I'm trying to separate different groups based on values from width and length using k-means and hierarchical clustering. My question relates to the possibility of using the area — measured as width * length — as another variable in the clustering. Does it make any sense or since this new variable came from the other two its value becomes redundant in the clustering and may add unwanted noise?
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$\begingroup$ That seems extremely likely to confuse analysis. With just two variables, the scatter plot is a clear guide to whether distinct groups exist. If they do, we can discuss how best to identify them automatically. $\endgroup$– Nick CoxCommented Feb 22, 2022 at 17:13
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$\begingroup$ Thanks. I didn't find any literature on this specific issue of variables' products and kept wondering if any addition of this type would make sense (the proportion of length by width was another idea I had in mind but also looked shady). $\endgroup$– hiperhiperCommented Feb 22, 2022 at 17:22
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$\begingroup$ Where to stop? You could add new variables such as the square root of area or the ratio of width and length. I think there are two points here that are easily confused: whether the data as they arrive are the best form for analysis (e.g. logarithmic scale might make more sense for certain goals) and whether there are other variables that might be used. $\endgroup$– Nick CoxCommented Feb 22, 2022 at 17:26
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$\begingroup$ Yes, you're indeed correct. $\endgroup$– hiperhiperCommented Feb 22, 2022 at 17:45
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$\begingroup$ @hiperhiper In general, using the product of two variables in an analysis is very common, and is called using those variables' interaction, if that helps with Googling. It's less common in K means (and indeed in any distance-based analysis) because it is implicitly considered in the distance computation (compare to linear regression, where it is not), though it is certainly not unheard of. $\endgroup$– John MaddenCommented Feb 22, 2022 at 20:07
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