On topological and algebraic structures of categorical random variables
By: Inocencio Ortiz, Santiago Gómez-Guerrero, Christian E. Schaerer
Potential Business Impact:
Finds patterns in data using math.
Based on entropy and symmetrical uncertainty (SU), we define a metric for categorical random variables and show that this metric can be promoted into an appropriate quotient space of categorical random variables. Moreover, we also show that there is a natural commutative monoid structure in the same quotient space, which is compatible with the topology induced by the metric, in the sense that the monoid operation is continuous.
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