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Does anyone know an outlier detection method for a univariate categorical (nominal, unordered) statistical variable? Without any assumptions about the categorical variable distribution (non-parametric method)?

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Outliers are extreme values that we come across, where they may be influential to the model or not. When it comes to categorical data (say Gender: as in male and female). There's no way of any outlier detection in that. If you mean something like this: You take a sample of 10 with 9 males and 1 female. So you mean that "1 female" is an outlier? NO! It's just the composition of the sample which you have selected.

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    $\begingroup$ The spirit is right, but the example isn't. If the data are supposedly for pregnant females, a single male is a puzzle, and may be a coding error or something more complicated with a transgender patient. A set of categories doesn't imply that seeing observations for one or more categories in a dataset might not be a real puzzle. Much depends on the context as well as the data. $\endgroup$ – Nick Cox Feb 1 '19 at 9:30
  • $\begingroup$ Thanks for the comment. I read it several times, but hard to capture what is referred to from the word "puzzle". Could you please clarify it further? $\endgroup$ – Dovini Jayasinghe Feb 1 '19 at 9:38
  • $\begingroup$ Puzzle = problem or difficulty. I don't know how to clarify further. Puzzle is just an everyday English word used informally as something that should puzzle a researcher: Why do I have this value in my data? Sorry, but I don't know any other language used in Sri Lanka to offer a translation. $\endgroup$ – Nick Cox Feb 1 '19 at 9:42
  • $\begingroup$ Anyhow, thank you so much for your comments/ editing and so on I consider it as a help to get used to this site. Now anyway, I got the meaning of your comment. Of course I do agree, that it depends on the data set which we consider. If the population is full of females, then a male data would be erroneous. That I suppose, the analyst should have an idea about the population where the sample is drawn from. Then a single male representation from a female population can be assumed to be a data entry error. $\endgroup$ – Dovini Jayasinghe Feb 1 '19 at 9:49
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    $\begingroup$ Not necessarily. As I said, transgender patients can be hard to fit in. People who regard themselves as male can still get pregnant, depending .... $\endgroup$ – Nick Cox Feb 1 '19 at 10:41
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Think about your question once more because you ask for an algorithm to detect which of these is an outlier:

  • London
  • Munich
  • Paris
  • Barcelona

Nominal scale means that you have just labels of items like city names or car brands. You can't tell which is an outlier without additional info.

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As per my understanding, there is no concept of outliers detection in categorical variables(nominal), as each value is count as labels. Based on frequency(Mode), we can't do outliers treatment for categorical variables. Plz prove me wrong :)..

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    $\begingroup$ No proof is needed or possible. This is not a topic for formal logic, just statistical judgment. But you need at least informally a definition of outlier. Here's one of mine for this context: An outlier is a unusual data value that causes surprise or needs some attention. If asked for gender, suppose 50 people say male, 49 people say female and 1 person says "none of your business". Then the last value could be regarded as an outlier in this sense only: you need to decide what to do about it. An outlier is not necessarily wrong or self-evidently to be ignored. $\endgroup$ – Nick Cox Sep 3 at 10:07
  • $\begingroup$ Yes, same way like if I had a below table having colors, based on frequency I can't say "Green' color is an outliers.It's applicable if the record counts in Millions as well. Red Red Red Black Black Black Green $\endgroup$ – Kapil Sep 3 at 10:13
  • $\begingroup$ I don't understand what you are saying but I think you're agreeing with my comment. The mode is usually irrelevant in assessing outliers. $\endgroup$ – Nick Cox Sep 3 at 10:42
  • $\begingroup$ Yes, for categorical variables there is no concept of outliers. $\endgroup$ – Kapil Sep 8 at 10:42
  • $\begingroup$ @NickCox: Also, can you clarify one more doubt regarding K-Mode Clustering. Like - 1) how we do feature engg. or dimensional reduction for categorical variables for ML model. 2) And how you evaluate your K-Model Clustering ML Model is giving good result (like- accuracy, etc). $\endgroup$ – Kapil Sep 8 at 10:45

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