Perform the following steps to perform nonlinear dimension reduction with ISOMAP:

1. First, install and load the RnavGraphImageData and vegan packages:

        > install.packages("RnavGraphImageData")
        > install.packages("vegan")
        > library(RnavGraphImageData)
        > library(vegan)  

2. You can then load the dataset, digits:

        > data(digits)  

3. Rotate and plot the image:

       > sample.digit = matrix(digits[,3000],ncol = 16, byrow=FALSE)
       > image(t(sample.digit)[,nrow(sample.digit):1])  

4. Next, you can randomly sample 300 digits from the population:

> set.seed(2)
> digit.idx = sample(1:ncol(digits),size = 600)
> digit.select = digits[,digit.idx] 

5. Transpose the selected digit data and then compute the dissimilarity between objects using vegdist:

        > digits.Transpose = t(digit.select)
        > digit.dist = vegdist(digits.Transpose, method="euclidean") 

6. Next, you can use isomap to perform dimension reduction:

        > digit.isomap = isomap(digit.dist,k = 8, ndim=6, fragmentedOK
        = TRUE)
        > plot(digit.isomap)  

7. Finally, you can overlay the scatter plot with the minimum spanning tree, marked in red:

        > digit.st = spantree(digit.dist)
        > digit.plot = plot(digit.isomap, main="isomap k=8")
        > lines(digit.st, digit.plot, col="red")