# Lp-norm (LP)
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The Lp-norm (LP) measures the p-norm distance between the facet distributions of the observed labels in a training dataset. This metric is non-negative and so cannot detect reverse bias. 

The formula for the Lp-norm is as follows: 

        Lp(Pa, Pd) = ( ∑y\|\|Pa - Pd\|\|p)1/p

Where the p-norm distance between the points x and y is defined as follows:

        Lp(x, y) = (\|x1-y1\|p \+ \|x2-y2\|p \+ … \+\|xn-yn\|p)1/p 

The 2-norm is the Euclidean norm. Assume you have an outcome distribution with three categories, for example, yi = {y0, y1, y2} = {accepted, waitlisted, rejected} in a college admissions multicategory scenario. You take the sum of the squares of the differences between the outcome counts for facets *a* and *d*. The resulting Euclidean distance is calculated as follows:

        L2(Pa, Pd) = [(na(0) - nd(0))2 \+ (na(1) - nd(1))2 \+ (na(2) - nd(2))2]1/2

Where: 
+ na(i) is number of the ith category outcomes in facet *a*: for example na(0) is number of facet *a* acceptances.
+ nd(i) is number of the ith category outcomes in facet *d*: for example nd(2) is number of facet *d* rejections.

  The range of LP values for binary, multicategory, and continuous outcomes is [0, √2), where:
  + Values near zero mean the labels are similarly distributed.
  + Positive values mean the label distributions diverge, the more positive the larger the divergence.