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Pattern Analysis and Applications
Erschienen in: Pattern Analysis and Applications 2/2014

01.05.2014 | Survey

Topology-oriented self-organizing maps: a survey

verfasst von: César A. Astudillo, B. John Oommen

Erschienen in: Pattern Analysis and Applications | Ausgabe 2/2014

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Abstract

The self-organizing map (SOM) is a prominent neural network model that has found wide application in a spectrum of domains. Accordingly, it has received widespread attention both from the communities of researchers and practitioners. As a result, several variations of the basic architecture have been devised, specifically in the early years of the SOM’s evolution, which were introduced so as to address various architectural shortcomings or to explore other structures of the basic model. The overall goal of this survey is to present a comprehensive comparison of these networks, in terms of their primitive components and properties. We dichotomize these schemes as being either tree based or non-tree based. We have embarked on this venture with the hope that since the survey is comprehensive and the bibliography extensive, it will be an asset and resource for future researchers.
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Fußnoten
1
The paper contains, without a detailed explanation, a list of some of the applications of the SOM.
 
2
During the doctoral research of the first author, we tried, in vain, to locate a single comprehensive refereed survey of the families of topology-based SOMs. This motivated the present work, and we hope that it is appreciated by the research community.
 
3
When we first introduced the principles of the SOM, we had mentioned the fact that different norms can be used for its training phase. The reader should note, however, that this must also be reflected in the calculation of the quantization error at the unit level. Indeed, one cannot use a specific norm for calculating the activation of the neurons and for determining the BMU, and subsequently utilize a different one for measuring the quantization characteristics of the map.
 
4
Boundary neurons are described in Sect. 3.4.
 
5
Other topological structures have been also reported for the SOM, such as the spherical topology reported in [52, 66].
 
6
Even though in the GHTSOM each neuron is represented by hyper-tetrahedrons, we have decided to classify it as being SOM layered to stress that each neuron of the tree is a layer, as explained above.
 
