In k-means clustering, is it convenient to include additional samples to the ones you are interested in? I have a collection of numeric quantitative variables from a series of samples; let’s say, for example, countries from the whole world. My goal is to discern how countries can be distributed, according to these variables, into classes by using k-means. But I am interested only about the results concerning European countries (always as an example), that is, how European countries alone distribute into classes.
So, my question is, do I perform the kmeans analysis taking into account only the European countries, and discarding from the beginning the other countries? 
Or is it better to perform first the kmeans analysis including all the world countries, and describe afterwards the results concerning the European countries? - assuming that the European countries do not appear all within the same cluster-.
Just to enter into details, the quantitative variables are gene expression data (4000 genes); and the “European countries”/samples are selected brain regions (in number of 400) from a total of 1000 brain regions.
 A: There would be no problem with adding extra data if those new points belonged to the same population. However, geography is often a relevant factor for the variables we want to study, and the new rest-of-the-world data will be very different from the European countries. 
What will most likely happen is that you will get a "better" clustering for the World countries, but most of the European ones will probably all go to the same group, thus serving no purpose to your particular study.
Anyway, as it's often the case in unsupervised learning, there is no real right or wrong answer, so try both and stick to what makes for sense for you. You'll probably want a bigger number of clusters if you work with the entire-World data
A: Definitely use the entire data for clustering.
This will "overfit" less in the sense that it has to explain more data with the same number of variables (clusters).
Also, it serves as a regularization and baseline.
Imagine that you find the brain regions you are interested in are literally "all over the place". Then you know your data does not support your hypothesis. Such negative results are the most valuable (because they are much more reliable). If you only used the data you are interested in, there is a good chance your algorithm finds a "cluster" that isn't actually there. For example k-means will always "find" k clusters, even on uniform noise.
