Optimal number of clusters in r

Question

In this SO answer on how to choose the number of clusters, one of the graphs contains the following:

These two components explain 100% of the point variability

. What components is it referring to? Are these the x and y components?

Answer 1

Component are principal components, e.g. the result of principal components analysis on the original variables.

clusplot(...) relies on clusplot.default(...), which documentation states:

... Creates a bivariate plot visualizing a partition (clustering) of the data. All observation are repre-sented by points in the plot, using principal components or multidimensional scaling...

Since the original data can have > 2 dimensions (e.g., more than two variables), and the cluster plot is restricted to 2D, it is desirable to perform some kind of dimensionality reduction on the original data. A common method of doing this is PCA, which creates a new set of variables as a linear combination of the original set. The new variables are called principal components and have the property that (usually) most of the variation in the original dataset is concentrated in the first few principal components. So clusplot(...) plots PC2 vs. PC1.

If there are only two dimensions in the original dataset, than there will be only 2 PCs and these will account for 100% of the variability in the data. I suspect that's what's happening in your example.