## 3 The Proposed Generalized SOMs with Splitting-Merging Structures
1000 (end of learning) as well as plots of the number of substructures (**j**) and the number of neurons (**k**) vs. epoch number  
We demonstrated that the proposed original GeSOMs with 1 DN (DSOMs) and GeSOMS with T-LSs outperform different alternative approaches in various complex clustering tasks. In particular:  
1. in [13] we applied our GeSOMs with 1 DN (DSOMs) to WWW-newsgroup-document clustering (the collection of 19997 documents was considered); our approach generated 58.41% of correct decisions, whereas alternative approaches achieved from 33.98% to 49.12% of correct decisions,
2. in [11] we tested our GeSOMs with 1 DN (DSOMs) in terms of their abilities to correctly determine the number of clusters in a given data set (8 benchmark data sets available from the University of California (UCI) Database Repository at [[https://archive.ics.uci.edu/ml](https://archive.ics.uci.edu/ml)]([https://archive.ics.uci.edu/ml](https://archive.ics.uci.edu/ml)) were considered); our approach achieved 100% of correct decisions for 6 out of 8 considered data sets, whereas an alternative method obtained such an accuracy only for 1 data set,
3. in [15] we applied our GeSOMs with T-LSs to microarray leukemia gene data clustering (the benchmark leukemia cancer data set containing 7129 genes and 72 samples was considered); our approach achieved 98.6% of correct decisions regarding the cluster assignments of particular data samples, whereas an alternative method gave only 93.14% accuracy,
4. in [16] we applied our GeSOMs with T-LSs to WWW-document clustering (the collection of 548 abstracts of technical reports and its 476-element subset, both available from the WWW server of the Department of Computer Science, University of Rochester, USA at [[https://www.cs.rochester.edu/trs](https://www.cs.rochester.edu/trs)]([https://www.cs.rochester.edu/trs](https://www.cs.rochester.edu/trs)) were considered); our approach obtained 87.23% and 84.87% clustering accuracies for bigger and smaller collections, respectively, whereas alternative approaches gave from 36.68% to 65.33% accuracy for bigger collection and from 38.45% to 69.96% for smaller collection,
5. in [18] our GeSOMs with T-LSs were used to uncover informative genes from colon cancer gene expression data via multi-step clustering (the benchmark colon cancer microarray data set containing 6500 genes and 62 samples was considered); our approach generated 88.71% of correct decisions regarding the clustering of samples, whereas alternative methods achieved from 51.61% to 85.73% accuracy,
6. in [19] we applied our GeSOMs with T-LSs to electricity consumption data clustering for load profiling (the benchmark Irish Commission for Energy Regulation data set containing 4066 customer profiles with 25728 recordings per profile was considered); our approach achieved 94.86% of correct decisions, whereas alternative methods generated from 89.77% to 94.76% of correct decisions,
7. finally, in [17] we applied our both approaches to microarray lymphoma gene data clustering (the benchmark lymphoma cancer data set containing 4026 genes and 62 samples was considered); our approaches achieved 91.9% (GeSOMs with 1 DN) and 93.6% (GeSOMs with T-LSs) of correct decisions, whereas alternative techniques gave from 61.3% to 75.8% of correct decisions. Concluding, our approaches provide up to 20% increase in the clustering accuracy in comparison with alternative methods. It is worth emphasizing that alternative methods require the number of clusters to be predefined to perform the clustering. Thus, they are favored in regard to our approaches which aim at an automatic detection of the number of clusters and the cluster multi-point prototypes in a given data set.