Visualizing High-Dimensional Input Data with Growing Self-Organizing Maps

A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps

“…On the other hand, obtaining a predetermined minimum number of In GCS networks without removal of units, the topology preserving map can be analyzed jointly with some of the topographic maps that make available the visualization of clusters in the dataset. In this work the well known U-map proposed for Kohonen networks [4][5], adapted to the GCS model [19] has been used. U-map shows an overview of the potential number of clusters present in the input space, and provides the necessary information to determine those connections on the topology preserving map, which correspond to topology violations in the network.…”

“…In [18], Fritzke presents a drawing method based on a physical force analogy that works reasonably well when the input space is low-dimensional (2D or 3D), but is not guaranteed to produce planar drawing. Delgado et al [19] proposed a new approach for avoiding this restriction in order to embed the GCS output layer structure in the plane, independently of the dimension of the input space, for the case d=2. The resulting graph is known as the topographic map, which shows the output neurons and the neighborhood connections, ensuring that neighbor units appear near in the map and neighborhood connections do not cross each other.…”

“…The resulting graph is known as the topographic map, which shows the output neurons and the neighborhood connections, ensuring that neighbor units appear near in the map and neighborhood connections do not cross each other. Topographic map provides the basic support to implement different visualization methods of multidimensional information, similar to those generated using Kohonen's network [19].…”

“…In the topology preserving map, neurons are placed in the coordinates calculated for the topographic map of the network [19]. where ¡i represents the mean value and a the variance of the strengths of all connections in CONN. Value 1 is associated with the weakest line and 4 with the strongest one.…”

“…Insertion and removal of units are performed in such way that the original architecture structure is maintained (i.e., every node must always be a member of at least one triangle). Using the method proposed in [19] by the authors of this paper, the GCS two-dimensional output layer can be plotted in a two-dimensional graph (the topographic map) giving a way to make use of this model in visualization techniques of high dimensional information. Usually, the flexibility of the output layer lattice in the GCS network provides better degrees of topology preservation than Kohonen's model.…”