1. Chapter 7 Complex Similarity Topix

2. About this chapter Extends previous discussed methods The reader can choose to read about only specific methods, depending on their application interest

3. Graph representation and graph similarities Some first similarities on graphs compare graphs and distinguish between different graph matching approaches: Graph isomorphism. Subgraph isomorphism. Largest common subgraphs, so-called cliques. -Exact matching vs inexact matching -Inexact requires graph edit distance for approximating graphs

4. Graph isomorphism: A radical way is to consider two graphs as similar if they are isomorphic. This is a binary predicate – which is a disadvantage Objects has to be identical to be similar Complex testing Subgraph isomorphism The same just with subgraphs Largest common subgraphs Looks at subgraphs that two graphs have in common The size|G| of a graph G is the cardinality of the nodes plus the cardinality of the edges.

5. -Editing operations -Inserting nodes, deleting nodes, inserting edges, deleting edges, replacements, changing marks on nodes and edges -The intuition is that graphs are more similar the easier or cheaper the transformations are. -This is useful if the operations have costs. -The costs can differ, not symmetric edit distance

6. Taxonomic Similarities Taxonomies relate objects to each other Hierarchical structure, going from general to more specific objects Branching leads to objects that have more in common Can be used as similarity measures as graphs For taxonomic structures like trees one can define structural similarities for representing knowledge about the structure. The structure-based similarity relates objects independent of their contents, based on the position in the taxonomy only Deepest common predecessor

7. Similarities for Object-Oriented Representation The problem of computing the similarity of complex objects has two aspects. One is based on the attributes defining the object and one is based on the classes in which those objects are located. intra-class similarity SIMintra, inter-class similarity SIMinter.

8. Intra-class similarity we take the most specific common class of the two objects and compute the similarity based on the attributes of this class only. the objects being compared are from the same class local similarities or object similarities are computed for all attributes and the resulting values are aggregated to compute the intra-class similarity Inter-class similarity The inter-class similarity represents the highest possible similarity of two objects, independent of their attribute-value, but dependent on the positions of their object classes in the hierarchy. We can therefore view the inter-class similarity as a measure of how many values the compared objects have in common. The final object similarity sim(q, c) between a query object q and a case object c can then be computed by the product of the inter- and intra-class similarity.

9. Similarity for Processes and Workflows Processes and workflows can be described as annotated graphs. They carry, however, in general, a very rich structure. The annotations can make use of any of the structures and therefore there is no unique similarity measure. Processes have workflows as instances. Useful representation structures are: Context representation Task context Task descriptions Attributes describing the control flow relationships between the tasks A set of parameters required for the execution User context The representation varies from different situations. The problem is how to organise this.