# Why Isn't This Outlier Score/Reconstruction Error Not Squared?

I was looking through a paper called "AI2 : Training a big data machine to defend", and saw this (http://people.csail.mit.edu/kalyan/AI2_Paper.pdf)

$score(X_{i}) = \sum_{j=1}^{p} (|X_{i} − R^{j}_{i}|) × ev(j)$

Where $ev(j)$ is the percentage of variance.

I was wondering, why isn't the the term $(|X_{i} − R^{j}_{i}|)$ squared like other reconstruction error functions, or at least the ones I saw?

I believe the term $\sum_{j=1}^{p} (|X_{i} − R^{j}_{i}|)$ is a mean absolute error and is used here because it is better than a mean square error because it is better for a time series and is more robust. If I am wrong, please correct me.