This is a collection of R functions I've used to plot singular vectors, principal components, and related quantities. Often, I explore multiple ways of visualizing outputs of dimension reduction techniques; it may aid in confirming correct applications, validating against known labels, or generating new hypotheses. Please feel free to add your favorite ways of visualizing dimension reduction techniques or latent variable models.
To use a stable version from CRAN:
install.packages("svdvis")To use a development version from GitHub:
install.packages("devtools")
library("devtools")
install_github("ncchung/svdvis")This package provides several visualization functions for singular value decomposition (SVD), principal component analysis (PCA), factor analysis (FA), logistic factor analysis (LFA), and other related methods.
To use in this vignette, we create a simulated dataset, with m=500 variables (rows) and n=20 samples (columns). Particularly, it contains a latent variable that resembles a case-control study. After applying SVD to the datasets, we also name the rows and the columns of the right singular vectors svd.obj$v for labels in visualization.
set.seed(1234)
library(svdvis)
B = c(runif(100, min=0, max=1), rep(0,400))
L = c(rep(1, 10), rep(-1, 10))
L = L / sd(L)
E = matrix(rnorm(500*20), nrow=500)
Y = B %*% t(L) + E
svd.obj = svd(Y)
colnames(svd.obj$v) = paste0("V",1:20)
rownames(svd.obj$v) = paste0("Sample",1:20)
In this setup, a few right singular vectors contained in svd.obj$v may capture systematic variation in the observed data Y. Since the right singular vectors are ordered according to the singular values in a descending order, the top (or first) r right singular vectors refers to svd.obj$v[,1:r]. Note that principal components (PCs) can be obtained by multiplying singular values svd.obj$d and right singular vectors svd.obj$v. All examples in this vignette and all functions in svdvis can utilize weights="sv" to quickly visualize PCs.
A scree plot visualizes percentages of variance explained by singular vectors in a descending order. svd.scree is simply a wrapper function using ggplot2. In high-dimensional datasets, the number of points in a scree plot may be too large. It may be good to look at a subset of singular values. You can specify subr in svd.scree function, which "zooms in" to the top subr singular values.
svd.scree(svd.obj, subr=5,
axis.title.x="Full scree plot", axis.title.y="% Var Explained")
Note that if subr is not specified, one full-sized scree plot is returned.
Scatter plots are often utilized to look at the top 2 right singular vectors. svd.scatter produces a matrix of scatterplots of all pairs among r right singular vectors.
svd.scatter(svd.obj)
The above plot crams in too many pairs. We can specify r to visualize only the top r right singular vectors. In this example, additional arguments such as group and alpha are included:
svd.scatter(svd.obj, r=3, alpha=.5,
group=c(rep("Group 1", 10), rep("Group 2", 10)))
Let's create a heat map of the top r=5 right singular vectors:
svd.heatmap(svd.obj, r=5)
A parallel coordinates plot shows r dimensions in r parallel lines, which are equally spaced. All data points are rescaled to (0,1) and the top r singular vectors are visualized from left to right. Different groups are colored accordingly:
svd.parallel(svd.obj, r=5, alpha=.5,
group=c(rep("Group 1", 10), rep("Group 2", 10)))
A radial coordinates plot visualize r dimensions in a circle, around where r anchors are placed. Each of n vectors is mapped onto a circle, using its data as spring constants. Prior to mapping, each column is rescaled to have numeric values between 0 and 1.
svd.radial(svd.obj, r=3,
group=c(rep("Group 1", 10), rep("Group 2", 10)))
All functions in svdvis use ggplot2. Therefore, the visual output can be saved and modified in a conventional manner. Feel free to experiment the source codes for more complex or interesting cases.
While this vignette focused on using the results of SVD, an optional argument weights="sv" can be used for visualizing PCs. Note that weights="sv" is simply calling weights = svd.obj$d[1:r].
Outputs from other dimension reduction methods can be used. Provide the r vectors to svd.obj in any function. Note that the input must be a n * r matrix that contains r vectors as columns. An optional argument group can be used to differentially indicate n samples (points, lines, etc).
For example, logistic factor analysis captures population structure from a large and diverse set of genome sequences and is related to SVD and PCA. A R package lfa computes r logistic factors, as columns. You can easily make a parallel coordinates plot (and others) by svd.parallel(svd.obj=lfa(genotypes, 10)).