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- 1. Dipartimento di Ingegneria e Scienze Università degli Studi dell’Aquila dell’Informazione e Matematica Mining Metrics for Understanding Metamodel Characteristics Alfonso Pierantonio Juri Di Rocco Davide Di Ruscio Ludovico Iovino
- 2. Alfonso Pierantonio 2 Outline Introduction Motivation Measuring metamodels Calculation of metrics correlation Selection of metrics correlation Data Analisys Conclusions Future works
- 3. Alfonso Pierantonio 3 Introduction Metamodels are a key concept in Model-Driven Engineering: they represent the «trait-d'union» among all constituent components Metamodels formally define the modeling primitives used in modeling activities
- 4. Alfonso Pierantonio 4 Motivation It is of crucial relevance to investigate common characteristics of metamodels, in order to have a better understanding on – how they evolve over time – what is the impact of metamodel changes throughout the modeling ecosystem Metamodel
- 5. Alfonso Pierantonio 5 Motivation It is of crucial relevance to investigate common characteristics of metamodels, in order to have a better understanding on – how they evolve over time – what is the impact of metamodel changes throughout the modeling ecosystem Analyse metamodels in order to evalutate their structural characteristics and the impact they might have during the whole metamodel life-cycle especially in case of metamodel evolutions
- 6. Analysing metamodel characteristics by investigating the correlations of different metrics applied on a corpus of more than 450 metamodels
- 7. Alfonso Pierantonio 7 Measuring Metamodels The applied process is able to identify linked structural characteristics Understand how they might change depending on the nature of metamodels
- 8. Alfonso Pierantonio 8 Metrics calculation Consists of the application of metrics on a data set of metamodels The applied metrics are borrowed from [1] and we added new ones by leading to a set of 28 metrics An excerpt of the considered metrics have been considered in rest of the presentation [1] W. James, Z. Athansios, M. Nicholas, R. Louis, K. Dimitios, P. Richard, and P. Fiona. What do metamodels really look like? Frontiers of Computer Science, 2013.
- 9. Alfonso Pierantonio 9 Metrics calculation The corpus of the analyzed metamodels has been obtained by retrieving metamodels from different repositories, i.e., EMFText Zoo, ATLZoo, Github, GoogleCode For a total number of 466 metamodels belonging to different technical spaces and domains
- 10. Alfonso Pierantonio 10 Metrics Calculation The metrics calculation has been implemented by exploiting a model-driven toolchain
- 11. Alfonso Pierantonio 11 Metrics Calculation The metrics calculation has been implemented by exploiting a model-driven toolchainThe Metamodel Metrics Calculator is able to calculate for each metamodel all the considered metrics
- 12. Alfonso Pierantonio 12 Metrics Calculation The metrics calculation has been implemented by exploiting a model-driven toolchain The Metamodel Metrics Calculator is an ATL transformation whose target models conform to the Metrics metamodel
- 13. Alfonso Pierantonio 13 Metrics Calculation The metrics calculation has been implemented by exploiting a model-driven toolchain Generating CVS files enables the adoption of statistical tools like IBM SPSS, Microsoft Excel, and Libreoffice Calc for subsequent analysis of the generated data
- 14. Alfonso Pierantonio 14 Calculation of metrics correlations Correlation is used to detect cross-links and assess relationships among observed data We have considered Pearson’s and Spearman’s coefficients to measure the correlations among calculated metamodel metrics Spearman only for highlighting curvilinear correlations Both Pearson’s and Spearman’s correlation indexes assume values in the range of -1.00 (perfect negative correlation) and +1.00 (perfect positive correlation) A correlation with value 0 indicates that between two variables there is no correlation
- 15. Alfonso Pierantonio 15 Selection of metrics correlations We have calculated the Pearson’s and Spearman’s correlation indexes for all the values of the considered metrics For each couple we have selected the coefficient index (between Pearson and Spearman) having higher correlation values
- 16. Alfonso Pierantonio 16 Selection of metrics correlations The bar chart shows the degree of metric correlation: the higher the bar, the more the metric is correlated with other metrics.
- 17. Alfonso Pierantonio 17 Pearson’s correlation matrix All the values greater than 0.7 or lesser than -0.73 have been highlighted to select the metrics that are most related according to the Pearson’s index.
- 18. Alfonso Pierantonio 18 Pearson’s correlation matrix All the values greater than 0.7 or lesser than -0.73 have been highlighted to select the metrics that are most related according to the Pearson’s index.
