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Brief introduction to graph based pattern recognition. It shows advantages and disantavantages of using graphs and how existing pattern recognition techniques are adapted to graph space.

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- 1. page.1 Introduction Graph-based Methods Graph-based Pattern Recognition Nicola Strisciuglio University of Groningen n.strisciuglio@rug.nl 28/10/2013 Conclusions
- 2. page.2 Introduction Graph-based Methods Statistical vs. Graph-based PR Statistical vs. Graph-based Pattern Recognition Statistical PR I = x1 , x2 , . . . , xn Graph-based PR Conclusions
- 3. page.3 Introduction Graph-based Methods Statistical vs. Graph-based PR Statistical vs. Graph-based Pattern Recognition Statistical PR I = y1 , y2 , . . . , yn Graph-based PR Conclusions
- 4. page.4 Introduction Graph-based Methods Conclusions Pure Impure and Extreme Methods Graph-based Methods Pure Methods Learning and classiﬁcation problems are faced directly in the graph space. Impure Methods Transposition of the methods of Statistical Pattern Recognition to graph space. Extreme Methods Transformation of graphs into vectors. Use of the well estabilished learning and classiﬁcation techniques.
- 5. page.5 Introduction Graph-based Methods Pure Impure and Extreme Methods Pure Methods: Graph Matching Exact Matching: ﬁnd an exact correspondence between graphs (or sub-graphs) Inexact Matching: deals with distortions in ﬁndinf a correspondence between graphs It needs a metric to deﬁne dissimilarities Conclusions
- 6. page.6 Introduction Graph-based Methods Conclusions Pure Impure and Extreme Methods Graph edit distance We need a distance metric between graphs: we have Graph edit distance. Cheapest sequence of operations to trasform one graph in another graph.
- 7. page.7 Introduction Graph-based Methods Conclusions Pure Impure and Extreme Methods Impure Methods: k-NN The reference set is made by a collection of graphs, instead of points in a m-dimensional space For a graph to classify, the graph edit distance is computed with respect to each of the graphs in the reference set The decision is taken as majority voting on the K nearest graphs Generally, the time needed for a classiﬁcation is very high
- 8. page.8 Introduction Graph-based Methods Conclusions Pure Impure and Extreme Methods Impure Methods: k-Means For the classical k-Means algorithm a centroid is computed as the average of the vectors around it, while for the graph a median graph should be computed.
- 9. page.9 Introduction Graph-based Methods Conclusions Pure Impure and Extreme Methods Impure Methods: k-Means For the classical k-Means algorithm a centroid is computed as the average of the vectors around it, while for the graph a median graph should be computed. Median Graph ˆ S = arg min Gi ∈S Dg (Gi , Gj ) Gj ∈S
- 10. page.10 Introduction Graph-based Methods Conclusions Pure Impure and Extreme Methods Impure Methods: k-Means For the classical k-Means algorithm a centroid is computed as the average of the vectors around it, while for the graph a median graph should be computed. Median Graph ˆ S = arg min Gi ∈S Dg (Gi , Gj ) Gj ∈S Generalized Median Graph Dg (Gi , Gj ) S = arg min Gi ∈U Gj ∈S
- 11. page.11 Introduction Graph-based Methods Conclusions Pure Impure and Extreme Methods Impure Methods: LVQ Given a pattern x, the winner prototype Pk moves towards x by ∆ = α(x − Pk ) if the class of x is the same of Pk (by ∆ = −α(x − Pk ) otherwise) Updating a prototype requires its transformation in another graph more similar to the input pattern x by a fraction α of the distance
- 12. page.12 Introduction Graph-based Methods Conclusions Pure Impure and Extreme Methods Impure Methods: LVQ Given a pattern x, the winner prototype Pk moves towards x by ∆ = α(x − Pk ) if the class of x is the same of Pk (by ∆ = −α(x − Pk ) otherwise) Updating a prototype requires its transformation in another graph more similar to the input pattern x by a fraction α of the distance We need to compute a fraction of edit distance!!! Pk → Gx needs D = 7 operations on graph
- 13. page.13 Introduction Graph-based Methods Conclusions Pure Impure and Extreme Methods Impure Methods: LVQ Given a pattern x, the winner prototype Pk moves towards x by ∆ = α(x − Pk ) if the class of x is the same of Pk (by ∆ = −α(x − Pk ) otherwise) Updating a prototype requires its transformation in another graph more similar to the input pattern x by a fraction α of the distance We need to compute a fraction of edit distance!!! Pk → Gx needs D = 7 operations on graph If α = 0.3, we do D ∗ α = 2 operations to move Pk to an intermediate graph
- 14. page.14 Introduction Graph-based Methods Conclusions Pure Impure and Extreme Methods Extreme methods: Graph Embedding Represent a graph as a point in a suitable feature space Use of the classical statistical pattern recognition tools The similarity of graph in graph space should be preserved in the vector space The translation of a graph (including all the attributes and relations) into a ﬁxed-lenght vector is diﬃcult
- 15. page.15 Introduction Graph-based Methods Conclusions Some Applications Structural description and matching of molecules Segmentation of shapes (e.g. letters) Stereo vision (e.g. for robot navigation) Learning and recognising objects in scenes Data mining Conclusions
- 16. page.16 Introduction Graph-based Methods Conclusions Some Applications Structural description and matching of molecules Segmentation of shapes (e.g. letters) Stereo vision (e.g. for robot navigation) Learning and recognising objects in scenes Data mining Conclusions
- 17. page.17 Introduction Graph-based Methods Conclusions Conclusions Statistical vs. Graph-based Pattern Recognition Statistical PR Advantages Graph-based PR Advantages Theoretically estabilished Variable representation size Many powerful algorithms More description power (relationships) Disadvantages Size of the feature vector ﬁxed Unary features: no relations Disadvantages Lack of algorithms Less mathematical foundations
- 18. page.18 Introduction Graph-based Methods Conclusions References Mario Vento (2013) A long trip in the charming world of graphs for Pattern Recognition Pattern Recognition Conclusions
- 19. page.19 Introduction Graph-based Methods Conclusions Thank you!!! Conclusions

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