Fast algorithm and implementation of dissimilarity self-organizing maps

1. Fast algorithm and implementation of dissimilarity self-organizing maps Reporter: Ming-Jui Kuo D9515007

2. Outline • Introduction • The DSOM • Simulation Results

3. Introduction

4. A drawback in standard SOM • Since vectors from a fixed and finite-dimensional vector space. Unfortunately, many real-world data depart strongly from this model. It is quite common, for instance, to have variable-sized data. • They are natural, for example, in online handwriting recognition where the representation of a character drawn by the user can vary in length because of the drawing conditions. Other data, such as texts for instance, are strongly non-numerical and have a complex internal structure: they are very difficult to represent accurately in a vector space.

5. Related papers • [1] Teuvo Kohonen*, Panu Somervuo, “Self-organizing maps of symbol strings,” Neurocomputing, vol 21, pp. 19-30, 1998 • [2] Teuvo Kohonen*, Panu Somervuo, “How to make large self-organizing maps for nonvectorial data,” vol. 15, pp. 945-152, 2002 • [3] Aïcha El Golli , Brieuc Conan-Guez, and Fabrice Rossi, “A Self Organizing Map for dissimilarity data,” IFCS, 2004, Proceedings. • [4] Aïcha El Golli , “Speeding up the self organizing map for dissimilarity data”

6. Alias Name • Median self-organizing map : Median SOM [2] • Dissimilarity self-organizing map : DSOM [3]

7. Related web sites • http://apiacoa.org/ • http://lists.gforge.inria.fr/pipermail/somlib-commits by Fabrice Rossi

8. The goal of this paper • A major drawback of the DSOM is that its running time can be very high, especially when compared to the standard vector SOM. • It is well known that the SOM algorithm behaves linearly with the number of input data. In contrast, the DSOM behaves quadratically with this number.

9. The goal of this paper (cont’d) • In this paper, the authors propose several modifications of the basic algorithm that allow a much faster implementation. • The quadratic nature of the algorithm cannot be avoided, essentially because dissimilarity data are intrinsically described by a quadratic number of one-to-one dissimilarities.

10. The goal of this paper (cont’d) • The standard DSOM algorithm cost is proportional to, where N is the number of observations and M the number of clusters that the algorithm has to produce, whereas the modifications of this paper lead to a cost proportional to. (save in the representation phase) • An important property of all modifications in this paper is that the obtained algorithm produces exactly the same results as the standard DSOM algorithm.

11. Dissimilarity Data • In a given data set X, use the dissimilarity measure to measure the dissimilarity between data instances (one-to-one, pairwise). Sometimes, the distance measurement can be used.

12. Dissimilarity Data (cont’d)

13. Dissimilarity Data (cont’d)

14. The DSOM

15. The DSOM algorithm 1: choose initial values for {Initialization phase} 2: forl = 1 to Ldo 3: forall do {Template for the affectation phase} 4: compute 5: end for 6: for alldo {Template for the representation phase} 7: compute 8: end for 9: end for

17. The DSOM

18. Partial Sums

19. Early Stopping

21. Simulation Results

25. Thank You for your attention!!