1. Intelligent Database Systems Lab 國立雲林科技大學 National Yunlin University of Science and Technology Graph self-organizing maps for cyclic and unbounded graphs M. Hagenbuchner, A.Sperduti, A.C.Tsoi NeuCom, Vol.72, 2009, pp. 1419–1430. Presenter : Wei-Shen Tai 2009/12/29

2. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 2 Outline Introduction Structured domains: concepts and notation SOMs for structured data Graph-SOM Experiments Conclusions Comments

3. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 3 Motivation SOM- SD or CSOM-SD  The requirement of knowing the maximum out-degree of the input graphs a priori.

4. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 4 Objective Graph SOM  Processing graph structured information for more general types of graphs, e.g. unbounded graphs..

5. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 5 Structured domains: concepts and notation Structured domains (SD)  Where each entity is typically composed of several components related to each other according to specific modalities. Out-ary trees  Are the directed positional acyclic graphs(DPAGs) with super source. Super source  A vertex s, with zero in-degree, such that every vertex in the graph can be reached by a directed path starting from s.

6. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 6 SOMs for structured data SOM-SD  Step 1: One sample input vector u finds its BMU.  Step 2: Update elements of the codebook vector by learning rate and neighborhood function. Vector encoding  Problem: it can only discriminate among trees.

7. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 7 CSOM-SD Contextual SOM-SD  The input representation for v includes also a contribution from the parents of v. Step 1: One sample input vector u finds its BMU. Step 2: Update elements of the codebook vector by learning rate and neighborhood function.

8. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 8 Graph-SOM Activation information of neighbor  the information about the mappings of neighbors is encoded on the display space.

9. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 9 Advantage of Graph SOM Directed graphs  By computing separate activation statistics for pa[v] and ch[v] resulting in vectors h pa[v] and h ch[v]. Simulation  Both CSOM-SD and SOM-SD can be simulated by Graph-SOM.

10. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 10 Experiments Dataset  Consists of 12,107 XML formatted documents which belong to one of 18 clusters. Preprocess  Corresponding to graph structures, 108,523 vertices were revealed and the maximum out-degree is 66 in the training set.

11. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 11 Experiment results Graph-SOM activated a larger number of neurons while the level of activation is more evenly distributed.

12. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 12 Conclusions Graph SOM  Process unbound and cyclic graphs effectively since the input dimension to the network remains unaffected. Each input can be represented by the same vector whatever the out-ary it is.  It is more time efficient in computation when d ≦ 2out.

13. N.Y.U.S.T. I. M. Intelligent Database Systems Lab 13 Comments Advantage  This method can process graph structured information for more general types of graph contrary to SOM-SD and CSOM-SOM. Drawback  If the input graphs have positional and directed edges, then SOM-SD would give better results than Graph-SOM.  Cold start problem exists in the beginning stage. Application  SOM for structured data.