I am currently working on a dataset concerning the color magnitude of astronomical point sources. There are 9 covariates, each representing a specific color of a point source. I used k-means, hierarchical clustering and self organizing maps. The results from these three methods are very similar. However, one thing I noticed is that these three methods created clusters mainly based on two of the covariates which have the largest range of magnitude.
I know it is recommended that we scale the data and I fear it is because I didn't scale the data that the clustering are dominated by the two covariates.
However, scaling the data will essentially change the physical meaning and relationship between different colors which is not something I want for this particular project.
Does anyone know what should be the best way to handle this? Thanks!