Clustering analysis and its implementation in R

Earlier I posted a blog for "k-means + heatmap" used for clustering analysis. Recently to prepare for the "Bioinformatics Tools" meeting, I made a slide with more details on "clustering analysis". Here it is:

https://docs.google.com/presentation/d/1vMS3VS3zZmT5Mty1-4R0a-1E-lstjdiXiWOeMdQ_O6M/edit

k-mean clustering + heatmap

If you want more info about clustering, I have another post about "Clustering analysis and its implementation in R". Here is the link:  

http://onetipperday.blogspot.com/2012/04/clustering-analysis-2.html

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Several R functions in this topic:

1. dist(X)  -- calculate the distance of rows of data matrix X. The default distance method is euclidean. It can be maximal, manhattan, binary etc.

> a=matrix(sample(9),nrow=3)
> a
     [,1] [,2] [,3]
[1,]    5    2    9
[2,]    8    7    1
[3,]    6    4    3
> dist(a, diag=T, method='max')
  1 2 3
1 0    
2 8 0  
3 6 3 0
 
> dist(a, diag=T, method='euc')
         1        2        3
1 0.000000                  
2 9.899495 0.000000         
3 6.403124 4.123106 0.000000

2. hclust(D)  -- hierarchical clustering of a distance/dissimilarity matrix (e.g output of dist function): join two most similar objects (based on similarity method) each time until there is one single cluster.

hclust(D) can be displayed in a tree format, using plot(hclust(D)), or plclust(hclust(D))

3. heatmap(X, distfun = dist, hclustfun = hclust, ...) -- display matrix of X and cluster rows/columns by distance and clustering method.

One enhanced version is heatmap.2, which has more functions. For example, you can use

• key, symkey etc. for legend, 
• "col=heat.colors(16)" or "col='greenred', breaks=16" to specify colors of image
• cellnote (text matrix with same dim), notecex, notecol for text in grid
• colsep/rowsep to define blocks of separation, e.g. colsep=c(1,3,6,8) will display a white separator at columns of 1, 3, 6, 8 etc.

Both have 'ColSideColors/RowSideColors', a color vector with length of cols/rows. Here is an example(http://chromium.liacs.nl/R_users/20060207/Renee_graphs_and_others.pdf).

Another enhanced version is pheatmap, which produced pretty heatmap with additional options:

• cellwidth/cellheight to set the size of cell
• treeheight_row/treeheight_col: height of tree
• annotation: a data.frame, each column is an annotation of columns of X. So, nrow(annotation)==ncol(X) 
• legend/annotation_legend: whether to show legend
• filename: save to file

4. kmeans(X, centers=k) -- partition points (actually rows of X matrix) into k clusters . For example:

# a 2-dimensional example
x <- rbind(matrix(rnorm(100, sd = 0.3), ncol = 2),
matrix(rnorm(100, mean = 1, sd = 0.3), ncol = 2))
colnames(x) <- c("x", "y")
(cl <- kmeans(x, 2))
plot(x, col = cl$cluster)
points(cl$centers, col = 1:2, pch = 8, cex=2)

The number of cluster can be determined by plot of sum of squares, eg. 

# Determine number of clusters
wss <- (nrow(x)-1)*sum(apply(x,2,var))
for (i in 2:20) wss[i] <- sum(kmeans(x,centers=i)$withinss)
plot(1:20, wss, type="b", xlab="Number of Clusters",ylab="Within groups sum of squares")

Using hclust and cutree can also set the number of clusters:

hc <- hclust(dist(x), "ward")
plot(hc) # the plot can also help to decide the # of clusters
memb <- cutree(hc, k = 2)

Note: kmean is using partition method to cluster, while hclust is to use hierarchical clustering method. Here is a series of nice lectures for this. A more detail for cluster can be found here: CRAN Task View: Cluster Analysis