Would K-means be Appropriate to Use with Four or More Variables? Just a general question that I'm trying to mentally visualize. I'm fairly new to using k-means clustering and have used it before on two variables, which creates a 2-D plot of points. I also know, although I haven't done it before, that you can plot a k-means cluster with three variables utilizing the x, y, and z axes. But now I'm currently in a position where I have four variables, normalized by their z-scores, in which I'm not sure how to use the k-means clustering appropriately. Should I be using a k-means cluster in this circumstance?

Thanks
You can use k-Means clustering in all the dimensions you need. This technique is based on a k number of centroids that self-adjust to the data and "cluster" them. The k centroids can be defined in any number of dimensions.

If you want to find the optimal number of centroids, the elbow method is still the best. You iterate the algorithm changing the value of k each time, and record how much error the clustering is producing; once you're done you plot the error levels against each k value and check the optimal k visually. There is plenty of tutorial on it, you can start here for example.