In this vignette, we will demonstrate basic functionalities of Rdimtools package by walking through from installation to analysis with the famous iris dataset.

1. Install and Load

Rdimtools can be installed in two handy options. A release version from CRAN can be installed

install.packages("Rdimtools")

or a development version is available from GitHub with devtools package.

## install.packages("devtools")
devtools::install_github("kisungyou/Rdimtools")

Now we are ready to go by loading the library.

2. Intrinsic Dimension Estimation

As of current release version 1.0.9, there are 17 intrinsic dimension estimation (IDE) algorithms. In the following example, we will only show 5 methods’ performance.

# load the iris data
X   = as.matrix(iris[,1:4])
lab = as.factor(iris[,5])

# we will compare 5 methods (out of 17 methods from version 1.0.0)
vecd = rep(0,5)
vecd[1] = est.Ustat(X)$estdim       # convergence rate of U-statistic on manifold
vecd[2] = est.correlation(X)$estdim # correlation dimension
vecd[3] = est.made(X)$estdim        # manifold-adaptive dimension estimation
vecd[4] = est.mle1(X)$estdim        # MLE with Poisson process
vecd[5] = est.twonn(X)$estdim       # minimal neighborhood information

# let's visualize
plot(1:5, vecd, type="b", ylim=c(1.5,3.5), 
     main="estimating dimension of iris data",
     xaxt="n",xlab="",ylab="estimated dimension")
xtick = seq(1,5,by=1)
axis(side=1, at=xtick, labels = FALSE)
text(x=xtick,  par("usr")[3], 
     labels = c("Ustat","correlation","made","mle1","twonn"), pos=1, xpd = TRUE)

As the true dimension is not known for a given dataset, different methods bring about heterogeneous estimates. That’s why we deliver 17 methods at an unprecedented scale to provide a broader basis for your decision.

3. Dimension Reduction

Currently, Rdimtools (ver 1.0.9) delivers 141 dimension reduction/feature selection/manifold learning algorithms. Among a myriad of methods, we compare Principal Component Analysis (do.pca), Laplacian Score (do.lscore), and Diffusion Maps (do.dm) are compared, each from a family of algorithms for linear reduction, feature extraction, and nonlinear reduction.

# run 3 algorithms mentioned above
mypca = do.pca(X, ndim=2)
mylap = do.lscore(X, ndim=2)
mydfm = do.dm(X, ndim=2, bandwidth=10)

# extract embeddings from each method
Y1 = mypca$Y
Y2 = mylap$Y
Y3 = mydfm$Y
  
# visualize
par(mfrow=c(1,3))
plot(Y1, pch=19, col=lab, xlab="axis 1", ylab="axis 2", main="PCA")
plot(Y2, pch=19, col=lab, xlab="axis 1", ylab="axis 2", main="Laplacian Score")
plot(Y3, pch=19, col=lab, xlab="axis 1", ylab="axis 2", main="Diffusion Maps")

As the figure above shows, in general, different algorithms show heterogeneous nature of the data. We hope Rdimtools be a valuable toolset to help practitioners and scientists discover many facets of the data.