# normalisation in k means clustering on percentages and other numerical variables

I have several variables to include in k-means, some of them are percentages (between 0-1) and some of them are numerical variables (positive values). I know normalisation is required when the variables are in different scales, so they are all in comparable ranges.

My question: since some of the variable are already between values 0-1 (the percentages), should I only normalise the other variables and leave the percentages as they are? or should I normalised the percentages too? (not sure if that would make sense).

I found several posts (for example: k-means clustering on percentages) but still not sure how to proceed... I really much appreciate your help. Thanks!

• Try to visualize your data first (say, a matrix bivariate scatterplots). I recommend you also to consider transforming the proportions into logits, to see if clusters appear more pronounced. And yes, it is a reasonable idea - to standardize the variables. Commented Jun 29, 2016 at 9:24
• @ttnphns Thanks for your comment. I have 4 vbles giving the % of X consumption during the day (f ex: 5% in the morning, 40% day, 45% evening, 10% night) as I want to see if there are clusters according to the distribution of X (among other vbles). So, I would like to see if there is a cluster which groups together those individuals with a high night consumption for instance. I am not entirely sure how I would interpret the logit transformation though... As for the standarisation, do you mean to standarise all variables (including the %)? Commented Jun 29, 2016 at 9:46
• Yes, all variables. Why not? If V1 is percentage and V2 is dollars (say), how one should "compare" if he needs to compare? Only some way of rescaling/standardizing/normalizing could help. Commented Jun 29, 2016 at 9:56
• @ttnphns. If V1, V2, V3, V4 are percentages (being V1+V2+V3+V4 =1) and V5 is dollars. Would it be possible to standarise V5 (so it goes from dollars to [0-1]) and leave the other 4 variables as they are (since they already are between [0-1])? As I mentioned to HelloWorld, my fear is that if I normalise all of them I will be loosing the relationship/proportion of V1-V4. What do you think? Commented Jun 29, 2016 at 10:01
• (I'm not in your shoes (know not details of your study), so you're warned.) In situation described in your last comment, I probably would discard any one of the 4 percentage variables as "redundant" in clustering (since they sum to a constant). Then I probably would z-standardize (to mean 0, st. dev. 1) all 5 variables. I would probably also do the analysis with logits (discard -> logits of proportions -> z-standardize) and see if the results are better in some respect. Commented Jun 29, 2016 at 10:12