# Understanding cluster plot and component variability

I have run k-means clustering. I have also plotted the results using the following code in R:

library(cluster)
library(fpc)
km <- kmeans(Mydata,3)
clusplot(data, km\$cluster, color=TRUE, shade=T,   lines=0) I do not understand what the "component 1" and "component 2" in the graph are. I also have no clue about what is meant by "These two components explain 46.78% of the point variability".

What are the components? How are they helpful in understanding the clustered data?

## 1 Answer

These are the first two principal components (see Principal component analysis, PCA). There is a huge amount of information on PCA on this site, including the encyclopedic thread, and, for you, this is my simple explanation.

Because data may be multivariate it may be tedious to inspect all the many bivariate scatterplots. Instead, a single "summarising" scatterplot is more convenient, the scatterplot of the first two (or possibly the first three) principal components which were derived from the data. "48.76% of variability" says that, with your data, almost half of the information about the multivariate data is captured by this plot of components 1 and 2. If you add the 3rd component - by adding the 3rd axis or by means of a bubble scatterplot - the percent of explained variability will be higher, and you might find, perhaps, that the two clusters on the right do not mix and are more nearly separate in the space.

While typically you can expect that a 1-2 or 1-2-3 component scatterplot will demonstrate clusters as separate (if there are any), there is no rule or guarantee that this will happen. Sometimes clusters appear distinct only in high dimensions capturing a small portion of variability, that is, in "weak" components. I would recommend you read these and other posts of this site: 1, 2, 3.

You should also be aware that principal components can be quite different when PCA is based on unscaled variability ("on covariances") and on uniscaled variability ("on correlations").

• thanks I will take a look at PCA. But quick question is 46.78% of point of variability is good or bad. – shakthydoss Mar 11 '15 at 12:46
• The higher is the percent the less "information" about the data remain hidden from your eye. I don't know what is "good" or "bad". It is relative the goal of the study and the field the data come from. – ttnphns Mar 11 '15 at 12:54