Dimension reduction

Last updated: 2022-10-27

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File	Version	Author	Date	Message
Rmd	cfb532a	Dave Tang	2022-10-27	Dimension reduction

Dimension reduction is useful for identifying correlated features and reducing the data size, which is very useful for visualising large datasets.

PCA.

pca <- prcomp(iris[, 1:4])
my_col <- as.integer(iris$Species)

plot(pca$x, col = my_col, pch = 16)

t-SNE default perplexity of 30.

if(!require(tsne)){
  install.packages("tsne")
}

Loading required package: tsne

library(tsne)

tsne_ <- tsne(iris[, 1:4])

sigma summary: Min. : 0.486505661043274 |1st Qu. : 0.587913800179832 |Median : 0.614872437640536 |Mean : 0.623051089344394 |3rd Qu. : 0.654914112723525 |Max. : 0.796707932771489 |

Epoch: Iteration #100 error is: 13.1171061837296

Epoch: Iteration #200 error is: 0.238938736285296

Epoch: Iteration #300 error is: 0.237580495588205

Epoch: Iteration #400 error is: 0.2374547569615

Epoch: Iteration #500 error is: 0.237448878840098

Epoch: Iteration #600 error is: 0.237448500418977

Epoch: Iteration #700 error is: 0.237448477241058

Epoch: Iteration #800 error is: 0.237448475805662

Epoch: Iteration #900 error is: 0.23744847571858

Epoch: Iteration #1000 error is: 0.237448475713213

plot(tsne_, col = my_col, pch = 16)

Perplexity of 20.

tsne_p20 <- tsne(iris[, 1:4], perplexity = 20)

sigma summary: Min. : 0.42864778740551 |1st Qu. : 0.523593962475894 |Median : 0.553545139847788 |Mean : 0.563823813379956 |3rd Qu. : 0.596877396756174 |Max. : 0.752227354673175 |

Epoch: Iteration #100 error is: 13.5073150056192

Epoch: Iteration #200 error is: 0.268228858442339

Epoch: Iteration #300 error is: 0.262336620485244

Epoch: Iteration #400 error is: 0.261018858034014

Epoch: Iteration #500 error is: 0.260588711691426

Epoch: Iteration #600 error is: 0.260399044375287

Epoch: Iteration #700 error is: 0.260293870035397

Epoch: Iteration #800 error is: 0.260228227596464

Epoch: Iteration #900 error is: 0.260186737975538

Epoch: Iteration #1000 error is: 0.260157652086673

plot(tsne_p20, col = my_col, pch = 16)

Perplexity of 40.

tsne_p40 <- tsne(iris[, 1:4], perplexity = 40)

sigma summary: Min. : 0.527309628938834 |1st Qu. : 0.636786401601399 |Median : 0.667089986073136 |Mean : 0.671796474888864 |3rd Qu. : 0.70053875222358 |Max. : 0.836996944234283 |

Epoch: Iteration #100 error is: 12.620846895381

Epoch: Iteration #200 error is: 0.258452741303131

Epoch: Iteration #300 error is: 0.257015837325158

Epoch: Iteration #400 error is: 0.256962711285107

Epoch: Iteration #500 error is: 0.256962707558697

Epoch: Iteration #600 error is: 0.256962707553156

Epoch: Iteration #700 error is: 0.256962707553153

Epoch: Iteration #800 error is: 0.256962707553153

Epoch: Iteration #900 error is: 0.256962707553153

Epoch: Iteration #1000 error is: 0.256962707553153

plot(tsne_p40, col = my_col, pch = 16)

Perplexity of 50.

tsne_p50 <- tsne(iris[, 1:4], perplexity = 50)

sigma summary: Min. : 0.565012665854053 |1st Qu. : 0.681985646004023 |Median : 0.713004330336136 |Mean : 0.716213420895748 |3rd Qu. : 0.74581655363904 |Max. : 0.874979764925049 |

Epoch: Iteration #100 error is: 12.0664597536258

Epoch: Iteration #200 error is: 0.20135560570987

Epoch: Iteration #300 error is: 0.199907660516558

Epoch: Iteration #400 error is: 0.199720346311414

Epoch: Iteration #500 error is: 0.199720055735862

Epoch: Iteration #600 error is: 0.199720055732102

Epoch: Iteration #700 error is: 0.199720055732101

Epoch: Iteration #800 error is: 0.199720055732101

Epoch: Iteration #900 error is: 0.199720055732101

Epoch: Iteration #1000 error is: 0.199720055732101

plot(tsne_p50, col = my_col, pch = 16)

UMAP default settings.

if(!require(umap)){
  install.packages("umap")
}

Loading required package: umap

library(umap)
umap.defaults

umap configuration parameters

           n_neighbors: 15

          n_components: 2

                metric: euclidean

              n_epochs: 200

                 input: data

                  init: spectral

              min_dist: 0.1

      set_op_mix_ratio: 1

    local_connectivity: 1

             bandwidth: 1

                 alpha: 1

                 gamma: 1

  negative_sample_rate: 5

                     a: NA

                     b: NA

                spread: 1

          random_state: NA

       transform_state: NA

                   knn: NA

           knn_repeats: 1

               verbose: FALSE

       umap_learn_args: NA

UMAP with default settings.

umap_ <- umap(iris[, 1:4])

plot(umap_$layout, col = my_col, pch = 16)

Adjust number of neighbours.

umap_conf <- umap.defaults
umap_conf$n_neighbors <- 20

umap_n20 <- umap(iris[, 1:4], config = umap_conf)
plot(umap_n20$layout, col = my_col, pch = 16)

sessionInfo()

R version 4.2.0 (2022-04-22)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.4 LTS

Matrix products: default
BLAS:   /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/liblapack.so.3

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] umap_0.2.9.0    tsne_0.1-3.1    workflowr_1.7.0

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.8.3     RSpectra_0.16-1  highr_0.9        bslib_0.3.1     
 [5] compiler_4.2.0   pillar_1.7.0     later_1.3.0      git2r_0.30.1    
 [9] jquerylib_0.1.4  tools_4.2.0      getPass_0.2-2    digest_0.6.29   
[13] lattice_0.20-45  jsonlite_1.8.0   evaluate_0.15    tibble_3.1.7    
[17] lifecycle_1.0.1  png_0.1-7        pkgconfig_2.0.3  rlang_1.0.2     
[21] Matrix_1.4-1     cli_3.3.0        rstudioapi_0.13  yaml_2.3.5      
[25] xfun_0.31        fastmap_1.1.0    httr_1.4.3       stringr_1.4.0   
[29] knitr_1.39       askpass_1.1      sass_0.4.1       fs_1.5.2        
[33] vctrs_0.4.1      grid_4.2.0       rprojroot_2.0.3  reticulate_1.25 
[37] glue_1.6.2       R6_2.5.1         processx_3.5.3   fansi_1.0.3     
[41] rmarkdown_2.14   callr_3.7.0      magrittr_2.0.3   whisker_0.4     
[45] ps_1.7.0         promises_1.2.0.1 htmltools_0.5.2  ellipsis_0.3.2  
[49] httpuv_1.6.5     utf8_1.2.2       stringi_1.7.6    openssl_2.0.1   
[53] crayon_1.5.1

Dimension reduction

Dave Tang

2022-10-27