## Clustering with selected Principal Components

In the Visualizing Principal Components post, I looked at the Principal Components of the companies in the Dow Jones Industrial Average index over 2012. Today, I want to show how we can use Principal Components to create Clusters (i.e. form groups of similar companies based on their distance from each other)

Let’s start by loading the historical prices for the the companies in the Dow Jones Industrial Average index that we saved in the Visualizing Principal Components post.

############################################################################### # Load Systematic Investor Toolbox (SIT) # https://systematicinvestor.wordpress.com/systematic-investor-toolbox/ ############################################################################### setInternet2(TRUE) con = gzcon(url('http://www.systematicportfolio.com/sit.gz', 'rb')) source(con) close(con) #***************************************************************** # Load historical data #****************************************************************** load.packages('quantmod') # load data saved in the bt.pca.test() function load(file='bt.pca.test.Rdata') #***************************************************************** # Principal component analysis (PCA), for interesting discussion # http://machine-master.blogspot.ca/2012/08/pca-or-polluting-your-clever-analysis.html #****************************************************************** prices = data$prices ret = prices / mlag(prices) - 1 p = princomp(na.omit(ret)) loadings = p$loadings[] x = loadings[,1] y = loadings[,2] z = loadings[,3]

To create Clusters, I will use the hierarchical cluster analysis, hclust function, in stats package. The first argument in the hclust function is the distance (dissimilarity) matrix. To compute distance matrix, let’s take the first 2 principal components and compute the Euclidean distance between each company:

#***************************************************************** # Create clusters #****************************************************************** # create and plot clusters based on the first and second principal components hc = hclust(dist(cbind(x,y)), method = 'ward') plot(hc, axes=F,xlab='', ylab='',sub ='', main='Comp 1/2') rect.hclust(hc, k=3, border='red')

Similarly we can use the first three principal components:

# create and plot clusters based on the first, second, and third principal components hc = hclust(dist(cbind(x,y,z)), method = 'ward') plot(hc, axes=F,xlab='', ylab='',sub ='', main='Comp 1/2/3') rect.hclust(hc, k=3, border='red')

Another option is to use the Correlation matrix as a proxy for a distance matrix:

# create and plot clusters based on the correlation among companies hc = hclust(as.dist(1-cor(na.omit(ret))), method = 'ward') plot(hc, axes=F,xlab='', ylab='',sub ='', main='Correlation') rect.hclust(hc, k=3, border='red')

Please note that Clusters will be quite different, depending on the distance matrix you use.

To view the complete source code for this example, please have a look at the bt.clustering.test() function in bt.test.r at github.

Dear systematicinvestor,

Just found your blog and I absolutely love it! I am somewhat new to R, but have have a long history with both Excel and finance, you keep amaze me with both your and R’s powers when dealing with financial data.

Thank you and keep doing what you are doing!

Hugo

Nice post!

Here is a good tutorial on clustering with different R packages

http://research.stowers-institute.org/efg/R/Visualization/cor-cluster/index.htm

provided by Earl F. Glynn.

Take a look at pvclust package on stability issue. This package use bootstrap and calculates p-values.

Happy New Year!

Mike

You might also be interested in FactoMineR (http://factominer.free.fr/), a package not mentioned in the tutorial linked. It offers a GUI (as part of Rcmdr) for those less comfortable with the command line, and apparently you can also use it within Excel (using RExcel).

Hi,

Excellent blog. The question now is how to use these clusters further.

I was wondering about trying to find the most representative element of each cluster and using the list of those to do a further portfolio opt. I.e.

Sp500 (500 names) –> cluster (20 or so clusters) –> for each cluster take most representative name (20 names) –> portfolio opt these 20 names

Any ideas on what procedure would best find each cluster’s most representative stock?