## 2 Conventional SOM, Its Selected Generalizations, and Related Work
### Related Recent Work  
Earlier in this section we presented several SOM's generalizations illustrating the evolution of their applications that range from data visualization to data clustering. We also developed computer implementations of learning algorithms for particular approaches and we showed simulation results illustrating their operation. In this section we present some literature context for the SOMs-based data visualization and clustering by briefly reviewing recently published related work.  
An extension of U-matrix Equation (4) for data visualization is proposed in [24]. However, although the generalized U-matrix is able to visualize the similarities and dissimilarities among high-dimensional data points in a scatter plot of the projected points, it is unable to visualize the disruption of clusters, based on which the quality of structure preservation is defined [25]. An extension of the SOM that utilizes several landmarks, e.g., pairs of nodes and data points (referred to as LAMA) is proposed in [26]. LAMA generates a user-intended nonlinear projection in order to achieve, e.g., the landmark-oriented data visualization. However, missetting of the LAMA's learning parameters, which are manually adjusted, may cause the mesh grid of codebook vectors to be twisted or wrinkled [26]. An emergent SOM (ESOM) concept is proposed in [25]. The structure of a ESOM's feature map is toroidal, i.e., the borders of the map are cyclically connected. It allows the problem of neurons on map borders and thus, boundary effects to be avoided. However, the structure of the input data emerges only when U-matrix SOM-visualization technique is used [25]. In turn, a nonlinear dimensionality reduction method for data visualization based on combination of extreme learning machine (ELM) approach with SOM and referred to as ELM-SOM+ is proposed in [27]. The SOM-based data visualization finds diverse applications ranging from gearbox fault feature extraction and classification [28] to evaluation of ground water potential to pollution in Iran [29]. A solution building a bridge between SOM-based data visualization and clustering is an improved SOM network combining clustering and clustering visualization into the same computational process. Such an approach--applied to gene data cluster analysis--is proposed in [30].  
As far as SOM-based or SOM-inspired data clustering is concerned, a SOM prototype-based methodology for cluster analysis is proposed in [31]. It makes use of topology preserving indices by means of which the most appropriate size of the map is selected. It also automatically analyzes the most relevant number of clusters in data. However, one real-life example in [31] does not allow for a deeper evaluation of its performance. Hierarchical SOM-based approach that can handle numerical, categorical, and mixed data clustering is proposed in [32]. In turn, a SOM-inspired algorithm for partition clustering is proposed in [33]. The SOM-based or inspired data clustering finds applications ranging from dengue expression data analysis [33] to house data grouping [34]. It is worth mentioning here also a collection of earlier published two-level approaches to data clustering using SOMs [35; 36; 37; 38] (see also [39; 40] for brief reviews). At the first level, each data point is mapped, by the standard SOM approach, into a lower dimensional space that preserves the data topology. Then, at the second level, the obtained data are subject to clustering using traditional methods.