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I am doing customer segmentation using RFM. Prior to proceeding with the clustering, I log transformed my Monetary variable to account for skewness.

df_RFM$log_monetary <- log(df_RFM$monetary)

After which, I did the z-standardization using scaling. 

df_RFM2 <- scale(df_RFM2)

Summary statistics before scaling, after scaling, and after clustering are as attached. My question is, how do I interpret the scaled values, especially the negative ones? It doesn't make sense to say negative frequency and negative monetary retail purchases for instance.

Thanks in advance.

before scaling

after scaling

cluster summaries

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  • $\begingroup$ RFM is a pretty blunt instrument that direct marketers should have dumped years ago. That said, it doesn't make sense to log transform a variable and then standardize the rescaled variable using z-scores. This wiki piece makes clear that the appropriate metric for the central tendency of such a variable is either the geometric mean or the median, as well as a geometric std dev ... see Properties section en.wikipedia.org/wiki/Log-normal_distribution $\endgroup$
    – user78229
    Commented Dec 14, 2017 at 1:51
  • $\begingroup$ @DJohnson, noted on using another central tendency measure for the monetary variable. However, even for recency and frequency, which are both non-transformed variables, I am getting negative values after scaling. For instance a customer who purchased today would have 0 recency values, which would turn negative upon scaling. I understand scaling is a must prior to segmentation though since my variables are of different magnitudes. Is there any other workaround? $\endgroup$
    – lb0389
    Commented Dec 14, 2017 at 2:17
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    $\begingroup$ If $z$-standardization means what I think it does, then $z$ = (value $-$ mean) / SD and negative $z$ just means values below the mean. Whether that's what you want to use or report is a good question but some negative $z$ values are expected in practice. The only exception is that if a variable is constant, all $z$ values are 0. Note that if you take logs first, the mean of the logs is the log of the geometric mean, so taking logs can be combined with standardization. (For me, RFM is a truncation of Read The Fine Manual, but the software or tool you're using doesn't seem the issue here.) $\endgroup$
    – Nick Cox
    Commented Dec 14, 2017 at 13:47
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    $\begingroup$ I remain puzzled at what the real question is here. As already flagged, and as is standard, negative $z$ scores just indicate values below whatever is your mean, either as originally measured or on a transformed scale. Personally, I don't find $z$-scores especially helpful in identifying outliers as (a) I would want to look directly at the data always (b) standardization doesn't affect skewness or tail weight (c) mean and SD are themselves influenced by outliers, so if I had to choose a standardization it would more likely be (value $-$ median) / IQR. $\endgroup$
    – Nick Cox
    Commented Dec 15, 2017 at 12:03
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    $\begingroup$ Here that's secondary, as a value 128 SDs above the mean is almost always going to be a massive outlier. But why in doubt here? More crucially, how far you should be working and thinking on a logarithmic scale depends also on your practical objectives. In some fields outliers may be suspect values to be discounted or even discarded, but here my guess is that 359086 is in no sense an illusion; it's real money in the bank for someone. $\endgroup$
    – Nick Cox
    Commented Dec 15, 2017 at 12:07

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