Got Milk?

Have you ever wondered whether the makeup of milk was the same for different species?  If not, what animals would you consider to produce similar milks?  In this analysis we looked at the percent water, protein, fat and lactose found in different types of milk.  The animals under consideration were Horses, Donkeys, Mules, Camels, Llamas, Zebras, Sheep, Buffalo, Foxes, Guinnea Pigs, Pigs, Rabbits, Rats, Deer, Reindeer and Whales.  We used various methods of Cluster Analysis to see which of these animals had similar milk types.  After examining hierarchical tree diagrams, ROC curves, Hotellings T - squared statistic, RSQ and SPRSQ we found that the Average Linkage Method, producing 3 clusters was the best analysis.  This analysis put the following animals into clusters:

Cluster 1: Horse, Donkey, Mule, Llama, Camel, and Zebra

Cluster 2: Sheep, Buffalo, Fox, Guinnea Pig, Pig, Rabbit and Rat

Cluster 3: Deer, Reindeer and Whale

According to our analysis these groups of animals have milk with similar makeups.  After perfoming Cluster Analysis with the Average Linkage Method, we then compared our results using the Kmeans Clustering Method.  Both methods resulted with 3 clusters and the same animals in each cluster.

 Heirarchical Tree Diagrams

Single Linkage Method







































When looking for jumps in the hierarchical tree diagram we would conclude that 4 or 5 clusters may be appropriate.  Using the pseudo Hotelling�s T² statistic we find that 9, 5 or 2 clusters would be appropriate.  Looking at the RSQ values, the appropriate number or clusters might be 8, 5, or 2. The SPRSQ values would recommend 8, 5, or 2 as appropriate clusters. 

 We think that 5 clusters should be formed using the single linkage agglomerative method.  Five clusters is a candidate in each of the methods used to determine the appropriate number of clusters.

Average Linkage Method

 






When looking for jumps in the hierarchical tree diagram we would conclude that 7, (4 or 3) or 2 clusters may be appropriate.  Using the pseudo Hotelling�s T² statistic we find that 10, 3 or 2 clusters would be appropriate.  Looking at the RSQ values, the appropriate number or clusters might be 7, 4, or 2.  The SPRSQ values would recommend 10, 7, 3, or 2 as appropriate clusters. 

The original data set can be found at http://www.csit.fsu.edu/~burkardt/datasets/hartigan/file02.txt
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