Editing Self-organizing map (section)

== Alternative approaches ==

* The '''[[generative topographic map]]''' (GTM) is a potential alternative to SOMs. In the sense that a GTM explicitly requires a smooth and continuous mapping from the input space to the map space, it is topology preserving. However, in a practical sense, this measure of topological preservation is lacking.<ref>{{cite journal |last=Kaski |first=Samuel |title=Data Exploration Using Self-Organizing Maps |journal=Acta Polytechnica Scandinavica |series=Mathematics, Computing and Management in Engineering Series |volume=82 |year=1997 |publisher=Finnish Academy of Technology |location=Espoo, Finland |isbn=978-952-5148-13-8}}</ref>
* The '''[[growing self-organizing map]]''' (GSOM) is a growing variant of the self-organizing map. The GSOM was developed to address the issue of identifying a suitable map size in the SOM. It starts with a minimal number of nodes (usually four) and grows new nodes on the boundary based on a heuristic. By using a value called the ''spread factor'', the data analyst has the ability to control the growth of the GSOM.<ref>{{cite journal |last1=Alahakoon |first1=D. |last2=Halgamuge |first2=S.K. |last3=Sirinivasan |first3=B. |year=2000 |title=Dynamic Self Organizing Maps With Controlled Growth for Knowledge Discovery |journal=IEEE Transactions on Neural Networks |volume=11 |issue=3 |pages=601–614 |pmid=18249788 |doi=10.1109/72.846732}}</ref>
* The '''conformal map''' approach uses conformal mapping to interpolate each training sample between grid nodes in a continuous surface. A one-to-one smooth mapping is possible in this approach.<ref>{{cite journal | last1=Liou | first1=C.-Y. | last2=Tai | first2=W.-P. | title=Conformality in the self-organization network |journal=Artificial Intelligence |volume=116 | issue=1–2 |pages=265–286 |date=2000 |doi=10.1016/S0004-3702(99)00093-4  | doi-access= }}</ref><ref>{{cite journal | last1=Liou | first1=C.-Y. | last2=Kuo | first2=Y.-T. | title=Conformal Self-organizing Map for a Genus Zero Manifold |journal=The Visual Computer |volume=21 |issue=5 |pages=340–353 |date=2005 |doi=10.1007/s00371-005-0290-6 | s2cid=8677589 }}</ref>
* The '''time adaptive self-organizing map''' (TASOM) network is an extension of the basic SOM. The TASOM employs adaptive learning rates and neighborhood functions. It also includes a scaling parameter to make the network invariant to scaling, translation and rotation of the input space. The TASOM and its variants have been used in several applications including adaptive clustering, multilevel thresholding, input space approximation, and active contour modeling.<ref>{{cite journal |first1=Hamed |last1=Shah-Hosseini |first2=Reza |last2=Safabakhsh |title=TASOM: A New Time Adaptive Self-Organizing Map |journal=IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics |volume=33 |number=2 |date=April 2003 |pages=271–282 |doi=10.1109/tsmcb.2003.810442|pmid=18238177 }}</ref> Moreover, a Binary Tree TASOM or BTASOM, resembling a binary natural tree having nodes composed of TASOM networks has been proposed where the number of its levels and the number of its nodes are adaptive with its environment.<ref>{{cite journal |first=Hamed |last=Shah-Hosseini |title=Binary Tree Time Adaptive Self-Organizing Map |journal=Neurocomputing |volume=74 |number=11 |date=May 2011 |pages=1823–1839 |doi=10.1016/j.neucom.2010.07.037}}</ref>
* The '''[[elastic map]]''' approach borrows from the [[spline interpolation]] the idea of minimization of the [[elastic energy]]. In learning, it minimizes the sum of quadratic bending and stretching energy with the [[least squares]] [[approximation error]].<ref>{{cite journal |first1=A.N. |last1=Gorban |first2=A. |last2=Zinovyev |arxiv=1001.1122 |title=Principal manifolds and graphs in practice: from molecular biology to dynamical systems] |journal=[[International Journal of Neural Systems]] |volume=20 |issue=3 |date=2010 |pages=219–232 |doi=10.1142/S0129065710002383|pmid=20556849 |s2cid=2170982 }}</ref>
* The '''oriented and scalable map''' (OS-Map) generalises the neighborhood function and the winner selection.<ref>{{cite journal | last1 = Hua | first1 = H | year = 2016 | title = Image and geometry processing with Oriented and Scalable Map | journal = Neural Networks | volume = 77 | pages = 1–6 | doi = 10.1016/j.neunet.2016.01.009 | pmid = 26897100 }}</ref> The homogeneous Gaussian neighborhood function is replaced with the matrix exponential. Thus one can specify the orientation either in the map space or in the data space. SOM has a fixed scale (=1), so that the maps "optimally describe the domain of observation". But what about a map covering the domain twice or in n-folds? This entails the conception of scaling. The OS-Map regards the scale as a statistical description of how many best-matching nodes an input has in the map.