I have cluster results with good values on etc Silhuette Width. The cluster sizes are: 4998, 1, 1 which isn't good knowing my customers doesn't have that particular partition (it's more balanced). I have therefore ignored these clustering results and concluded it was bad. Does this mean I used external validation since my conclusion that the clustering was bad was based on my domain knowledge?
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$\begingroup$ External cluster validity indices: stats.stackexchange.com/q/586470/3277 $\endgroup$– ttnphnsCommented Jun 2 at 20:58
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$\begingroup$ Nope... you are good. Your clustering here seems more like it detected two outliers and not nuch else. $\endgroup$– usεr11852Commented Jun 2 at 21:54
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$\begingroup$ What is the definition of 'external validation'? If you answer that, then the answer from the question will follow. $\endgroup$– Sextus EmpiricusCommented Jun 3 at 15:46
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2 Answers
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Short answer: No.
Longer answer: As far as I know "external validation is not a statistical term, but "external validity" is. And, while your interpretation of the term sort of makes sense, it doesn't match with how the term is used in statistics. "External validity" In brief, it is the extent to which you can generalize the results to other situations. See Wikipedia for a much longer discussion.
For what it's worth, "external validation" is a phrase from psychology where it means "relying on the approval of others for your own sense of self-worth".
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2$\begingroup$ Exactly. (+1) A clustering algorithm is only as good as the utility of the produced partioning. While a clustering metric $d$ might show "how good" a given partioning is based on the metric's properties, that doesn't equate at all with the external validity (or let alone with the usefulness) of clustering result. $\endgroup$ Commented Jun 2 at 21:52
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You (implicitly) applied an "external cluster evaluation metric", since you used a ground truth about the customer clusters, see Google books for more about external evaluation metrics.
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2$\begingroup$ It would be so if the OP knew which observation of the sample to what "true" cluster belongs. As for present, they only "know" that the "true" cluster structure is more balanced, pronounced. This domain knowledge is not an external validation. $\endgroup$– ttnphnsCommented Jun 2 at 20:57
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$\begingroup$ I agree, but the question seems to be "I rejected using a clustering method XYZ although the internal cluster metrics (like Shilouette score etc.)" were good. I did it because I had external knowledge and knew that some metric ABC looked bad. So I feel internal vs. External cluster evaluation metrics are on topic. I do not imply that using an "external cluster evaluation metric" is "external validation". $\endgroup$– Ggjj11Commented Jun 2 at 21:21