BACKGROUND: I'm working with a nominal feature variable
cancer_type with $5$ different classes to develop a machine learning model.
One-hot encoding this feature column will result in $5$ columns, one for each class, in the new data frame. The information that these columns are linked is lost with this procedure because the model has no way of knowing that they refer to the same original feature. The columns are in a sense independent from the perspective of the model, whereas we know that there is a dependency. (A $1$ in any one of the one-hot encoded columns necessitates that all other columns must have a $0$ for that particular training example.)
QUESTION: Does one-hot encoding result in information loss?