# Interpretation of the final cluster centers (cluster analysis)

I have a question concerning the interpretation of the final cluster centers. I performed a cluster analysis based on a pca (the variables are based on a five point Likert-scale). I got the following result for one factor:

        cluster_1        cluster_2       cluster_3      cluster_4       cluster_5
0,31            0,39               -0,82          0,63            0,35


Is this factor also interesting for the description of cluster 1, 2 and 5? Or should I only mention its influence for the clusters 3 and 4?

Thanks a lot!

• Why not to plot it (the results in 2d or 3d main components) to get impressed yourself? – ttnphns Oct 24 '13 at 15:39

Each cluster center is a point in the dimensional space with as many dimensions as extracted factors from your PCA. The row you report is the value of one dimension for each of the cluster centers. If you want to report on the position of the cluster centers, then you need the full coordinates. It is misleading though, to say that a factor "influences" a cluster, as the clusters are built based on factor values, in other words there would be no clusters if you did not start out with those factors.

Whether 0 is a special position for a cluster center depends on the nature of the input variables, but even if you assume that 0 represents mean and median for the values on this dimension it is informative. To give an intutiive demosntration why a value of 0 is informative: imagine a cluster analysis based on a one-dimensional variablwe and you learn that the cluster centers are located at -3,0, and 5. Then you know something about the relative position of the cluster centers. If you ignored the factor you could not even describe the middle cluster.

I think the question might be motivated by the practice of dropping small factor laodings when reporting the results of PCAs, which is offered by some statistical packages (and of dubious value in many practical applications).

• Thanks to all for helping me!!! @Anony-Mousse: I have treated the ordinal data (1: strongly agree, ..., 5: strongly disagree) as intervall data and then performed the pca. Afterwards I have done a cluster analysis (k-means) on the raw data as well as on four factors. Both results were quite similar. – cathy Oct 25 '13 at 3:55
• You did exactly what @Anony-Mousse mentioned could be misleading. This is a very popular way to approach this problem and is widely used in studies like market segmentation because it is simple but you definitely should be careful. – JEquihua Oct 31 '13 at 18:07

Be really careful when using PCA on discrete values such as likert scales. PCA is designed for continuous variables, not for discrete values.

There is a high chance that you will discover artifacts from the discrete scale.

In fact, the vector looks susceptible much like the frequencies of the 5 answers, or something like this...

If you would share more of what you've been doing, it would be easier to help you.