Log2FWC

Log2FWC is a logarithmic transform applied to the Feature Weight Calibration (FWC) score, a nonnegative quantity used to express the importance or calibrated weight of features in a dataset. The standard definition is log2FWC = log2(FWC + 1). The addition of 1 ensures the transform is defined when FWC is zero and provides a stable zero output at FWC = 0. The transform compresses large weights and expands small ones on a base-2 scale, aiding comparison across features with skewed distributions.

The transformation is monotone increasing, with an inverse given by FWC = 2^(log2FWC) − 1. It is differentiable for FWC ≥ 0, and its range is from 0 to infinity in the log2FWC space. The offset also means a unit change in low FWC values corresponds to roughly equal relative changes in the transformed space, while changes in very large FWC values have diminishing impact on log2FWC.

Applications of log2FWC appear in data analysis and machine learning workflows where feature weights vary dramatically. It is used to normalize and visualize weight distributions, stabilize numerical behavior in linear models, and reduce the influence of extreme weights before downstream processing. The method is particularly helpful when features exhibit a long-tail distribution of weights.

Example: FWC values 0, 1, 3, 7 map to log2FWC values 0, 1, 2, 3, respectively, since log2(0+1)=0, log2(1+1)=1, log2(3+1)=2, and log2(7+1)=3.

Limitations include the requirement of nonnegative FWC and the fixed offset, which may not suit all datasets. Alternatives such as log1p or Box-Cox transforms can be considered when appropriate. See also: log base 2, log1p, feature weighting, data normalization.