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I have data that looks like this: enter image description here

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?

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  • $\begingroup$ most clustering algorithms can cluster anything given the approprate distance metric $\endgroup$
    – Nikos M.
    Feb 23, 2021 at 19:45
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    $\begingroup$ 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. $\endgroup$
    – Erwan
    Feb 24, 2021 at 23:36
  • $\begingroup$ @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? $\endgroup$
    – thentangler
    Feb 26, 2021 at 18:57
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    $\begingroup$ 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. $\endgroup$
    – Erwan
    Feb 26, 2021 at 23:03
  • $\begingroup$ @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) $\endgroup$
    – thentangler
    Mar 1, 2021 at 17:29

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In hierarchical clustering, both agglomerative and divisive, you do not have to pre-specify the number of clusters. You can create all possible clusters and then select the number cluster to use at the end.

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