By creating a binary feature variable for each feature with missing values to indicate whether a value has been imputed, the data scientist can preserve information about the original state of the data. This approach maintains the integrity of the dataset by marking which values are original and which are synthetic (imputed). Here are the steps to implement this approach:

Identify Missing Values: Determine which features contain missing values.

Impute Missing Values: Continue with median imputation or choose another method (mean, mode, regression, etc.) to fill missing values.

Create Indicator Variables: For each feature that had missing values, add a new binary feature. This feature should be '1' if the original value was missing and imputed, and '0' otherwise.

Data Integration: Integrate these new binary features into the existing dataset. This maintains a record of where data imputation occurred, allowing models to potentially weight these observations differently.

Model Adjustment: Adjust machine learning models to account for these new features, which might involve considering interactions between these binary indicators and other features.

Reference

'Feature Engineering for Machine Learning' by Alice Zheng and Amanda Casari (O'Reilly Media, 2018), especially the sections on handling missing data.

Scikit-learn documentation on imputing missing values: https://scikit-learn.org/stable/modules/impute.html