- 19. Alfonso Pierantonio 19 Data analysis The aim is to discuss and interpret the most relevant correlations between structural characteristics which have been found in the previous stages
- 20. Alfonso Pierantonio 20 Data analysis: abstraction How the number of metaclasses is related to the adoption of abstraction constructs, ie. abstract metaclasses and supertypes
- 21. Alfonso Pierantonio 21 Data analysis: abstraction How the number of metaclasses is related to the adoption of abstraction constructs, ie. abstract metaclasses and supertypes
- 22. Alfonso Pierantonio 22 Data analysis: abstraction How the number of metaclasses is related to the adoption of abstraction constructs, ie. abstract metaclasses and supertypes MGHL Maximum hierarchical depth
- 23. Alfonso Pierantonio 23 Data analysis: abstraction How the number of metaclasses is related to the adoption of abstraction constructs, ie. abstract metaclasses and supertypes MHS Maximum Hierarchy Siblings
- 24. Alfonso Pierantonio 24 Data analysis: abstraction How the number of metaclasses is related to the adoption of abstraction constructs, ie. abstract metaclasses and supertypes MTCWS Number of metaclasses having at least one super type
- 25. Alfonso Pierantonio 25 Metrics
- 26. Alfonso Pierantonio 26 Data analysis: abstraction The #metaclasses and the #classes with supertypes are strongly correlated (with Pearson index 0.99) When the metamodel grows in size, the number of inheritance hierarchies also increases, however the hierarchy depth is somehow independent from the metamodel size. Interestingly, metamodel designers prefer to add siblings in hierarchies instead of adding new hierarchy levels
- 27. Alfonso Pierantonio 27 Data analysis: abstraction This is testified by the graph that shows the values of the MHS (Max Hierarchy Sibling) and MGHL (Max generalization hierarchical level) metrics Confirmed by the Pearson correlation indexes between MC and MHS (0.70) and that between MC and MGHL (0.66).
- 28. Alfonso Pierantonio 28 Data analysis: abstraction In metamodels with at most 50 metaclasses: – the number of supertypes in hierarchy is in between 0 and 20 – the number of siblings in a hierarchy is in between 0 and 10 – the maximum height of a hierarchy is in between 0 and 5
- 29. Alfonso Pierantonio 29 Data analysis: structural features How structural features are used with hierarchies We can consider the average number of features (ASF) and the total number of metaclasses with supertypes (MCWS) metrics The Spearman approach permits to identify a greater correlation index
- 30. Alfonso Pierantonio 30 Data analysis: structural features Increasing the #metaclasses with supertypes, the average # of structural features in a metaclass decreases
- 31. Alfonso Pierantonio 31 Data analysis: structural features By considering metamodels having in between 1 and 50 metaclasses, the average number of features (excluding the inherited ones) of a metaclass ranges between 1 and 5
- 32. Alfonso Pierantonio 32 Data analysis: structural features How the number of featureless metaclasses is related to hierarchies height This can indicate how specializations of metaclasses can introduce or reduce structural features in metamodels MCWS and IFLMC are strongly correlated as supported by the Pearson’s index having value 0.890
- 33. Alfonso Pierantonio 33 Data analysis: structural features How the number of featureless metaclasses is related to hierarchies height
- 34. Alfonso Pierantonio 34 Data analysis: structural features By increasing the number of metaclasses with super types, the number of metaclasses without attributes or references increases too This means that when hierarchies are introduced, usually existing features are subject to refactoring operations mainly to move them to super classes and to create leaves in the hierarchies inheriting features from the super types.
- 35. Alfonso Pierantonio 35 Data analysis: isolated metaclasses How isolated metaclasses are distributed In this case we considered another statistical instrument named Pareto analysis, which is commonly referred to as the 80-20 principle (20% of the causes account for 80% of the defects) About 80% of the analyzed metamodels have a percentage of isolated metaclasses in the range 0- 19%, by testifying the fact that isolated metaclasses are not commonly used
- 36. Alfonso Pierantonio 36 Data analysis: isolated metaclasses We can claim that they are used only for testing or educational purposes
- 37. Alfonso Pierantonio 37 Conclusions We proposed a number of metrics which can be used to acquire objective, transparent, and reproducible measurements of metamodels. The major goal is to better understand the main characteristic of metamodels, how they are coupled, and how they change depending on the metamodel structure A correlation analysis has been performed to identify the most cross-linked metrics, which have, in turn, been computed over 450 metamodels
- 38. Alfonso Pierantonio 38 Conclusions These figures have been discussed in detail highlighting the followings - the adoption of inheritance is proportional to the size of metamodels - the number of metaclasses with supertypes are inversely proportional to the average number of structural features - the number of metaclasses with supertypes is proportional to the number of metaclasses without attributes or references - isolated metaclasses are not commonly used apart from testing or educational purposes.
- 39. Alfonso Pierantonio 39 Conclusions These figures have been discussed in detail highlighting the following
- 40. Thank you

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