Power transformations

Power transforms are functions that we can use to transform numerical features into a more convenient form, for instance to conform better to a normal distribution. A very common transform for values, which vary by orders of magnitude, is to take the logarithm. Taking the logarithm of a zero and negative values is not defined, so we may need to add a constant to all the values of the related feature before taking the logarithm. We can also take the square root for positive values, square the values, or compute any other power we like.

Another useful transform is the Box-Cox transform named after its creators. The Box-Cox transform attempts to find the best power need to transform the original data into data that is closer to the normal distribution. The transform is defined as follows: