classification performance relative to existing alternatives, making them more suitable for application in situations where misclassification may present health risks.

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Textural fingerprints: A comprehensive descriptor for biofilm structure development

Milferstedt

Pons

Morgenroth

2008

Biotech & Bioengineering

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Automated tools to determine biofilm structure are necessary to interpret large time series of biofilm images. Image analysis based on the evaluation of Spatial Gray Level Dependence Matrices (SGLDM) enabled us to monitor biofilm structure development in response to external disturbances (i.e., periodic increases of wall shear stress) at a large scale (i.e., >1 mm). We applied our method to an experiment conducted in an annular reactor over a 10-week period. Six states of biofilm development were differentiated by their unique structure. Previous exposure to rapidly increased shear influenced the resulting biofilm structure after additional shear increases. In addition, on the scale of the biofilm images, the biofilm structure after a shear increase was spatially heterogeneous and resulted in spatially differentiated regrowth after detachment at different locations in the biofilm. SGLDM was developed further as an alternative to approaches based on image binarization as binarization leads to information loss for low-magnification and low-resolution images. During post-processing of image data, structural states of biofilm development were identified by K-means clustering and data display in Principal Component plots. Quantitatively selected representative images were used to illustrate the meaning of the clusters. Post-treatment of image data was essential for managing several thousands of raw biofilm images and therefore improved the usefulness of the image analysis.

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Drawing Area-Proportional Venn and Euler Diagrams

Cited by 98 publications

References 3 publications

General Euler Diagram Generation

General Euler Diagram Generation

American College of Rheumatology classification criteria for Sjögren's syndrome: A data‐driven, expert consensus approach in the Sjögren's International Collaborative Clinical Alliance Cohort

Textural fingerprints: A comprehensive descriptor for biofilm structure development

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