# What is the best way to cluster this kind of data?

I have data that looks like this:

The chart on the left is the trend and the smaller chart on the right is the box plot showing the distribution of means. Each color is the output of a particular tool. I dont need to do an ANOVA and Tukey tests on it because it can easily be seen that there are statistically significant differences between the tools. However, I would like to group/cluster the tools based on their mean.

For example, visually speaking, one can separate all the tools into 4 groups. 4 tools with a mean around 32, 12 tools with a mean around 30, 5 tools whose variance is quite high, and whose mean don't really fall into a particular group and the rest whose mean is around 30.

Update:

I have used the k-means clustering technique and the Hierarchical Agglomeration techniques. However, I have to specify the number of clusters in advance. Is there any clustering technique where I don't have to specify the number of clusters a-priori?

• most clustering algorithms can cluster anything given the approprate distance metric – Nikos M. Feb 23 at 19:45
• It looks like you have good labelled data and that the number of clusters/classes is predefined, so why not using supervised classification? This would certainly give better results. – Erwan Feb 24 at 23:36
• @Erwan I was thinking more of unsupervised. Since all I want to do is cluster based on the mean. What would I supervise it on? – thentangler Feb 26 at 18:57
• In a supervised setting you could decide yourself what should be the 4 groups, but maybe that's not what you want. The problem is a bit unusual to me so I'm not sure what to recommend, but I'd say that K-means is worth trying yes. – Erwan Feb 26 at 23:03
• @Erwan Would I be able to use K-Means if one of my axis was labelled and not continuous? I basically want to do the clustering on the smaller chart to the right of the trend. There, the x-axis is labelled (Tool Name) and the y-axis is continuous (Mean of Tool output) – thentangler Mar 1 at 17:29