Self-Organizing Map

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A Self-Organizing Map (SOM) is an artificial neural network that represent a low-dimensional (typically two-dimensional), discretized representation of the input space of the training samples



References

2018

  • (Wikipedia, 2018) ⇒ https://en.wikipedia.org/wiki/Self-organizing_map Retrieved:2018-7-22.
    • A self-organizing map (SOM) or self-organizing feature map (SOFM) is a type of artificial neural network (ANN) that is trained using unsupervised learning to produce a low-dimensional (typically two-dimensional), discretized representation of the input space of the training samples, called a map, and is therefore a method to do dimensionality reduction. Self-organizing maps differ from other artificial neural networks as they apply competitive learning as opposed to error-correction learning (such as backpropagation with gradient descent), and in the sense that they use a neighborhood function to preserve the topological properties of the input space.

      This makes SOMs useful for visualization by creating low-dimensional views of high-dimensional data, akin to multidimensional scaling. The artificial neural network introduced by the Finnish professor Teuvo Kohonen in the 1980s is sometimes called a Kohonen map or network (Kohonen & Honkela, 2007, Kohonen, 1982). The Kohonen net is a computationally convenient abstraction building on biological models of neural systems from the 1970s and morphogenesis models dating back to Alan Turing in the 1950s. While it is typical to consider this type of network structure as related to feedforward networks where the nodes are visualized as being attached, this type of architecture is fundamentally different in arrangement and motivation. Useful extensions include using toroidal grids where opposite edges are connected and using large numbers of nodes. It has been shown that while self-organizing maps with a small number of nodes behave in a way that is similar to K-means, larger self-organizing maps rearrange data in a way that is fundamentally topological in character. It is also common to use the U-Matrix (Ultsch & Siemon, 1990). The U-Matrix value of a particular node is the average distance between the node's weight vector and that of its closest neighbors (Ultsch, 2003) In a square grid, for instance, we might consider the closest 4 or 8 nodes (the Von Neumann and Moore neighborhoods, respectively), or six nodes in a hexagonal grid.

      Large SOMs display emergent properties. In maps consisting of thousands of nodes, it is possible to perform cluster operations on the map itself (Ultsch, 2007).

2017

2007a

2007b

2003

  • (Ultsch, 2003) ⇒ Alfred Ultsch.(2003); "U*-Matrix: A tool to visualize clusters in high dimensional data", Department of Computer Science, University of Marburg, Technical Report Nr. 36:1-12
    • ESOM are a self organizing projection from the high dimensional data space onto a grid of neuron locations. The grid of neurons is usually embedded in a two dimensional manifold. This space is called a map with a geographical interpretation in mind. The learning algorithm of the SOM is designed to preserve the neighborhood relationships of the high dimensional space on the map (Kohonen, 1982). Therefore the map can be regarded as a roadmap of the data space.

      (...) The U-Matrix has become the standard tool for the display of the distance structures of the input data on ESOM (Kohonen, 1982).

2001

1990

1982

1973