Literatur
1.
Alahakoon D, Halgamuge SK, Srinivasan B (2000) Dynamic self-organizing maps with controlled growth for knowledge discovery. IEEE Trans Neural Netw 11(3):601–614CrossRef
2.
Arsuaga Uriarte E, Díaz Martín F (2005) Topology preservation in SOM. Int J Appl Math Comput Sci 1(1):19–22
3.
Astudillo CA, Oommen BJ (2009) On using adaptive binary search trees to enhance self organizing maps. In: Nicholson A, Li X (eds) 22nd Australasian joint conference on artificial intelligence (AI), pp 199–209
4.
Astudillo CA, Oommen BJ (2011) Imposing tree-based topologies onto self organizing maps. Inf Sci 181(18):3798–3815MathSciNetCrossRef
5.
Astudillo CA, Oommen BJ (2013) On achieving semi-supervised pattern recognition by utilizing tree-based SOMs. Pattern Recognit 46(1):293–304
6.
Astudillo CA, Oommen BJ (2014) Self-organizing maps whose topologies can be learned with adaptive binary search trees using conditional rotations. Pattern Recognit 47(1):96–113CrossRef
7.
Bacciu D, Micheli A, Sperduti A (2010) Compositional generative mapping of structured data. In: Proceedings of the international joint conference on neural networks (IJCNN), pp 1–8
8.
Bacciu D, Micheli A, Sperduti A (2012) Compositional generative mapping for tree-structured data—part I: bottom-up probabilistic modeling of trees. IEEE Trans Neural Netw Learn Syst 23(12):1987–2002CrossRef
9.
Bacciu D, Micheli A, Sperduti A (2013) Compositional generative mapping for tree-structured data—part II: topographic projection model. IEEE Trans Neural Netw Learn Syst 24(2):231–247CrossRef
10.
Bauer HU, Herrmann M, Villmann T (1999) Neural maps and topographic vector quantization. Neural Netw 12(4–5):659–676CrossRef
11.
Bauer HU, Pawelzik KR (1992) Quantifying the neighborhood preservation of self-organizing feature maps. Neural Netw 3(4):570–579CrossRef
12.
Berglund E, Sitte J (2006) The parameterless self-organizing map algorithm. Neural Netw IEEE Trans 17(2):305–316CrossRef
13.
Bishop CM, Svensén M, Williams CKI (1998) GTM: the generative topographic mapping. Neural Comput 10(1):215–234CrossRef
14.
Bishop CM, Svensén M, Williams CKI (1996) GTM: a principled alternative to the self-organizing map. In: Proceedings of the 1996 international conference on artificial neural networks (ICANN’96). Springer, London, pp 165–170
15.
Blackmore J (1995) Visualizing high-dimensional structure with the incremental grid growing neural network. Master’s thesis, University of Texas at Austin
16.
Budinich M (1995) On the ordering conditions for self-organizing maps. Neural Comput 7(2):284–289CrossRef
17.
Campos MM, Carpenter GA (2001) S-tree: self-organizing trees for data clustering and online vector quantization. Neural Netw 14(4–5):505 – 525CrossRef
18.
Carpenter GA, Grossberg S (1988) The art of adaptive pattern recognition by a self-organizing neural network. Computer 21(3):77–88CrossRef
19.
Cheetham RP, Oommen BJ, Ng DTH (1993) Adaptive structuring of binary search trees using conditional rotations. IEEE Trans Knowl Data Eng 5(4):695–704CrossRef
20.
Chow TWS, Rahman MKM (2009) Multilayer SOM with tree-structured data for efficient document retrieval and plagiarism detection. Neural Netw IEEE Trans 20(9):1385–1402CrossRef
21.
Conti PL, De Giovanni L (1991) On the mathematical treatment of self organization: extension of some classical results. Int Conf Artif Neural Netw ICANN 2:1089–1812
22.
23.
Dempster AP, Laird NM, Rubin DB (1977) Maximum likelihood from incomplete data via the EM algorithm. J R Stat Soc Ser B 39(1):1–38MATHMathSciNet
24.
DeSieno D (1988) Adding a conscience to competitive learning. IEEE Int Conf Neural Netw 1:117–124CrossRef
25.
Dittenbach M, Merkl D, Rauber A (2000) The growing hierarchical self-organizing map. In: Proceedings of the IEEE-INNS-ENNS international joint conference on neural networks (IJCNN), vol 6, pp 15–19
26.
Dopazo J (2007) Fundamentals of data mining in genomics and proteomics, chapter clustering—class discovery in the post-genomic era. Springer, US, pp 123–148
27.
Dopazo J, Carazo JM (1997) Phylogenetic reconstruction using an unsupervised growing neural network that adopts the topology of a phylogenetic tree. J Mol Evol 44(2):226–233CrossRef
28.
Duda R, Hart PE, Stork DG (2000) Pattern classification, 2nd edn. Wiley-Interscience, USA
29.
Forti A, Foresti GL (2006) Growing hierarchical tree SOM: an unsupervised neural network with dynamic topology. Neural Netw 19(10):1568–1580MATHCrossRef
30.
Fritzke B (1991) Unsupervised clustering with growing cell structures. In: IJCNN-91-seattle international joint conference on neural networks, vol 2, pp 531–536
31.
Fritzke B (1994) Growing cell structures—a self-organizing network for unsupervised and supervised learning. Neural Netw 7(9):1441–1460CrossRef
32.
Fritzke B (1995) Growing grid—a self-organizing network with constant neighborhood range and adaptation strength. Neural Process Lett 2(5):9–13CrossRef
33.
Fritzke B (1995) A growing neural gas network learns topologies. In: Tesauro G, Touretzky DS, Leen TK (eds) Advances in neural information processing systems, vol 7. MIT Press, Cambridge, pp 625–632
34.
Fuertes J, Domínguez M, Díaz I, Prada M, Morán A, Alonso S (2012) Visualization maps based on SOM to analyze MIMO systems. Neural Comput Appl 1–13. doi:10.​1007/​s00521-012-1090-3
35.
36.
Greene D, Cunningham P, Mayer R (2008) Machine learning techniques for multimedia: case studies on organization and retrieval (cognitive technologies), chapter unsupervised learning and clustering. Springer, Berlin, pp 51–90
37.
Guan L (2006) Self-organizing trees and forests: a powerful tool in pattern clustering and recognition. In: Campilho A, Kamel M (eds) Image analysis and recognition. Proceedings of the 3rd international conference, ICIAR 2006, Póvoa de Varzim, Portugal, September 18–20, 2006. Lecture notes in computer science, vol 4141. Springer, Berlin, pp 1–14
38.
