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I'm intending to make a cluster analysis of 100 objects. I've read a couple of books and determined that a Hierarchical agglomerative procedure with Ward's linkage method should be used in my case. As for the distance measure between objects, I am choosing the Euclidean distance.

The problem, however, is that in the books, these distance measures are performed using a maximum of 3 variables per object. In some papers, I have found research that uses 6 variables per object, but that's it. My objects have 114 variables each.

My question is the following: Is there a maximum number of variables per object that a distance measurement can work with?

Some insight into the nature of my objects: Each object has 6 different sets of 19 variables, every set has the same nature, but are different between each other. Every one of the 114 (6x19) variables is a float number between -1 and 1.

If 114 are indeed above the maximum, is there a tool or a procedure that I am missing that could help me perform the cluster analysis given the nature of my objects? Maybe group them into subsets before clustering?

Any help is appreciated. Maybe a book or research I can read on the topic.

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  • $\begingroup$ There is no technical problem to compute euclidean distance with 114 features and to do the clustering you want. The problem, though, is that in 114 dimensions (or, rather, 99 dimensions, because you have only 100 objects, 100-cardinality) euclidean distance is not very good for clustering due to so called "curse of dimensionality". You can read a lot about that problem on this site (search). $\endgroup$ – ttnphns Jul 27 '18 at 13:54
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There's no reason why you can't do clustering with the number of objects lower than the dimensionality of each object.

However, there are practical reasons for why you shouldn't do this. 114 variables is a lot. You should consider going through and removing variables that you would consider unimportant if you have domain knowledge. If you don't, you could opt for dimensionality reduction methods such as PCA or perhaps factor analysis.

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