# 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\$1\$1Pa - Pd\$1\$1p)1/p

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

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

The 2-norm is the Euclidean norm. Assume you have an outcome distribution with three categories, for example, yi = \$1y0, y1, y2\$1 = \$1accepted, waitlisted, rejected\$1 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 \$1 (na(1) - nd(1))2 \$1 (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.