Hagenbuchner M, Sperduti A, Tsoi AC (2009) Graph self-organizing maps for cyclic and unbounded graphs. Neurocomputing 72(79):1419–1430. Advances in machine learning and computational intelligence 16th European symposium on artificial neural networks 2008
39.
Hagenbuchner M, Sperduti A, Chung Tsoi A (2003) A self-organizing map for adaptive processing of structured data. IEEE Trans Neural Netw 14(3):491–505CrossRef
40.
Haykin S (2008) Neural networks and learning machines, 3rd edn. Prentice Hall, USA
41.
Heskes T (1999) Energy functions for self-organizing maps. In: Oja E, Kaski S (eds) Kohonen maps. Elsevier, Amsterdam, pp 303–315
42.
Huang G, Babri HA, Li H (1998) Ordering of self-organizing maps in multi-dimensional cases. Neural Comput 10:19–24CrossRef
43.
Iwasaki Y, Wada K, Itoh M, Ikemura T, Abe T (2011) A novel bioinformatics strategy to predict directional changes of influenza a virus genome sequences. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 198–206
44.
Kaski S, Kangas J, Kohonen T (1998) Bibliography of self-organizing map (SOM) papers: 1981–1997. Neural Comput Surv 1:102–350
45.
Kiviluoto K (1996) Topology preservation in self-organizing maps. In: IEEE Neural Networks Council (ed) Proceedings of international conference on neural networks (ICNN’96), vol 1, pp 294–299, New Jersey, 1996
46.
47.
Kohonen T (1995) Self-organizing maps. Springer, New York
48.
Koikkalainen P, Oja E (1990) Self-organizing hierarchical feature maps. IJCNN Int Joint Conf Neural Netw 2:279–284
49.
Maia J, Barreto G, Coelho A (2011) Evolving a self-organizing feature map for visual object tracking. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 121–130
50.
Martinetz M, Schulten KJ (1991) A “neural-gas” network learns topologies. In: Proceedings of international conference on articial neural networks, vol I, pp 397–402, North-Holland, 1991
51.
Martinetz T, Schulten K (1994) Topology representing networks. Neural Netw 7(3):507–522CrossRef
52.
Matsuda N, Tokutaka H (2011) Decision of class borders on a spherical som with non-equal class distributions. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 328–337
53.
Mehmood Y, Abbas M, Chen X, Honkela T (2011) Self-organizing maps of nutrition, lifestyle and health situation in the world. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 160–167
54.
Miikkulainen R (1990) Script recognition with hierarchical feature maps. Connect Sci 2(1, 2):83–101CrossRef
55.
Oja M, Kaski S, Kohonen T (2003) Bibliography of self-organizing map (SOM) papers: 1998–2001 addendum. Neural Comput Surv 3:1–156
56.
Olier I, Vellido A, Giraldo J (2010) Kernel generative topographic mapping. In: European symposium on artificial neural network (ESANN’10), pp 481–486
57.
Pakkanen J, Iivarinen J, Oja E (2004) The evolving tree—a novel self-organizing network for data analysis. Neural Process Lett 20(3):199–211CrossRef
58.
Pampalk E, Widmer G, Chan A (2004) A new approach to hierarchical clustering and structuring of data with self-organizing maps. Intell Data Anal 8(2):131–149
59.
Pöllä M, Honkela T, Kohonen T (2009) Bibliography of self-organizing map (SOM) papers: 2002–2005 addendum. Technical report TKK-ICS-R23, Department of Information and Computer Science, Helsinki University of Technology, Espoo, Finland
60.
Pölzlbauer G (2004) Survey and comparison of quality measures for self-organizing maps. In: Paralič J, Pölzlbauer G, Rauber A (eds) Proceedings of the fifth workshop on data analysis (WDA’04), pp 67–82. Sliezsky dom, Vysoké Tatry, Slovakia. Elfa Academic Press, Kosice
61.
Rauber A, Merkl D, Dittenbach M (2002) The growing hierarchical self-organizing map: exploratory analysis of high-dimensional data. IEEE Trans Neural Netw 13(6):1331–1341CrossRef
62.
Rojas R (1996) Neural networks: a systematic introduction. Springer, New York
63.
Sarlin P, Eklund T (2011) Fuzzy clustering of the self-organizing map: some applications on financial time series. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 40–50
64.
Strickert M, Hammer B (2005) Merge SOM for temporal data. Neurocomputing 64(0):39–71. Trends in neurocomputing: 12th European symposium on artificial neural networks 2004
65.
Tasdemir K, Merenyi E (2009) Exploiting data topology in visualization and clustering of self-organizing maps. IEEE Trans Neural Netw 20(4):549–562CrossRef
66.
Tokutaka H, Ohkita M, Hai Y, Fujimura K, Oyabu M (2011) Classification using topologically preserving spherical self-organizing maps. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 308–317
67.
Venna J, Kaski S (2001) Neighborhood preservation in nonlinear projection methods: an experimental study. In: Dorffner G, Bischof H, Hornik K (eds) ICANN, vol 2130. Lecture Notes in Computer Science. Springer, Berlin, pp 485–491
68.
Vesanto J (1999) SOM-based data visualization methods. Intell Data Anal 3(2):111–126MATHCrossRef
69.
Vesanto J, Himberg J, Alhoniemi E, Parhankangas J (2000) Self-organizing map in matlab: the som toolbox. In: Proceedings of the matlab DSP conference, pp 35–40
70.
Villmann T, Der R, Herrmann M, Martinetz TM (1997) Topology preservation in self-organizing feature maps: exact definition and measurement. IEEE Trans Neural Netw 8(2):256–266CrossRef
71.
Wang Y, Van hamme H (2011) Gaussian selection using self-organizing map for automatic speech recognition. In: Laaksonen J, Honkela T (eds) Advances in self-organizing maps, vol 6731. Lecture Notes in Computer Science. Springer, Berlin, pp 218–227
72.
Wehrens R, Buydens LMC (2007) Self- and super-organizing maps in R: the Kohonen package. J Stat Softw 21(5):1–19
Metadaten
Titel
Topology-oriented self-organizing maps: a survey
verfasst von
César A. Astudillo
B. John Oommen
Publikationsdatum
01.05.2014
Verlag
Springer London
Erschienen in
Pattern Analysis and Applications / Ausgabe 2/2014
Print ISSN: 1433-7541
Elektronische ISSN: 1433-755X
DOI
https://doi.org/10.1007/s10044-014-0367-9

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