Last updated: 2023-06-10
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Principal Components analysis with Iris data
Collecting data
data <- irisPreparing data for the principal components analysis (PCA)
let’s prepare this prepare this data to plot some boxplot of all the
four traits, for that you will need the function melt of
the reshape2 package and the tidyverse package.
install.packages("reshape2", repos = "https://cloud.r-project.org")Installing package into 'C:/Users/USUARIO/Documents/R/win-library/4.1'
(as 'lib' is unspecified)package 'reshape2' successfully unpacked and MD5 sums checkedWarning: cannot remove prior installation of package 'reshape2'Warning in file.copy(savedcopy, lib, recursive = TRUE): problem copying
C:\Users\USUARIO\Documents\R\win-library\4.1\00LOCK\reshape2\libs\x64\reshape2.dll
to C:\Users\USUARIO\Documents\R\win-library\4.1\reshape2\libs\x64\reshape2.dll:
Permission deniedWarning: restored 'reshape2'
The downloaded binary packages are in
C:\Users\USUARIO\AppData\Local\Temp\RtmpKsJN06\downloaded_packageslibrary(reshape2); library(tidyverse)-- Attaching core tidyverse packages ------------------------ tidyverse 2.0.0 --
v dplyr 1.1.2 v readr 2.1.4
v forcats 1.0.0 v stringr 1.5.0
v ggplot2 3.4.2 v tibble 3.2.1
v lubridate 1.9.2 v tidyr 1.3.0
v purrr 1.0.1 -- Conflicts ------------------------------------------ tidyverse_conflicts() --
x dplyr::filter() masks stats::filter()
x dplyr::lag() masks stats::lag()
i Use the conflicted package (<http://conflicted.r-lib.org/>) to force all conflicts to become errorsdataMelted <- data %>% reshape2::melt(data = .,
id.vars = "Species",
variable.name = "trait",
value.name = "y")
head(dataMelted) Species trait y
1 setosa Sepal.Length 5.1
2 setosa Sepal.Length 4.9
3 setosa Sepal.Length 4.7
4 setosa Sepal.Length 4.6
5 setosa Sepal.Length 5.0
6 setosa Sepal.Length 5.4Great, now we have the data at the format to make boxplot from all
traits at the same code line. so lets keep moving. For that we will use
ggplot2 package.
dataMelted %>% ggplot(aes(x = Species, y = y, fill = Species)) +
geom_boxplot() + facet_wrap(~trait, scales = "free_y") +
theme(legend.position = "none")
Great data, we can see a lot of differences between the
Species for these traits. It seems that we may have some
correlation between Petal Length and Width. We
also have different amplitude for these traits this will certainly
results in different phenotypic variance between the
traits, so we need to scale these traits before the
PCA.
DataSc <- data %>% select(-Species) %>%
scale(x = ., center = TRUE, scale = TRUE) %>%
as.data.frame() %>%
mutate(Species = data$Species)
head(DataSc) Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1 -0.8976739 1.01560199 -1.335752 -1.311052 setosa
2 -1.1392005 -0.13153881 -1.335752 -1.311052 setosa
3 -1.3807271 0.32731751 -1.392399 -1.311052 setosa
4 -1.5014904 0.09788935 -1.279104 -1.311052 setosa
5 -1.0184372 1.24503015 -1.335752 -1.311052 setosa
6 -0.5353840 1.93331463 -1.165809 -1.048667 setosaPrincipal Component Analysis (PCA)
So let’s proceed for the PCA analysis, here we will use the
prcomp function from R status package, so no
need to call any package.
PCA <- prcomp(DataSc %>% select(-Species))Saving results
Let’s save the important results in objects, so we could make some
graphs with them.
1. Accumulate percent of the total phenotypic variance explained by the principal components (PC)
Perc <- 100 * PCA$sdev^2 / sum(PCA$sdev^2)
PercAc <- as.vector(rep(NA, times = length(Perc)))
for(i in 1:length(Perc)) {
PercAc[i] <- sum(Perc[1:i])
names(PercAc)[i] <- i
}
names(PercAc) <- c("PC1", "PC2", "PC3", "PC4")
PercAc PC1 PC2 PC3 PC4
72.96245 95.81321 99.48213 100.00000 Oh these data are high correlated.
