Results of a projection of the z-standardized log-transformed lipidomics data onto a lower-dimensional space by means of a self-organizing map of artificial neurons (bottom).
a): 3D display of an emergent self-organizing map (ESOM), providing a 3-dimensional U-matrix visualization (78) of distance-based structures of the serum concentrations of d = 255 lipid mediators following projection of the data points onto a toroid grid of 4,000 neurons where opposite edges are connected. The dots represent the so-called “best matching units” (BMU), i.e., neurons on the grid that after ESOM learning carried a data vector that was most similar to a data vector of a sample in the data set. Only those neurons of the originally 4000 neurons are shown that carried vectors of cases from the present data set. Please also note that one BMU can carry vectors of several cases, i.e., the number of BMUs is not necessarily equal to the number of cases. A cluster structure emerges from visualization of the distances between neurons in the high-dimensional space by means of a U-matrix (79). The U-matrix was colored as a geographical map with brown or snow-covered heights and green valleys with blue lakes, symbolizing high or low distances, respectively, between neurons in the high-dimensional space. Thus, valleys (left and right of the “mountain range” in the middle indicate clusters and watersheds, i.e.,, i.e., the line of large distances between neighboring points, indicate borderlines between different clusters. Tat is, the mountain range with “snow-covered” heights separates main clusters according to probe acquisition at day 1 or day 2, i.e., before and after treatment with paclitaxel. BMUs belonging to the two different clusters are colored green or bluish. b): Mosaic plot of the prior classes (day 1 or day 2) versus the ESOM/Umatrix based clusters. The separation corresponded to the previous classification into pre- and post-therapy probes (day1/2). Cluster #1 was composed of more probes taken on day #1, while probes from day 2 were overrepresented in cluster #2. The figure has been created using the R software package (version 4.1.2 for Linux; https://CRAN.R-project.org/ (26)), R library “ggplot2” (https://cran.r-project.org/package=ggplot2 (80)) and our R package “Umatrix” (https://cran.r-project.org/package=Umatrix (37)).