1d:T465,# Function that calculates the Saturn coefficient to quantify the quality of a UMAP dimensionality reduction ```r Saturn_coefficient(original_matrix, umap_output_layout, VERBOSE) ``` ## Arguments - `original_matrix`: input matrix - `umap_output_layout`: output matrix of UMAP applied to original_matrix - `VERBOSE`: prints some intermediate message to standard output or not ## Returns a real value containing the Saturn coefficient ## Examples ```r this_nrows <- 200 this_ncols <- 100 this_min <- 0 this_max <- 10000 noise_random_matrix <- matrix(runif(n = this_nrows * this_ncols, min = this_min, max = this_max), nrow = this_nrows) input_matrix <- as.matrix(noise_random_matrix) these_nearest_neighbors <- 15 this_min_dist <- 0.05 library("umap") custom.settings <- umap::umap.defaults custom.settings$"n_neighbors" <- these_nearest_neighbors custom.settings$"min_dist" <- this_min_dist x_umap <- umap::umap(input_matrix, config=custom.settings) this_verbose <- FALSE thisSaturn <- Saturn_coefficient(input_matrix, x_umap$"layout", this_verbose) cat("Saturn coefficient = ", thisSaturn, "\n", sep="") ```1e:T49a,M7.49933 0.25C3.49635 0.25 0.25 3.49593 0.25 7.50024C0.25 10.703 2.32715 13.4206 5.2081 14.3797C5.57084 14.446 5.70302 14.2222 5.70302 14.0299C5.70302 13.8576 5.69679 13.4019 5.69323 12.797C3.67661 13.235 3.25112 11.825 3.25112 11.825C2.92132 10.9874 2.44599 10.7644 2.44599 10.7644C1.78773 10.3149 2.49584 10.3238 2.49584 10.3238C3.22353 10.375 3.60629 11.0711 3.60629 11.0711C4.25298 12.1788 5.30335 11.8588 5.71638 11.6732C5.78225 11.205 5.96962 10.8854 6.17658 10.7043C4.56675 10.5209 2.87415 9.89918 2.87415 7.12104C2.87415 6.32925 3.15677 5.68257 3.62053 5.17563C3.54576 4.99226 3.29697 4.25521 3.69174 3.25691C3.69174 3.25691 4.30015 3.06196 5.68522 3.99973C6.26337 3.83906 6.8838 3.75895 7.50022 3.75583C8.1162 3.75895 8.73619 3.83906 9.31523 3.99973C10.6994 3.06196 11.3069 3.25691 11.3069 3.25691C11.7026 4.25521 11.4538 4.99226 11.3795 5.17563C11.8441 5.68257 12.1245 6.32925 12.1245 7.12104C12.1

Saturn_coefficient function