2. Correlations of the traits with the principal components (PC)
CorTraits <- PCA$rotation
rownames(CorTraits) <- c("SepLen", "SepWid", "PetLen", "PetWid")
CorTraits PC1 PC2 PC3 PC4
SepLen 0.5210659 -0.37741762 0.7195664 0.2612863
SepWid -0.2693474 -0.92329566 -0.2443818 -0.1235096
PetLen 0.5804131 -0.02449161 -0.1421264 -0.8014492
PetWid 0.5648565 -0.06694199 -0.6342727 0.5235971LabelsPCA <- CorTraits %>% as.data.frame %>%
mutate(PC1 = PC1 + 0.15, .keep = "unused")3. Individuals scores for the principal components (PC)
ScoresSpecies <- PCA$x %>%
as.data.frame %>%
mutate(Species = data$Species)
head(ScoresSpecies) PC1 PC2 PC3 PC4 Species
1 -2.257141 -0.4784238 0.12727962 0.024087508 setosa
2 -2.074013 0.6718827 0.23382552 0.102662845 setosa
3 -2.356335 0.3407664 -0.04405390 0.028282305 setosa
4 -2.291707 0.5953999 -0.09098530 -0.065735340 setosa
5 -2.381863 -0.6446757 -0.01568565 -0.035802870 setosa
6 -2.068701 -1.4842053 -0.02687825 0.006586116 setosaGreat we got what we need to create our figures.
Figures
The first figure will be a barplot of the accumulated variances
explained by the PC. We will use the color red the PC
selected to use at the next figures.
barplot(PercAc, main = "Variance explained by PCA",
ylab = "Cumulative variance (%)", xlab = "Number of retained PCs",
col = c("red", "red", "gray", "gray", "gray"))
R markdown allows us to hide the code that create the figure, this
could be done adding the argument echo = FALSE inside the
curly brackets at the chunk. Using echo argument will print
just the result of you chunk, link below.
The last figure will be a scatter plot of the individuals with their score for the first two PCs with the correlation of the traits with the first two PCs.
ggplot(data = ScoresSpecies, aes(x = PC1, y = PC2, color = Species)) +
geom_point() + geom_rug(alpha = 0.2, size = 1.5) +
geom_segment(mapping = aes(x = 0, xend = 3*PC1, y = 0, yend = 3*PC2),
colour = "red",
data = CorTraits %>% as.data.frame,
arrow = arrow(type = "closed",
length = unit(0.2,units = "cm"))) +
geom_text(mapping = aes(x = PC1*3, y = PC2*3, label = rownames(LabelsPCA)),
data = LabelsPCA, colour = "black") +
theme_bw() +
xlab(paste("PC1 - ", round(Perc[1], digits = 2), "%", sep = "")) +
ylab(paste("PC2 - ", round(Perc[2], digits = 2), "%", sep = ""))Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
i Please use `linewidth` instead.
This warning is displayed once every 8 hours.
Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
generated.
This is the final results of the PC. Mostly of the variance explained
by the 1˚PC is due to the between species Setosa Vs
Versicolor and Virginica. The 2˚PC just
explain variance within the species. Also the traits
Petal Length, Petal Width and
Sepal Length could be used to discriminate the species.
sessionInfo()R version 4.1.3 (2022-03-10)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 19045)
Matrix products: default
locale:
[1] LC_COLLATE=Portuguese_Brazil.1252 LC_CTYPE=Portuguese_Brazil.1252
[3] LC_MONETARY=Portuguese_Brazil.1252 LC_NUMERIC=C
[5] LC_TIME=Portuguese_Brazil.1252
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] lubridate_1.9.2 forcats_1.0.0 stringr_1.5.0 dplyr_1.1.2
[5] purrr_1.0.1 readr_2.1.4 tidyr_1.3.0 tibble_3.2.1
[9] ggplot2_3.4.2 tidyverse_2.0.0 reshape2_1.4.4
loaded via a namespace (and not attached):
[1] tidyselect_1.2.0 xfun_0.38 bslib_0.4.2 colorspace_2.1-0
[5] vctrs_0.6.1 generics_0.1.3 htmltools_0.5.5 yaml_2.3.7
[9] utf8_1.2.3 rlang_1.1.0 jquerylib_0.1.4 later_1.3.0
[13] pillar_1.9.0 glue_1.6.2 withr_2.5.0 lifecycle_1.0.3
[17] plyr_1.8.8 munsell_0.5.0 gtable_0.3.3 workflowr_1.7.0
[21] evaluate_0.20 labeling_0.4.2 knitr_1.42 tzdb_0.3.0
[25] fastmap_1.1.1 httpuv_1.6.9 fansi_1.0.4 highr_0.10
[29] Rcpp_1.0.10 promises_1.2.0.1 scales_1.2.1 cachem_1.0.7
[33] jsonlite_1.8.4 farver_2.1.1 fs_1.6.1 hms_1.1.3
[37] digest_0.6.31 stringi_1.7.12 rprojroot_2.0.3 grid_4.1.3
[41] cli_3.6.1 tools_4.1.3 magrittr_2.0.3 sass_0.4.5
[45] crayon_1.5.2 whisker_0.4.1 pkgconfig_2.0.3 timechange_0.2.0
[49] rmarkdown_2.21 rstudioapi_0.14 R6_2.5.1 git2r_0.30.1
[53] compiler_4.1.3 Weverton Gomes da Costa, Pós-Doutorando, Departamento de Estatística - UFV, wevertonufv@gmail.com↩︎