# Follow up of cluster analysis with membership prediction

I have 11 scale parameters for each of 218 observations belonging to subjects, I did standardized PCA to reduce dimensionality of the data and found two meaningful components. Using Euclidean distances this was followed by cluster analysis of these two components (explaining about 75% of the variance) with bottom-up approach using the hierarchical agglomerative clustering (HAC) by FactoMineR R package and Ward's linkage method. The optimal number of clusters was 4 as suggested by the package based on minimizing the ratio of two successive partition inter-clusters inertia gains.
This is just the number of observations per cluster:

> table(df\$clust)

1   2   3   4
6  21  46 145


These 4 clusters turned out to be clinically important and subjects with cluster 1 were severely affected by disease. Cluster 4 were non-reactive subjects, Cluster 3 showed some reaction, and finally cluster 2 was like a special entity protected from disease. I don't know if these clusters can assume some kind of ordinal ranking or not. It is difficult to judge from the theoretical point of view related to the field, but I can say that cluster 4->3->1 is somehow showing some direction, and hence could be regarded as ordinal, on the other hand, cluster 2 is a little bit different but very important as subjects with this clusters were protected from disease. So, I am really confused as whether to consider these 4 clusters ordinal or not.

Suppose that I have another set of 11 new readings of the scale parameters for one subject as new data, what statistical analysis would be useful to predict the membership of this subject to those 4 clusters? Could you please refer to a similar example with R code if possible? that would be greatly appreciated.

Providing a professional answer would be highly esteemed, but also recommending some books using R code would also be encouraged, as I am searching for such a book that covers this topic thoroughly, many books are out there but it is difficult to judge which one would do the job. May be someone, has more experience with this kind of problems and can give a word of advise here.