Dimension reduction
Dave Tang
2023-09-10
Last updated: 2023-09-10
Checks: 7 0
Knit directory: bioinformatics_tips/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | ec130da | Dave Tang | 2023-09-10 | Boxplots |
| html | 9ae8e51 | Dave Tang | 2023-09-10 | Build site. |
| Rmd | b6d9d00 | Dave Tang | 2023-09-10 | Normalise data |
| html | ca74424 | Dave Tang | 2022-10-27 | Build site. |
| 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.
Data
Use iris.
dat <- as.matrix(iris[, 1:4])
dat[1:6, 1:4] Sepal.Length Sepal.Width Petal.Length Petal.Width
[1,] 5.1 3.5 1.4 0.2
[2,] 4.9 3.0 1.4 0.2
[3,] 4.7 3.2 1.3 0.2
[4,] 4.6 3.1 1.5 0.2
[5,] 5.0 3.6 1.4 0.2
[6,] 5.4 3.9 1.7 0.4Normalise data using scale.
dat_norm <- scale(dat)
dat_norm[1:6, 1:4] Sepal.Length Sepal.Width Petal.Length Petal.Width
[1,] -0.8976739 1.01560199 -1.335752 -1.311052
[2,] -1.1392005 -0.13153881 -1.335752 -1.311052
[3,] -1.3807271 0.32731751 -1.392399 -1.311052
[4,] -1.5014904 0.09788935 -1.279104 -1.311052
[5,] -1.0184372 1.24503015 -1.335752 -1.311052
[6,] -0.5353840 1.93331463 -1.165809 -1.048667Before normalising.
apply(dat, 2, summary) Sepal.Length Sepal.Width Petal.Length Petal.Width
Min. 4.300000 2.000000 1.000 0.100000
1st Qu. 5.100000 2.800000 1.600 0.300000
Median 5.800000 3.000000 4.350 1.300000
Mean 5.843333 3.057333 3.758 1.199333
3rd Qu. 6.400000 3.300000 5.100 1.800000
Max. 7.900000 4.400000 6.900 2.500000boxplot(dat)
After normalising.
round(apply(dat_norm, 2, summary), digits = 6) Sepal.Length Sepal.Width Petal.Length Petal.Width
Min. -1.863780 -2.425820 -1.562342 -1.442245
1st Qu. -0.897674 -0.590395 -1.222456 -1.179859
Median -0.052331 -0.131539 0.335354 0.132067
Mean 0.000000 0.000000 0.000000 0.000000
3rd Qu. 0.672249 0.556746 0.760211 0.788031
Max. 2.483699 3.080455 1.779869 1.706379boxplot(dat_norm)
PCA
The prcomp() function:
Performs a principal components analysis on the given data matrix and returns the results as an object of class prcomp.
pca <- prcomp(dat_norm)
my_col <- as.integer(iris$Species)
plot(pca$x, col = my_col, pch = 16)
t-SNE
Install (if necessary) and load.
if(!require(tsne)){
install.packages("tsne")
}
library(tsne)t-SNE default perplexity of 30.
tsne_ <- tsne(dat_norm)
plot(tsne_, col = my_col, pch = 16)
Perplexity of 20.
tsne_p20 <- tsne(dat_norm, perplexity = 20)
plot(tsne_p20, col = my_col, pch = 16)
Perplexity of 40.
tsne_p40 <- tsne(dat_norm, perplexity = 40)
plot(tsne_p40, col = my_col, pch = 16)
Perplexity of 50.
tsne_p50 <- tsne(dat_norm, perplexity = 50)
plot(tsne_p50, col = my_col, pch = 16)
UMAP
Install (if necessary) and load.
if(!require(umap)){
install.packages("umap")
}
library(umap)UMAP default settings.
umap.defaultsumap 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: NAUMAP with default settings.
umap_ <- umap(dat_norm)
plot(umap_$layout, col = my_col, pch = 16)
Adjust number of neighbours.
umap_conf <- umap.defaults
umap_conf$n_neighbors <- 20
umap_n20 <- umap(dat_norm, config = umap_conf)
plot(umap_n20$layout, col = my_col, pch = 16)
sessionInfo()R version 4.3.0 (2023-04-21)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 22.04.2 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/libopenblasp-r0.3.20.so; LAPACK version 3.10.0
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
time zone: Etc/UTC
tzcode source: system (glibc)
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] umap_0.2.10.0 tsne_0.1-3.1 workflowr_1.7.0
loaded via a namespace (and not attached):
[1] Matrix_1.5-4 jsonlite_1.8.4 compiler_4.3.0 highr_0.10
[5] promises_1.2.0.1 Rcpp_1.0.10 stringr_1.5.0 git2r_0.32.0
[9] callr_3.7.3 later_1.3.0 jquerylib_0.1.4 png_0.1-8
[13] yaml_2.3.7 fastmap_1.1.1 reticulate_1.31 lattice_0.21-8
[17] R6_2.5.1 knitr_1.42 tibble_3.2.1 openssl_2.0.6
[21] rprojroot_2.0.3 bslib_0.4.2 pillar_1.9.0 rlang_1.1.0
[25] utf8_1.2.3 cachem_1.0.7 stringi_1.7.12 httpuv_1.6.9
[29] xfun_0.39 getPass_0.2-2 fs_1.6.2 sass_0.4.5
[33] cli_3.6.1 magrittr_2.0.3 ps_1.7.5 grid_4.3.0
[37] digest_0.6.31 processx_3.8.1 rstudioapi_0.14 askpass_1.1
[41] lifecycle_1.0.3 vctrs_0.6.2 RSpectra_0.16-1 evaluate_0.20
[45] glue_1.6.2 whisker_0.4.1 fansi_1.0.4 rmarkdown_2.21
[49] httr_1.4.5 tools_4.3.0 pkgconfig_2.0.3 htmltools_0.5.5