Data Discretization
What if we want to transform a continuous attribute to a categorical?
EqualWidth Partitioning
Also called distance partitioning
 want to divide $X = (x_1, ..., x_m)$ into $N$ equal intervals
 let $A = \min X$ and $B = \max X$
 width: $W = \cfrac{B  A}{N}$

 suppose that in one such partition you have all your data
 you'll lose a lot of information
 so it's sensible to Outliers
EqualDepth Partitioning
Also called frequency partitioning
 Divides $X$ into $N$ intervals,
 with each interval containing approximately same number of samples
 not sensible to outliers
 distribution of values is taken into account

EntropyBased Discretization
Uses entropy to find the best way to split your data
 find the value $\alpha$ that maximizes the Information Gain
 split by $\alpha$
 repeat recursively until have $N$ intervals or no information gain is possible
Sources