equalfrequency

Equalfrequency, also called equal-frequency binning or quantile discretization, is a method for converting a continuous variable into a categorical variable by dividing its values into a predefined number of bins such that each bin contains roughly the same number of observations. Unlike equal-width binning, which splits the value range into intervals of equal size, equalfrequency bins are defined by data-driven thresholds at specific quantiles.

To apply equalfrequency binning, you choose the desired number of bins k. The data are sorted by the feature value, and cut points are placed at the i/k quantiles for i from 1 to k-1. Each observed value is then assigned to the bin corresponding to its interval between consecutive cut points. In practice, ties at cut points can complicate bin assignment, and some bins may end up with slightly different counts when the total number of observations is not divisible by k.

Advantages of this approach include robustness to skewed distributions and outliers, and the ability to ensure that each bin carries a similar amount of information or observations. This can be beneficial for certain machine learning models and for summarizing features in exploratory analysis.

Drawbacks include irregular bin widths in the original value scale, which can obscure meaningful thresholds or relationships present in the data. Binning can also lead to information loss, particularly when the underlying relationship is smooth or monotonic, and it may create bins with many identical values clustered at the boundaries.

Common applications include preprocessing for machine learning models that benefit from categorized inputs, such as logistic regression with nonlinear effects, decision trees, or when preparing features for visualization. It is often used as a data-driven alternative to equal-width binning.